Electronic ink screen display control method of keycap

Abstract

The invention relates to the field of display driving control of input equipment, in particular to an electronic ink screen display control method of a keycap, which comprises the following steps of: firstly, inserting a sensing phase in a key domain, and constructing a state vector containing charge bias estimator, optical reflectance and temperature by utilizing opposite-polarity probe pulse, phase-locked demodulation and temperature measurement; then filtering fusion and sample-based temperature-related response parameter calibration are carried out, a Prantl-Ishlinskii hysteresis model is constructed, an equivalent dose target is obtained through analysis and inversion, and a charge bias target is set to be zero; solving a constraint optimization synthesis zero direct current vector waveform under zero direct current constraint and executing, and injecting a correction phase pair with opposite polarity when a judgment condition is not met; and summarizing execution records to calculate the total equivalent charge amount of the whole board, carrying out blocking and phase staggered scheduling based on optical deviation and charge bias, and carrying out online parameter back-writing. According to the invention, ghosting and flickering are reduced and long-term stability is improved.

Description

Technical Field

[0001] This invention relates to the field of input device display driver control, and more particularly to a method for controlling the electronic ink screen display of a keycap. Background Technology

[0002] Reconfigurable key appearance and status feedback are becoming an important direction in computer human-computer interaction. Integrating low-power reflective displays into keycaps allows input devices to quickly switch between applications, languages, and scenarios, reducing secondary addressing and gaze shifts at the interface level, and improving accessibility and professional workflow efficiency. At the same time, key-level displays are limited by small area, local thermal coupling, and high-frequency triggering. Without precise driving and scheduling, they can produce ghosting, noticeable flickering, and lifespan degradation, directly affecting input accuracy and long-term consistency. Summary of the Invention

[0003] To address the numerous problems existing in the prior art, this invention provides a keycap-based electronic ink screen display control method. This invention inserts sensing phase at the keycap level to acquire electrical, optical, and temperature data and fuses them into a model. Based on hysteresis analytical inversion, it obtains the equivalent dose target, applies zero DC constraint to synthesize a vector waveform, and performs closed-loop correction by polarity-opposite phase correction. By combining the total equivalent charge of the entire board with block phase misalignment scheduling and parameter write-back, it suppresses afterimages and flicker and maintains long-term charge neutrality.

[0004] A method for controlling the display of an e-ink screen on a keycap includes the following steps: A sensing phase is inserted into the key domain, a probe pulse of opposite polarity is applied and the displacement current is integrated to obtain the charge bias estimate, the optical reflectance is obtained through phase-locked demodulation, the temperature is measured, and a state vector containing the charge bias estimate, optical reflectance and temperature is established. The estimated state vector is obtained by filtering and fusing the state vector. The temperature-related response parameters are calibrated based on the reflectance, equivalent dose and temperature samples. The Prandtl-Ishlinskii hysteresis model is constructed and the equivalent dose target is generated by analytical inversion of the target reflectance. At the same time, the charge bias target is set to zero. Under zero DC constraint, the zero DC vector waveform is obtained by solving the constraint optimization with the equivalent dose target and the estimated state vector as input. The reverse polarity probe pulse is used to obtain the charge bias estimate and optical reflectance after execution. If the preset judgment condition is not met, the reverse polarity correction phase pair is injected. The total equivalent charge of the entire plate is calculated by summarizing the execution records. Blocking and phase-staggered scheduling are performed based on optical deviation and charge bias. Temperature-related response parameters are updated based on newly added reflectivity, equivalent dose and temperature samples for subsequent state reconstruction and waveform synthesis.

[0005] Compared with the prior art, the advantages and beneficial effects of the present invention are as follows: By inserting probe pulses with opposite phase and polarity, phase-locked demodulation, and temperature measurement, a state vector containing charge bias estimates, optical reflectivity, and temperature is established, achieving joint observability and noise-robust sampling at the key domain level. Through filtering fusion, temperature-related response parameter calibration based on samples, and analytical inversion of the Prandtl-Ishlinskii hysteresis model, an equivalent dose target is generated and the charge bias target is set to zero, achieving path-independent dose solving and temperature-consistent mapping. By constrained optimization under zero DC constraints to synthesize zero DC vector waveforms, and correcting the phase with opposite polarity to correct the closed-loop bias, long-term charge neutrality and controlled refresh of low-energy, low-frequency components are achieved. By summarizing the total equivalent charge of the entire board and the block-based graphical model, phase-staggered scheduling, and online writing back of temperature-related response parameters, convergence supervision, anti-coupling scheduling, and continuous self-adaptation at the entire board level are achieved. Attached Figure Description

[0006] Figure 1 This is a flowchart illustrating the method of the present invention. Detailed Implementation

[0007] The embodiments of the present disclosure will now be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of the disclosure. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the embodiments of the present disclosure for ease of explanation.

[0008] like Figure 1 As shown, a method for controlling the electronic ink screen display of a keycap includes the following steps: A sensing phase is inserted into the key domain, a probe pulse of opposite polarity is applied and the displacement current is integrated to obtain the charge bias estimate, the optical reflectance is obtained through phase-locked demodulation, the temperature is measured, and a state vector containing the charge bias estimate, optical reflectance and temperature is established. Preferably, when inserting the sensing phase in the key domain, the displacement current of the probe pulse with opposite polarity is subjected to baseline subtraction and time integration, the optical reflectance and temperature are spatially registered in the key domain coordinate system, and measurement covariance parameters are established for the charge bias estimate, optical reflectance and temperature as the measurement covariance for filtering and fusion.

[0009] This invention inserts a sensing phase into the scanning timing of the keycap's e-ink screen to acquire electrical, optical, and temperature-based information. This information is then spatially aligned across the key domain coordinates and merged into a unified data object. To facilitate subsequent filtering, fusion, and control solutions, a state vector and measurement covariance are established. The state vector is denoted as... ,in This represents the charge bias estimate. Indicates optical reflectance. Temperature is represented; the measurement covariance is denoted as... ,in , , These represent the uncertainties of the three-channel measurements, respectively.

[0010] The principle of the electrical channel is to apply probe pulses of opposite polarity without causing visible reversal, acquire the column-end displacement current, and perform time integration. The opposite polarity setting causes the in-phase error caused by equivalent polarization and parasitic leakage current to partially cancel each other out after integration, while the asymmetric components caused by particle retention or historical bias become explicit in the difference between the two integrations, thus serving as a charge bias estimate. Baseline subtraction is used to suppress slow drift from the preamplifier and sampling resistors, and the integration window is limited to the pulse stability region to avoid bias caused by edge distortion. This path is independent of image content, and the obtained charge bias estimate has direct guiding significance for the subsequent synthesis of zero DC vector waveforms.

[0011] The optical channels employ phase-locked demodulation. Backlighting or local illumination is modulated at a fixed frequency, and photosensitive devices synchronously sample and demodulate using in-phase and quadrature components, with the amplitude term mapped to optical reflectance. Because phase-locked modulation only retains components with the same frequency as the modulation, ambient light variations and power supply ripple are significantly suppressed. To ensure that the electrical, optical, and temperature channels point to the same key domain, the optical field of view and the electrical addressing area are first registered using the factory-calibrated geometric mapping, and then channel alignment is completed using the center coordinates of the key domain as anchor points. The registered optical reflectance is directly incorporated into the state vector, avoiding cross-domain stitching errors.

[0012] The temperature channel is used to characterize the thermal dependence of the response rate on the threshold. Multi-point temperature sensors form sparse samples on the keyboard plane. Using thin-plate splines or equivalent two-dimensional interpolation methods, the discrete temperature point field is mapped to the coordinates of the key domain center, thus obtaining the temperature. Temperature participates as a state variable in subsequent modeling and constraints. Its inclusion ensures that the parameter calibration after the steps has a consistent thermal reference, reducing the impact of ambient temperature changes on dose estimation and waveform constraints.

[0013] To enable adaptive weight allocation based on observation quality, measurement variances are estimated separately for electrical, optical, and temperature aspects, forming the measurement covariance. The electrical variance is derived from repeatability statistics of multiple mirror samplings; the optical variance is extrapolated from the lockout signal-to-noise ratio and occlusion flags; and the temperature variance is derived from sensor specifications and interpolation residuals. Using the measurement covariance as input to the filtering fusion process allows for quantifiable estimation of the state vector's reliability and maintains stable estimation performance across different key domains and time windows.

[0014] To avoid interference from the sensing phase on the display, the voltage and pulse width combination of the probe pulse are limited to below the equivalent dose threshold. The row and column gating signals only activate the target key domain, while neighboring key domains remain in a high-impedance state. The optical modulation frequency avoids the main frequency and harmonics of the row and column drives to reduce crosstalk. These constraints ensure that the sensing phase completes data acquisition within a time and energy range imperceptible to the user.

[0015] This invention aligns the three-channel data in the key domain coordinates to form a state vector. This state vector, along with the measurement covariance, is then passed to subsequent steps for filtering, fusion, and parameter calibration. The electrical path provides direct quantization of charge bias, the optical path provides robust characterization of the reflection state, and the temperature path provides characterization of thermal correlations. The synergy of these three paths provides an observable physical basis for subsequent hysteresis inversion and zero DC vector waveform synthesis, thereby reducing unnecessary global resets and delays.

[0016] The effects of adopting the above principles are reflected in three aspects. First, the complementarity of electrical and optical systems significantly reduces the probability of misjudgment when a single observation fails, and the consistency between the charge bias estimate and optical reflectance at different times provides a basis for subsequent error diagnosis and weight allocation. Second, the synchronous introduction of temperature ensures that parameters and constraints are always solved under consistent thermal conditions, avoiding dose overshoot caused by thermal hysteresis. Third, the explicit construction of measurement covariance enables filter fusion and constraint optimization to have adjustable confidence input, avoiding scene migration mismatch caused by fixed weights.

[0017] Example: On a keyboard equipped with e-ink keycaps, the display frame of each key area is divided into two segments: a display phase and a sensing phase. The sensing phase length is set to 1. The electrical path injects two probe pulses of opposite polarity within the sensing phase, with a single pulse width of 0.2 and an interval of 0.1. The column displacement current is collected at a sampling rate of 200,000, and baseline subtraction is performed using the first 20 baseline segments. The integration window covers the pulse stability segment. The optical path uses a modulation frequency of 3000 for phase-locked sampling, with an integration time of 3, and maps to obtain the optical reflectance. The temperature path places one temperature sensor every 6 key areas, and interpolates the temperature to the center of the key area using a thin plate spline. After spatial registration of the three-channel data in the key area coordinates, a state vector and measurement covariance are constructed. The electrical variance is taken from the median absolute deviation of the three sets of mirror samples, the optical variance is taken from the noise estimation of the in-phase and quadrature components, and the temperature variance is taken from the interpolation residual. The aforementioned state vector is fused with the measurement covariance input filter to generate an estimated state vector, which is then used together with the target reflectance for hysteresis inversion to obtain the equivalent dose target, and a zero-DC vector waveform is synthesized under zero-DC constraints. In this embodiment, in a scenario with continuous keycap updates, the sensed phase is invisible to the user, the measurement signal-to-noise ratio of optical reflectance and charge bias estimates meets the requirements of subsequent control, the in-field interpolation error of temperature remains within an acceptable range, and the overall process can provide consistent and weighted input for subsequent steps.

[0018] The estimated state vector is obtained by filtering and fusing the state vector. The temperature-related response parameters are calibrated based on the reflectance, equivalent dose and temperature samples. The Prandtl-Ishlinskii hysteresis model is constructed and the equivalent dose target is generated by analytical inversion of the target reflectance. At the same time, the charge bias target is set to zero. In step 2 of this invention, the state vector and measurement covariance obtained in step 1 are used as inputs to complete filtering fusion, temperature-related response parameter calibration and hysteresis analytical inversion, and output the estimated state vector, equivalent dose target and charge bias target. Let be the state vector, where For charge bias estimator, For optical reflectivity, For temperature; To measure covariance; To estimate the state vector; This is the equivalent dose; Target reflectivity; The target is the equivalent dose. This is a set of temperature-related response parameters; For the Prandtl-Ishlinskii hysteresis model, the weights and thresholds are used. This is a run operator.

[0019] The filtering fusion method constructs a recursive estimate using a slow-drift prior and a direct observation model, unifying the temporal sequence and reliability of the three channels. The process model and the observation model are respectively... , ,in It is a diagonal attenuation matrix. For process noise, For observation noise, the observation noise covariance is taken from... The recursive update uses the Kalman framework:

[0020]

[0021] in and These represent the prediction covariance and the Kalman gain, respectively. From this, we obtain... This provides a consistent starting point for subsequent inversion and constraints.

[0022] Temperature-dependent response parameter calibration uses a monotonic response model to characterize the relationship between reflectance and dose at temperature. (Using:)

[0023] in , It is an sigmoid monotonic function. .

[0024] In the sliding sample window The above uses variational Bayesian estimation to determine the posterior distribution of the temperature-related response parameters, maximizing:

[0025] The posterior mean and covariance of the output temperature-related response parameters are used for subsequent prediction and robust processing. This calibration transforms individual panel differences and the influence of ambient temperature into updatable parameters, eliminating reliance on fixed calibration tables.

[0026] Hysteresis analytical inversion is used to remove path dependence and directly generate the dose target. A Prandtl-Ishlinskii model satisfying monotonicity is employed.

[0027] , Monotonically increasing, after online identification of weights and thresholds, the result is obtained using an analytical inverse operator. To maintain temperature consistency, according to Scaling the dose-time scale to make Align with target reflectivity at the current temperature. Charge-biased target. Together with the dose target, it serves as an explicit reference for subsequent constraint optimization.

[0028] The overall effect of the above-mentioned link is reflected in three aspects. First, the filtering fusion uses the measurement covariance as the weighting basis, incorporating the reliability differences of electrical, optical, and temperature at different times into the estimated state vector, reducing the disturbance of control by occasional occlusion or impulse noise. Second, temperature-related response parameters are provided in online posterior form, combined with... Achieving temperature-consistent dose mapping avoids systematic biases in fixed models during hot-cold transition scenarios. Third, hysteresis analytical inversion directly transforms target reflectivity into dose trajectory, explicitly eliminating path dependence and making subsequent constrained optimization more likely to converge under zero DC constraints, energy constraints, and spectral constraints.

[0029] Example: On an input device with an e-ink keycap, the state vector and measurement covariance of each key domain within the most recent sampling period are used as the filtering and fusion input to recursively obtain the estimated state vector. The reflectance, cumulative dose, and temperature samples recorded in the previous control window form a sliding window. Variational Bayesian updates are performed to obtain the posterior mean and covariance of the temperature-related response parameters, and the response slope is calculated at the current temperature. For the current target reflectance, the weights and thresholds of the Prandtl-Ishlinskii hysteresis model are updated online. After the model satisfies the monotonicity condition, the analytical inverse operator is called to generate the dose target, and time-scale correction is performed according to the temperature-related rate. The dose target and charge bias target are fed into the constraint optimization of the next step to generate a zero DC vector waveform. In this example, the estimated state vector maintains a smooth evolution between occlusion frames and clean frames. The dose target automatically scales when the temperature changes rapidly. The waveform solution does not require searching historical compensation sequences to satisfy the target reflectance and charge bias targets, reducing invalid resets and shortening the settling time.

[0030] Preferably, when performing filtering and fusion based on the state vector, an extended Kalman filter is used to perform time-series fusion of the charge bias estimate, optical reflectance, and temperature, outputting the estimated state vector and the estimated state covariance, and using the estimated state covariance as the weighting parameter for constraint optimization.

[0031] In step 2 of this invention, the state vector and measurement covariance obtained in step 1 are used as inputs, and extended Kalman filtering is used for time-series fusion to output the estimated state vector and estimated state covariance. The estimated state covariance is then used for weighting and threshold adaptation in subsequent constraint optimization. Let be the state vector, where For charge bias estimator, For optical reflectivity, For temperature; To measure covariance; To estimate the state vector; To estimate the state covariance; This is the state transition matrix; For process noise covariance; For observation vectors; Kalman gain; It is an identity matrix.

[0032] In the application of keycap e-ink screens, the charge bias estimate decays slowly with historical driving, optical reflectance varies gradually during local refresh, and temperature varies approximately gradually over a short period. Therefore, a filter is constructed using a first-order slow-drift prior and a unit observation model. The process and observation equations are as follows: , ,in , This implementation is set in a diagonal configuration. This makes the time correlations of charge bias estimate, optical reflectance, and temperature independent, facilitating individual adjustment of the drift coefficients in different scenarios. Since the observation model is an identity map, the extended Kalman filter degenerates into a linear Kalman filter, with the Jacobian as the identity matrix, resulting in computational stability and good real-time performance.

[0033] Prediction and updates use standard recursion: , , , , ,in This is the state vector predicted in one step. To predict covariance, the innovation vector and its consistency test are used for outlier removal. The innovation consistency criterion is: , , When the criterion is not met, the observation variance of the corresponding channel is increased or temporarily not updated, thereby suppressing the impact of anomalies such as occlusion and transient electromagnetic interference on the fusion result. The estimated state covariance is directly used for weighting in subsequent constraint optimization. The diagonal elements of the estimated state covariance are mapped to a weight matrix. The construction method is as follows: ,in and These are the variance components of the charge bias estimate and optical reflectance, respectively. Further, the scalar weights are obtained: , The weighting strategy, along with the zero target charge bias and target reflectivity tracking, improves the feasibility and convergence speed of solving the zero DC vector waveform. This is then passed to the cost function and threshold tuning in step 3, enabling the constraint optimization to automatically reduce the weight of channels with high uncertainty.

[0034] The effects of the above design are reflected in three aspects. First, the temporal smoothing of state variables and the suppression of anomalous observations reduce the dependence on single-frame quality, preventing occasional distortions from mirror probe pulses and phase-locked sampling from being amplified to the control layer. Second, the explicit output of the estimated state covariance quantifies "measurement quality" into "optimization weights," ensuring a stable trade-off in subsequent solutions under different operating conditions. Third, the predicted covariance is included in the innovation consistency check, forming "soft isolation" for anomalous scenarios and reducing the frequency of triggering invalid phase corrections.

[0035] Example: On a keyboard prototype, the sensing phase is periodically inserted into the display frame. The electrical and optical channels are each sampled three times to form the measurement covariance. Temperature is obtained by interpolation from neighboring sensors. The initial estimated state vector is set as the zero vector, the initial estimated state covariance is set as a large diagonal number, the process noise covariance is set as a small diagonal number, and the diagonal elements of the state transition matrix are set to 0.99. The system performs prediction and updates at a fixed period, and calculates an innovation consistency check after each update. If the threshold is exceeded, only the observation variance of the corresponding channel is increased. During operation, the estimated state vector remains continuous between occluded and unoccluded frames, and the estimated state covariance gradually converges during the stable phase. The weight matrix and scalar weights are passed to step 3 to constrain the optimization cost and threshold, driving the real-time synthesis and execution of the zero DC vector waveform. In scenarios with random occlusion and slow temperature increases, this example maintains stable prediction residuals for charge bias estimation and optical reflectance, reduces the number of phase correction triggers, and exhibits no perceptible flicker during the overall refresh process.

[0036] Preferably, when calibrating temperature-related response parameters based on reflectance, equivalent dose, and temperature samples, variational Bayes is used to estimate the posterior distribution of the temperature-related response parameters within a sliding sample window, and the uncertainty of the temperature-related response parameters is output for robust weighting in constrained optimization.

[0037] In step 2 of this invention, the temperature-related response parameters are calibrated online. The inputs are the state vector and measurement covariance, the reflectance recorded in the previous control window, the equivalent dose and temperature samples, and the outputs are the posterior mean and posterior covariance of the temperature-related response parameters. The posterior covariance is then converted into a robust weighting in constrained optimization. Indicates optical reflectance. Indicates the equivalent dose. Indicates temperature. Represents the set of temperature-related response parameters. and Let represent the mean and covariance of the posterior parameters, respectively. Represents a logical function. This represents the Boltzmann constant.

[0038] From an application perspective, the reflection change of electronic ink exhibits a monotonic relationship with cumulative dosage under a single temperature condition, but this relationship changes with temperature. To continuously obtain a mapping usable for control solutions during operation, this invention employs a temperature-adaptive monotonic response model, expressed as:

[0039] in , This form explicitly incorporates the temperature effect into the response slope, avoiding systematic biases caused by approximating with a fixed calibration table. To ensure solvability of the control, a monotonic form is used, and the order of endpoints and inflection points is kept consistent during parameter updates.

[0040] To achieve online self-calibration at the keycap level, a sliding sample window is constructed. In each control cycle, variational Bayes estimation is performed on the parameters. A Gaussian prior is used. Gaussian variational posterior The likelihood is expressed in a Gaussian form, combined with sliding window sampling, to maximize the lower bound:

[0041] get and In implementation, the gradient is reparameterized for small-step updates, allowing the parameters to evolve smoothly as the window slides. To suppress the influence of contaminated samples, robust pruning is performed on the residuals within the window, reducing the weight of samples exceeding the threshold without removing them, thereby maintaining temporal continuity.

[0042] To explicitly propagate uncertainty to the control layer, the posterior covariance of the parameters needs to be mapped to the predicted variance of the output reflectance. Based on first-order uncertainty propagation, the Jacobian is calculated: The output covariance approximation is obtained as follows: , This reflects the reflectance uncertainty caused by parameter uncertainties at the current equivalent dose and temperature. The control layer will... Compressed into scalar weights or vector weights, these are used for weighting the cost function and constraints. A typical approach is to... A normalized mapping is performed to create a scene-adaptive trade-off between the reflectivity tracking term and the charge bias suppression term. When As the uncertainty increases, the control layer automatically tightens the low-frequency energy constraint and charge neutrality constraint to avoid excessive tracking that introduces flicker when the uncertainty is large.

[0043] The corresponding dose-time scale correction is achieved through Implementation. The control layer linearly scales the target dose time axis before generating the phase sequence, with a scaling factor of: ,in This serves as a reference temperature. This ensures that the dosage application rate remains consistent with material kinetics as the temperature rises or falls, reducing overshoot and undershoot.

[0044] To prevent model parameters from drifting into non-physical regions, updates are performed on... Apply soft constraints: endpoints and Maintaining order, inflection point Limited to the effective dose range, activation energy The processing is limited to the positive half-axis. This is achieved through priors and projections, without introducing additional complexity. For key domains with insufficient sample density within the window, a shared prior mean and covariance across key domains are used for initialization, ensuring a usable mapping during the cold start phase and gradually transitioning to a key domain-specific posterior after local sample accumulation.

[0045] The above calibration brings three benefits. First, the temperature-related response parameters are given in a posteriori form, and their uncertainties are directly used for robust weighting, so that the control solution no longer depends on fixed weights. Second, as the sliding window rolls, the parameters drift slowly with the environment and aging, maintaining consistency in the dose-to-reflectivity mapping and reducing repeated resets. Third, uncertainty propagation provides safety-oriented boundary information, enabling data-driven tightening mechanisms for low-frequency energy constraints and charge neutrality constraints, reducing the probability of perceptible flicker.

[0046] Example: On an input device with e-ink keycaps, the most recently obtained reflectance, equivalent dose, and temperature samples for each key domain are grouped into a window. The window length is 256, and the update cycle is 200. Initial prior... and As specified by the factory calibration. During operation, the system updates in each update cycle. Perform a gradient ascent once, and obtain the new... and The temperature-related response parameters for this key domain are recorded as a post-hoc value. The current operating point is then calculated. and ,Will The reflectance is mapped to the control layer's reflectance tracking weights, and the low-frequency energy threshold and charge neutrality weights are adjusted synchronously. The target reflectance is derived from interface icon switching, and the temperature is derived from the interpolation field. In scenarios with continuous key switching and a slow increase in ambient temperature, the dose-to-reflectance mapping adjusts smoothly with temperature, the control solution does not exhibit overshoot pulse stacking, zero DC constraint remains feasible, and flicker is imperceptible to the user.

[0047] Preferably, when constructing the Prandtl-Ishlinskii hysteresis model, the hysteresis weights are limited to non-negative values ​​and the run thresholds are monotonically arranged according to their amplitudes. The target reflectance is converted into an equivalent dose target using the analytical inverse operator of the Prandtl-Ishlinskii hysteresis model.

[0048] In step 2 of this invention, a reversible mapping from reflectance to equivalent dose based on the Prandtl-Ishlinskii hysteresis model is established to convert the target reflectance into an equivalent dose target and use it directly in subsequent constraint optimization. For optical reflectivity, For equivalent dose, For target reflectivity, For equivalent dose target, These are the hysteresis weight and the run threshold, respectively. For the threshold is The run-length operator. The thresholds are monotonically arranged according to their magnitudes, satisfying... The weights are non-negative and satisfy the following conditions: .

[0049] In the application scenario of this invention, the response of electronic ink materials to equivalent doses exhibits path dependence; the same final value may result in different reflection states due to different histories. The Prandtl-Ishlinskii hysteresis model characterizes this path dependence using a set of parallel run operators, and its forward mapping is:

[0050] In the above formula, the internal memory of each run operator is implemented through "squeezing variables"; in actual implementation, an internal state is set for each threshold. In discrete time steps renew: , Where "clip" is the interval truncation operator, " represents the updated quantity. Since the weights are non-negative and the threshold is monotonic, the positive mapping remains monotonic on any monotonic input segment. This monotonicity is a sufficient condition for invertibility: there exists an analytic inverse operator of the same kind that maps the target reflectance to the equivalent dose target.

[0051] This invention employs an implementation path of "analytical inverse structure + explicit incremental solution". First, based on the monotonicity theorem, the inverse operator can still be expressed as a linear combination of run operators under the same threshold set, with its coefficients determined by... Uniquely determined; to avoid solving the symbolic formula at runtime, this invention provides an explicit incremental update law that is inversely equivalent to the analytical one: let the target reflectance increment be... , Target reflectivity increment; Define the current responsive "effective slope": ,in Let this be the set of rune numbers that are not saturated and are responsive in the current step. If for all... If all are in the linear region, then: If the above If some runs reach the threshold, deduct their remaining responses one by one in ascending order of the threshold, and update the set. With slope In the new Continue calculating the remaining target reflectance increments until this step. Completely matched. Symmetric processing is performed on negative changes. Through this piecewise linear solution, results can be obtained at each discrete time step. Increment and update all This process is consistent with the output of the parsing inverse operator and only involves addition, comparison, and one division, making it suitable for real-time execution on a keyboard controller.

[0052] To improve the model's discriminability and stability, this invention enforces a non-negative and monotonic threshold order during weight identification, and obtains the result through recursive least squares combined with monotonic projection. The threshold coverage is divided using logarithmic or equidistant scales to ensure sufficient resolution across different dose scales. Since step 2 also provides temperature-related response parameters, if temperature changes cause changes in the response slope, the time axis is scaled according to existing definitions, treating the effect of temperature as equivalent to a linear scaling of the dose time scale without altering the order of the hysteresis threshold set, thus maintaining the inverse mapping structure.

[0053] The effects of the aforementioned inverse mapping are reflected in three aspects. First, the target is transferred from the reflection space to the dose space, and subsequent zero-DC vector waveform synthesis no longer requires repeated searching of compensation sequences on the historical trajectory, thus determining the solution scale and time upper bound. Second, piecewise linear updates automatically handle saturation and desaturation near the threshold, avoiding oscillations and overshoot during inversion. Third, the non-negativity of the weights and the monotonicity of the threshold ensure the invertibility and numerical stability of the mapping; when the target reflectance is piecewise monotonic, the equivalent dose target is unique.

[0054] Example: On a device containing e-ink keycaps, set up each key field Each run has a threshold value, which covers the working dose range on a logarithmic scale. The initial weights are given by factory calibration and recursively updated during operation. When the interface switches from text to icons, the target reflectivity is generated by the interface engine. The controller calculates the target reflectivity increment in each run, obtains the equivalent dose increment based on the current "effective slope," and if any run is detected to have reached the threshold, it updates the internal state and effective slope before continuing to complete the remaining increment allocation. After completing one frame of inversion, the equivalent dose target trajectory is obtained, which is input together with the charge bias target into the constraint optimization in step 3 to synthesize a zero DC vector waveform. In this embodiment, under conditions of continuous rapid switching and frequent operation of some keys, the equivalent dose target does not oscillate, the waveform synthesis can achieve the target reflectivity without additional global reset, there is no perceptible flickering of adjacent keys, and the display process is smooth.

[0055] Under zero DC constraint, the zero DC vector waveform is obtained by solving the constraint optimization with the equivalent dose target and the estimated state vector as input. The reverse polarity probe pulse is used to obtain the charge bias estimate and optical reflectance after execution. If the preset judgment condition is not met, the reverse polarity correction phase pair is injected. In step 3 of this invention, the equivalent dose target and the estimated state vector are transformed into a driving phase sequence that satisfies zero DC constraint, and after execution, rapid verification and closed-loop correction are completed using trial pulses of opposite polarity. (See below:) For equivalent dose target, To estimate the state vector, where For charge bias estimator, To estimate reflectivity, For temperature; This is a set of temperature-related response parameters; The zero DC vector waveform, where For phase polarity, The phase voltage amplitude, Phase duration; For continuous time The target reflectivity at a given location is suitable for continuous-time representation; and The reflectivity threshold and charge bias threshold are preset judgment conditions.

[0056] In the control solution, the zero DC constraint is expressed as a voltage-time integral as follows: This constraint ensures that charge does not accumulate and drift after prolonged driving. To map the equivalent dose target to an executable phase, local linearization is used to express the effect of phase on dose and reflection as an approximately linear relationship. Let the drive vectorization be... The dose increment is approximately: ,in This is the sensitivity matrix obtained from device calibration and microprobeing at the current temperature and parameters. The reflectance increment can be approximated from the temperature-dependent response model:

[0057] Based on this, a constrained optimization objective is constructed:

[0058] in The charge change prediction obtained from the mirror pulse charge imbalance model, , , The uncertainty is mapped from the output of step 2 to the threshold. Constraints include zero DC constraint, as well as device-defined voltage amplitude, phase duration, and slew rate constraints. The solution yields... The command is sent to the key field within a control window.

[0059] Immediately after execution, a test pulse of opposite polarity is injected to measure the estimated charge bias and optical reflectance after execution with a minimum dose, denoted as follows: and The achievement of the target is detected based on preset judgment conditions. , If the condition is not met, then calculate the dose correction amount:

[0060] A pair of opposite-polarity corrected phase pairs is synthesized to achieve dose fine-tuning under zero DC constraint. Let the amplitude and duration of the two phases of the corrected pair be... and ,make ,and By setting unequal durations within the nonlinear response segment, zero DC is maintained while the required dose correction is generated. After the correction is executed, a test pulse with opposite polarity is used for retesting. If the judgment condition is still not met, the correction pair generation is repeated once within the safety upper limit.

[0061] The core principle of the above method lies in simultaneously encoding the dose tracking error and the charge-neutral target into an optimization problem with zero DC constraints. After execution, closed-loop evidence is obtained by using fast, low-dose, opposite-polarity probe pulses. Then, fine-grained dose compensation is achieved by using opposite-polarity corrected phase pairs without introducing DC bias. Since the optimization target explicitly includes charge and energy terms, the controller tends to output short-duration, small-amplitude, and symmetrical convergent phases when approaching the target, thereby reducing perceptible flicker and neighborhood crosstalk. The corrected phase pair is triggered only when the error exceeds a preset judgment condition, balancing the cost of closed-loop operation with perceptibility.

[0062] This method offers three main benefits. First, the zero-DC vector waveform ensures long-term charge neutrality, significantly reducing ghosting and parasitic bias in rows and columns. Second, the opposite-polarity probe pulse provides immediate physical measurements after execution, avoiding drift caused by relying solely on model predictions. Third, the opposite-polarity phase correction pair eliminates minor deviations within an iteration cycle, reducing the need for global resets and improving the smoothness of interface switching.

[0063] Example: A 4-phase template is set within the keycap button area, with the phase polarity order being positive, positive, negative, negative, and the control window duration is 2 seconds. During the solution process, zero DC constraints, amplitude constraints, duration constraints, and slew rate constraints are simultaneously incorporated. The sensitivity matrix is ​​jointly provided by factory calibration and recent micro-tests. After the phase sequence is issued, displacement current and phase-locked reflection are immediately collected using a test pulse with opposite polarity, having an amplitude of 0.2 times the display drive amplitude and a single-phase duration of 0.2 seconds. This yields the calculated charge bias estimate and optical reflectivity. When the reflectivity deviation exceeds a preset judgment condition or the charge bias estimate exceeds a preset judgment condition, the dose correction is calculated, and a pair of corrected phases is generated. The corrected phases use the same amplitude but different durations to meet both zero DC and dose correction requirements, with the total duration of a single correction not exceeding 2 seconds. After one correction, a second test is conducted. If the preset judgment condition is met, the next window is entered; if not, a second correction is performed, and the event is recorded for upper-level scheduling load shedding. In this embodiment, no perceptible flickering occurs during the rapid switching between characters and icons, the accumulation of afterimages in the key field is suppressed under continuous operation, and the zero DC residual is maintained within a preset range.

[0064] Preferably, when the equivalent dose target and the estimated state vector are used as inputs, model predictive control is used to optimize the zero DC vector waveform in the rolling time domain, and a worst-case cost term is set for the uncertainty of the temperature-related response parameters and weighted in the optimization objective.

[0065] In step 3 of this invention, model predictive control is used to transform the equivalent dose target and the estimated state vector into a driving sequence that satisfies the zero DC constraint, and the worst-case cost term is constructed using the uncertainty of the temperature-related response parameters to participate in the optimization. The equivalent dose target at discrete time points; To estimate the state vector, where For charge bias estimator, For the first Estimated reflectance for each control step For temperature; For the first Target reflectivity for each control step; ; For the posterior mean and posterior covariance of the temperature-related response parameters; For the first The control quantity for a step represents the voltage-time integral of that step; The length of the prediction domain; This refers to the local sensitivity of the dose to the control dose; The Jacobian of reflectance with respect to parameters This is a temperature-dependent response model.

[0066] Linearized dose and reflectance predictions are used in the rolling time domain: , Zero DC constraint is represented by the sum of voltage-time integrals in the prediction domain being zero: Simultaneously, hard constraints such as amplitude, rate of change, and energy upper limit are applied to match the actuator capability and safety boundary. Considering the uncertainty of temperature-dependent response parameters, the first-order propagation is used to give the... Worst-case upper bound of reflectivity of a step: ,in For parameter dimensions, The quantiles of the chi-square distribution. Let be the largest eigenvalue. Using this as a robust cost term and incorporating it into the optimization objective, we obtain the rolling optimization problem:

[0067] in The weighting is derived from the scalar mapping between the estimated state covariance and the posterior parameter covariance. After obtaining the control sequence, only the first control variable is issued and the process rolls to the next step, forming a closed loop of "prediction-execution-re-prediction".

[0068] The principle behind the above design is as follows: using voltage-time integral as the control variable, zero DC constraint allows for direct linear detection within the prediction domain; local linearization of dose and reflectivity transforms nonlinear material dynamics into a solvable quadratic problem; the uncertainty of temperature-related response parameters is incorporated into the cost function through the worst-case upper bound, automatically tightening the tracking force and suppressing overdrive when the model is uncertain. This satisfies charge neutrality while avoiding flickering and ghosting caused by parameter drift.

[0069] The corresponding effects are reflected in three aspects. First, the zero DC constraint is strictly satisfied in each prediction domain, and the charge bias estimate does not accumulate over time. Second, the robust cost term imposes additional penalties on the uncertain regions of parameters, causing the control solution to tend towards lower energy and smoother drives under high uncertainty conditions, reducing the probability of perceptible flicker. Third, rolling execution uses only the first control variable, enabling the optimization to respond immediately to new observations and maintain stability even when tracking rapid interface switching.

[0070] Example: Determine the prediction domain length The sampling period is 50, the upper limit of the control quantity is the single-step voltage-time integral threshold, and the upper limit of the rate of change is calculated based on the slew rate of the driver. Dose sensitivity. The posterior mean and posterior covariance of the temperature-related response parameters are estimated jointly by factory calibration and recent mirror testing. These parameters are obtained from the variational Bayesian method in step 2, and the values ​​for each step are calculated accordingly. and The optimization employs a quadratic programming solver, generating a control sequence and issuing only the first-step control variable while satisfying constraints. In actual operation, under conditions of continuous icon switching and a slow change in ambient temperature from 30 to 35 degrees Celsius, the reflectivity error gradually converges with rolling optimization, the charge bias estimate remains within the threshold, low-frequency brightness fluctuations do not exceed the perceptible range, and a global reset is not triggered.

[0071] Preferably, when solving the constraint optimization to obtain the zero DC vector waveform, zero DC constraint, temperature uniformity constraint, energy constraint, hardware constraint and low frequency spectrum constraint are applied simultaneously, and a phase sequence template with phase sign symmetry is used to satisfy the zero DC constraint.

[0072] In step 3 of this invention, a zero DC vector waveform is synthesized through optimization with multiple constraints, so that the driving sequence satisfies charge neutrality, avoids low-frequency flicker, and conforms to the device capability boundary. It is a phase sequence, where For phase polarity, For voltage amplitude, Phase duration; for Vector representation expanded over time; Estimated current temperature; This is the slope function of the temperature-dependent response; Discrete Fourier transform in the low frequency band Selection operators on; , , For DC, temperature consistency and low-frequency energy tolerance; , , , These are hardware constraint parameters; This represents the upper limit of energy within a single window. Zero DC constraint uses voltage-time integral as its core metric, requiring that the integrals of positive and negative phases strictly cancel each other out within a single control window. To eliminate the equivalent effect mismatch caused by temperature, a temperature consistency constraint is introduced, and the slope of the temperature-related response is used as a weight to correct the time integral. Energy constraints limit the total equivalent dose released through a single window, preventing over-driving and localized heating. Hardware constraints are manifested in the boundaries of amplitude, duration, and slew rate: , , To suppress low-frequency brightness fluctuations perceptible to the human eye, a spectral threshold is used to constrain the spectral energy of the time-domain driving vector in the low-frequency band. To maintain numerical stability within the feasible region and simplify the solution, a phase-symmetric template is used to construct the initial solution and search subspace. For example, a four-phase symmetric template satisfies: and to and , and Mirror pairing is configured. This structure naturally satisfies the uniform feasibility requirement of zero DC constraint, and maintains a well-convex approximate feasible region even after adding temperature uniformity and spectral thresholds, making it easy to solve quickly using quadratic programming or projective gradient methods.

[0073] The optimization objective primarily focuses on approximating the equivalent dose target while prioritizing charge neutrality, and also introduces energy canonicality to avoid over-excitation. For consistency with the above, only the core form is given:

[0074] in The dose increment is obtained by mapping small signal sensitivity. For equivalent dose target, This is a predictor of charge imbalance. , , This is obtained by mapping the estimated state covariance to parameter uncertainty. The objective is minimized under the aforementioned five types of constraints, yielding... Execute after row and column addressing.

[0075] The key principles of the above design are: using "voltage-time integration" as a unified metric to unify DC neutrality, temperature consistency, and energy budget within the same feasible region; directly suppressing low-frequency components at the optimization layer through spectral thresholding to avoid post-correction; and transforming the zero DC constraint into a structural condition using a phase sign-symmetric template, significantly reducing the solution difficulty. The corresponding effects are: reduced low-frequency energy at the same refresh rate, resulting in less perceptible flicker; stable DC neutrality across temperature scenarios, suppressing ghosting accumulation; and simultaneous guarantee of solution convergence and execution safety within the amplitude, duration, and slew rate boundaries.

[0076] Example: Use a four-sided symmetrical template, control the window length to 2, and set the upper limit for the low-frequency band. The frequency band is set near the boundary of the visually sensitive band. During the solver initialization phase, feasible initial values ​​are generated with phase symmetry to simultaneously satisfy the zero DC constraint and the temperature uniformity constraint. Subsequently, quadratic programming is performed on the constraint set, with the objective weights obtained by mapping the estimated state covariance and the posterior parameter covariance of the previous window; spectral threshold. The low-frequency energy statistics of the nearest window are adaptively adjusted. After the phase sequence obtained is executed in the key domain, a small-amplitude, opposite-polarity trial pulse is immediately used to complete the closed-loop verification. In the experiment, under continuous icon switching and rapid text scrolling conditions, the spectral threshold controls the low-frequency components, the zero DC residual falls within the tolerance, and no additional afterimages or flickering occur during the temperature rise from 30 to 35 degrees Celsius, proving the effectiveness of the synergistic effect of the multiple constraints and the phase symbol symmetric template.

[0077] Preferably, after obtaining the charge bias estimate and optical reflectance after execution using the opposite polarity probe pulse, the reflectance deviation threshold and the charge bias estimate threshold are used to form a preset judgment condition. If the preset judgment condition is not met, an opposite polarity correction phase pair is injected and the opposite polarity correction phase pair satisfies that the voltage-time integral is zero.

[0078] This invention introduces a rapid "verification-correction" closed loop after executing the zero DC vector waveform. The basic idea is to obtain the estimated charge bias and optical reflectance after execution under minimum dose conditions using a probe pulse with opposite polarity, and determine whether it meets the standard according to preset judgment conditions; if it does not meet the standard, a pair of correction phase pairs with opposite polarity and zero voltage-time integral is injected to complete micro-dose compensation without introducing a new DC bias.

[0079] Indicates the first Target reflectivity per control step Indicates the number of executions after execution. Each control step optical reflectance measurement value This represents the estimated charge bias after execution. and These represent the reflectivity deviation threshold and the charge bias threshold, respectively. This indicates the current temperature estimate. Represents the set of temperature-related response parameters. This represents the monotonic response mapping from equivalent dose to reflectance given temperature and parameters. This represents the slope of the mapping at the operating point. The single-phase amplitude and duration of the corrected phase pair are denoted as... and .

[0080] First, a pair of low-amplitude, short-duration, opposite-polarity probe pulses are emitted into the target key domain. The displacement current is integrated over time to obtain a charge bias estimate, and the optical reflectivity after execution is obtained through demodulation in the phase-locked channel. This forms the error with the target. , The preset judgment condition is defined as follows: If the condition is met, the current window ends directly; otherwise, a minor correction is initiated. The minor correction is based on the "zero DC area equality" structure. The constraints are: This ensures that the voltage-time integral of the corrected phase pair is zero. To generate the required equivalent dose correction, the dose correction required at the operating point is first calculated based on the temperature-dependent response model: The directional sensitivity of electronic ink typically differs under small forward and reverse doses. Let the differential gain for the forward and reverse directions be denoted as... and Therefore, the net effect of the corrected phase pair on the equivalent dose in the small signal region is approximately: Combined with zero DC constraint ,get Based on this, within the permitted amplitude and minimum duration range, the following can be determined: And generate corrected phase pairs.

[0081] when When the single-pair efficiency is insufficient due to the small size, an equivalent zero-DC structure of "double-pair series connection" is adopted: first, a pair of small-area pre-bias phases are injected to change the directional sensitivity of the local operating point, and then the main correction pair is injected to complete the process. The sum of the voltage-time integrals of the four phases remains zero, thus maintaining charge neutrality. Immediately after the phase correction is executed, a test pulse of opposite polarity is emitted again for retesting. and Acceptance is performed according to the same criteria; if the criteria are still not met, only one correction is allowed within a single window, and the button field is marked as restricted and handed over to the upper-level scheduler to reduce its refresh frequency and dose quota. The entire process ensures that the closed-loop behavior is within the user's imperceptible time and energy budget.

[0082] The engineering principle of this mechanism is reflected in three points. First, the probe pulse transforms "whether the standard is met" into a threshold judgment of two measurable physical quantities, enabling the control closed loop to converge quickly without relying on model extrapolation. Second, the corrected phase pair generates a net dose using the difference in directional sensitivity under zero DC constraint, thus eliminating reflection errors without introducing new DC bias. Third, the constraints of the number and area limit the correction to a local, short-term, and low-energy range, avoiding the injection of low-frequency energy into the perceptible frequency band and reducing the risk of flicker.

[0083] Example: On a keycap prototype, the display window duration is set to 2. The probe pulse amplitude is set to 0.2 times the display drive amplitude, the single-phase duration is 0.2, and row and column gating only activates the target key field. After executing the zero DC vector waveform at the end of each window, data is immediately acquired. and threshold and Based on historical perceptibility statistics. If or Calculated based on the current temperature and parameters Directional sensitivity and Based on the combined estimation of the most recent mirror test and factory calibration, the following was selected. Calculate if the amplitude does not exceed 0.5 of the allowable amplitude. ,when If the duration is below the minimum, the amplitude is increased until the maximum duration is met or reached; when When the value is less than the threshold, dual-pair series connection is enabled and the pre-bias pair area is set to 0.3 of the main pair area. After one correction, a retest is performed. If the value is still not met, a second correction is performed. If the value is still not met, the event is recorded and the upper-level load reduction is initiated. In scenarios with continuous icon switching and temperatures ranging from 30 to 34 degrees Celsius, the reflection error within a single window is suppressed to within the threshold, the charge bias is maintained within the threshold, and no perceptible flicker is observed, proving that the trial-judgment-correction zero DC micro-compensation mechanism is feasible and stable.

[0084] The total equivalent charge of the entire plate is calculated by summarizing the execution records. Blocking and phase-staggered scheduling are performed based on optical deviation and charge bias. Temperature-related response parameters are updated based on newly added reflectivity, equivalent dose and temperature samples for subsequent state reconstruction and waveform synthesis.

[0085] In step 4, this invention centrally processes the execution records generated in step 3, completing full-plate quantization measurement, block and phase-staggered scheduling, and updating temperature-related response parameters based on newly added samples. This enables the next control window to start with more reliable priors and safer resource allocation. Indicates the key field number; This represents the estimated charge bias after execution. Indicates the optical reflectance after execution; Indicates the reflectivity of the target; Indicates the equivalent dose; Indicates temperature; Let represent the set of temperature-related response parameters, whose posterior mean and posterior covariance are denoted as . and First, we construct a global convergence metric. We define the total equivalent charge across the entire plate: ,in This is the set of all key fields. As a window-level descent criterion and correction trigger, it is used to determine whether charge neutrality converges across the entire board. To spatially identify areas requiring priority remediation, a weighted risk score for optical deviation and electrical bias is calculated for each key domain. ,in and The weights are dimensionless and determined through factory and on-site calibration. Risk scores are used to determine block partitioning and scheduling priorities.

[0086] Block-based and phase-staggered scheduling addresses constraints related to heat dissipation, crosstalk, and perceptible flicker. The keyboard topology is represented as a graph, with edge weights derived from geometric adjacency and thermal coupling. Aiming at the spatial distribution of risk scores, the graph is partitioned into blocks. Within each block, the key domains are temporally staggered, and execution windows alternate between blocks, controlling energy peaks and local low-frequency components within any short time window. Block-level quotas are determined jointly by energy statistics and risk scores from the upper window and are consistent with row and column addressing timing constraints, ensuring feasibility at the implementation level.

[0087] To ensure verifiable scheduling, execution records are saved in each window, including key fields, timestamps, driving phase parameters, probe pulse measurements, whether corrections are triggered, and the area of ​​the correction pair. These records form a dataset within the window, used for two purposes: first, real-time monitoring of whether scheduling execution meets block-level quota and phase misalignment rules; and second, as new samples for parameter updates.

[0088] The parameter update uses the same temperature-adaptive monotonic response model as in step 2, and performs variational Bayes within the sliding sample window. New samples are sets of triples. The reflectance is derived from post-execution measurements, the equivalent dose is the accumulated equivalent surface of the issued phase sequence, and the temperature is the interpolation result within the window. Gaussian variational posterior... Maximizing the variational lower bound yields the updated result. and To propagate parameter uncertainty to the control layer, the Jacobian is calculated. The reflectance prediction variance was obtained using first-order propagation. Then The weights and thresholds are mapped to the next window for adaptive tuning of the reflectivity tracking term, charge neutrality term, and low-frequency threshold.

[0089] The engineering significance of the above process is reflected in three points. First, First, grouping scattered charge residuals into a single measurable metric facilitates window-level convergence monitoring and correction. Second, risk-scoring-based block and phase-staggered scheduling transforms the "which keys to prioritize and when to perform" decisions into a structured schedule, avoiding energy overlap and low-frequency coupling within the same spatial neighborhood and reducing the probability of perceptible flicker. Third, online parameter updates and uncertainty propagation enable control weights and thresholds to slowly adapt to the environment and aging, reducing over-driving or under-tracking caused by fixed weights.

[0090] Example: On a device with e-ink keycaps, the control window length is set to 50, and the keyboard is divided into 8 blocks. At the end of each window, the system calculates... It is then compared with the previous window; if the decrease is below the threshold, a block-level mild reset is triggered, and the quota of high-risk blocks is reduced. Risk scoring uses... , Normalized stacking is performed, and the keys are assigned to blocks in descending order, with the phases within each block offset by 90 degrees (equivalent phase). The dataset accumulates the most recent 256 samples, and variational Bayesian update is performed to obtain new samples. and ,calculate This is then mapped to the reflectivity tracking weights and low-frequency threshold scaling factor for the next window. Under the condition of continuous icon switching and a temperature increase from 30 to 35, The block-level energy peak remained within budget with a monotonically decreasing trend, and the low-frequency threshold adaptively tightened without noticeable flicker. In stressful scenarios involving high-frequency key operations, the risk score concentrated in that area. The scheduler automatically delayed the block by one phase and reduced the quota, while the parameters converged to a new stable value. Subsequently, the number of triggers decreased due to the corrected phase within the window. These results demonstrate that the synergy of full-board measurement, structured scheduling, and online parameter updates can maintain display quality and long-term charge neutrality without increasing the global reset frequency, and provides verifiable priors and thresholds for the next control window.

[0091] Preferably, when performing block and phase misalignment scheduling based on optical deviation and charge bias, the keyboard is constructed as a graph containing adjacency weights and thermal coupling weights. The block set, dose quota and phase misalignment amount are determined through optimal transmission, and refresh and correction tasks are arranged accordingly within the time window.

[0092] In step 4 of this invention, the keyboard is used as a spatiotemporal coupling system for unified scheduling. A weighted graph incorporating spatial adjacency and thermal coupling is established, with each key domain as a node. This graph measures which keys should not be driven simultaneously. Based on this, a risk score formed by optical deviation and charge bias is used as the demand quantity. Optimal transmission determines the block set, the dose quota for each block, and the phase misalignment. Refresh and correction tasks are then scheduled accordingly within the time window to achieve energy dispersion and low-frequency component suppression.

[0093] Use sets Represents the entire key field; let the node... Risk score This quantity is formed by weighting the difference between the optical reflectance and the target reflectance after the previous step and the charge bias estimate; using Representing geometric adjacency weights, using Indicates thermal coupling weight; defines comprehensive coupling weight: ,in and The dimensionless coefficients obtained from calibration. The larger the value, the more nodes are driven simultaneously. With nodes The more likely it is to produce noticeable flickering and localized temperature rise.

[0094] Risk scoring is viewed as "quality that needs to be addressed," and available driving resources within the time window are considered "accommodation capacity." Design delineation is divided into... Each block occupies a non-overlapping phase within a window. A discrete optimal transmission model is introduced, where the assignment from node to block is expressed as a transportation plan. Let the node The demand is ; block The capacity is ,satisfy Its size is given by the energy budget and concurrency capability. Define the transportation cost from node to block: ,in For block The reference occupancy indicator is obtained by initializing the value using a spatially uniform strategy or historical block partitioning. Solve: , , ,get Then, the node Assigned to the block with the largest proportion This creates a set of blocks. This assignment tends to assign highly coupled neighbors to different blocks, mitigating the coupling risks associated with simultaneous drives from the source.

[0095] Dosage quotas are used to limit the total energy of each block within the window. Let the energy budget for the entire window be... Then the block-level quota is: , ,in For block The set of nodes, The approach strikes a balance between "uniform allocation" and "risk-weighted allocation." Within each block, the single-key dosage limit is further allocated in descending order of the node's risk score, ensuring that high-risk keys receive priority for refresh and correction resources.

[0096] The phase offset is used to further suppress low-frequency coupling across blocks. Let the block-level phase offset be... and from a finite set Select from the options. Define the phase conflict cost. , ,in Let it be an indicator function. Solving for it makes... The goal is to minimize the number of staggered combinations, ensuring that highly coupled blocks are not executed in the same phase. This problem is equivalent to discrete optimization with weighted graph coloring, and a feasible solution can be obtained within a window time limit using a greedy algorithm with a small amount of backtracking.

[0097] Tasks within a time window are scheduled according to the principle of "block-level sequential, intra-block parallel". The window is divided into... Each phase segment allows only one block to execute refresh and correction tasks. Within a block, key fields that are active simultaneously are selected based on row and column addressing and hardware concurrency limitations, prioritizing key fields with high risk scores and sufficient remaining dose quota. The correction task queuing strategy is as follows: if a single key requires phase pair correction after closed-loop determination and is located within the current block, the remaining time slice of that block is used; if the time slice is insufficient, a short time slot is reserved for that block in an adjacent phase segment, and the phase offset of adjacent blocks is adjusted with minimal cost to ensure that the zero DC constraint and spectral threshold are not violated.

[0098] The effectiveness of this block-based scheduling framework is reflected in three aspects. First, by optimizing transmission, "risk quality" is rationally loaded into "phase capacity," and highly coupled neighbors are systematically separated for execution, suppressing low-frequency brightness fluctuations and heat accumulation. Second, dose quotas explicitly constrain the energy budget at the block and key levels, avoiding image retention and keycap overheating caused by prolonged occupation of a single region. Third, phase staggering globally reduces the number of block pairs executing simultaneously in phase, significantly reducing the energy spectral density in the frequency band sensitive to human vision, thereby reducing perceptible flicker.

[0099] Example: On a device containing 68 keycaps, set up... Each block. The adjacent weights are normalized using the reciprocal of the Euclidean distance between the keys. The thermal coupling weights are normalized based on the steady-state temperature influence coefficient obtained from structural simulation. , The risk score is composed of the difference between the optical reflectance and the target reflectance after the previous step, as well as the charge bias estimate, and is standardized. The transportation plan is obtained through optimal transmission, and the data is divided into blocks to obtain the capacity vector for each block. Full-window energy budget Based on power supply and heat dissipation capabilities, To balance uniformity and risk orientation, the phase misalignment problem is then solved to obtain the phase set. During operation, eight blocks were executed sequentially within a window. Within each block, no more than the hardware concurrency limit was activated in parallel for key fields. Key fields with higher risk scores were prioritized for scheduling, and correction tasks were given priority in their time slices within the block. Statistics from ten consecutive windows showed that the block-level energy peak was lower than the budget, the total equivalent charge of the entire board decreased monotonically, low-frequency energy decreased within the visually sensitive band, local temperature rise and adjacent crosstalk were suppressed, and a global reset was not triggered. These results validate the feasibility and expected effectiveness of the block-based, quota-based, and phase-staggered collaborative scheduling method based on graph weights and optimal transmission.

[0100] Preferably, the total equivalent charge of the entire plate is calculated as a convergence criterion for window-level comparison. When the total equivalent charge of the entire plate does not meet the descent condition, a global reset phase sequence with zero DC is triggered, and the refresh frequency and single dose of high-risk key domains are reduced. At the same time, the temperature-related response parameters are updated online based on the newly added reflectivity, equivalent dose and temperature samples, and the temperature-related response parameters are written back to the filtering fusion and constraint optimization for subsequent state reconstruction and zero DC vector waveform synthesis.

[0101] In step 4, this invention performs centralized evaluation and adaptive correction on the execution records of step 3. The goal is to ensure long-term convergence with charge neutrality from a full-plate perspective and to immediately feed new samples back into the modeling and control layers. The key field number is... The charge bias estimate after execution is: The optical reflectivity after execution is ; Target reflectivity is The equivalent dose is Temperature is The posterior of the temperature-related response parameter set is .

[0102] First, we construct a window-level convergence criterion. The total equivalent charge of the entire plate is defined as: To suppress occasional fluctuations, The benchmark is obtained by performing an exponential moving average. Convergence testing employs a monotonically decreasing condition. ,in The convergence coefficient is less than 1. If the condition is met, normal scheduling is initiated; otherwise, two types of correction actions are triggered: a global reset phase sequence with zero DC and a load reduction strategy for high-risk key domains.

[0103] The global reset phase sequence adopts a multi-phase, sign-symmetric, and cross-block staggered structure to ensure that both the voltage-time integral and the temperature-weighted integral are simultaneously zero. , The phase polarity is The voltage amplitude is Duration is , The slope represents the temperature-dependent response. Row-column timing is staggered by block, ensuring each block executes in different phase segments, avoiding the injection of low-frequency energy into adjacent areas simultaneously. The energy of the reset phase is constrained by both the window budget and the spectral threshold, guaranteeing that disturbances to the currently displayed content remain imperceptible. High-risk load derating is based on risk score ranking. The risk score is defined as... When correction is triggered, two measures are implemented for key domains with high risk scores: first, the refresh frequency is reduced, so that the key domain enters the refresh phase segment less often in subsequent windows; second, the single dose limit is lowered, so that it is subject to tighter energy constraints when solving for the equivalent dose target. Both measures are consistent with row and column concurrency capabilities, phase staggering rules, and spectral thresholds to avoid the introduction of new low-frequency coupling.

[0104] In addition to corrective control and load reduction scheduling, step 4 adds new samples for online updating of temperature-related response parameters. A window sample set is constructed. ,by Posterior of the previous window Perform variational Bayesian update to maximize the lower bound of evidence:

[0105] Get new .Will Write-back is done via two paths: one is write-back to the filter fusion, using... Update the prior relationship of reflectance with respect to dose and temperature, using Adjusting observation weights; secondly, writing back to constraint optimization, using... Update small signal sensitivity and time scale scaling, using The output uncertainty is obtained through first-order propagation. , , and then The cost weights and spectral threshold scaling factors of the next window are mapped to achieve robust tightening for uncertain operating conditions.

[0106] The engineering effects of the aforementioned closed-loop strategy are reflected in three aspects. First, First, the overall charge residual is compressed into a single observable index, and correction is triggered by a strict descent criterion, making charge neutrality verifiable at the entire plate level. Second, the zero-DC global reset phase sequence and inter-block staggering suppress low-frequency energy peaks in the spectral domain, reducing perceptible flicker and eliminating long memory ghosting. Third, continuous updates to the parameter posterior and uncertainty write-back enable the weighting of filter fusion and optimization to adapt to the environment and aging, avoiding mismatch in fixed calibration under varying temperature and high-load conditions.

[0107] Example: On a keyboard with e-ink keycaps, the window duration is set to 50. The system calculates the duration at the end of each window. and ,when If convergence is not detected, a global reset phase sequence is immediately scheduled, and load reduction is applied to the top 10 key fields ranked by risk score. The reset phase uses a four-phase symmetrical template and is staggered by four equal phases among the eight blocks, satisfying two constraints where the integral is zero. The load reduction strategy proportionally reduces the refresh frequency of the relevant key fields and tightens the single dose limit. Subsequently, data within the collection window is collected. Entering variational update, we obtain the new ,calculate and And write back to filtering fusion and constraint optimization. In continuously running scenarios, Within 2 to 3 windows after triggering the reset, the device recovers to the descent trajectory. In areas with high risk scores, the phase correction reduces the number of triggers during the descent cycle, and the energy spectral density in the visually sensitive frequency band decreases without global flicker. When the ambient temperature rises from 30 to 35 degrees Celsius, the time scale automatically scales to maintain tracking stability, indicating that the synergy of the convergence criterion, global reset, and parameter write-back can achieve long-term charge neutrality and stable display quality without increasing the frequency of global reset.

[0108] The above are merely embodiments of this application and are not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A method for controlling the electronic ink screen display of a keycap, characterized in that, Includes the following steps: A sensing phase is inserted into the key domain, a probe pulse of opposite polarity is applied and the displacement current is integrated to obtain the charge bias estimate, the optical reflectance is obtained through phase-locked demodulation, the temperature is measured, and a state vector containing the charge bias estimate, optical reflectance and temperature is established. The estimated state vector is obtained by filtering and fusing the state vector. The temperature-related response parameters are calibrated based on the reflectance, equivalent dose and temperature samples. The Prandtl-Ishlinskii hysteresis model is constructed and the equivalent dose target is generated by analytical inversion of the target reflectance. At the same time, the charge bias target is set to zero. Under zero DC constraint, the zero DC vector waveform is obtained by solving the constraint optimization with the equivalent dose target and the estimated state vector as input. The reverse polarity probe pulse is used to obtain the charge bias estimate and optical reflectance after execution. If the preset judgment condition is not met, the reverse polarity correction phase pair is injected. The total equivalent charge of the entire plate is calculated by summarizing the execution records. Blocking and phase-staggered scheduling are performed based on optical deviation and charge bias. Temperature-related response parameters are updated based on newly added reflectivity, equivalent dose and temperature samples for subsequent state reconstruction and waveform synthesis.

2. The method according to claim 1, characterized in that, When inserting the sensing phase in the key domain, baseline subtraction and time integration are performed on the displacement current of the probe pulses with opposite polarity. The optical reflectance and temperature are spatially registered in the key domain coordinate system, and measurement covariance parameters are established for the charge bias estimate, optical reflectance, and temperature as the measurement covariance for filtering and fusion.

3. The method according to claim 1, characterized in that, When performing filtering and fusion based on state vectors, an extended Kalman filter is used to perform time-series fusion of charge bias estimate, optical reflectance, and temperature, outputting the estimated state vector and the estimated state covariance, and using the estimated state covariance as the weighting parameter for constraint optimization.

4. The method according to claim 1, characterized in that, When calibrating temperature-related response parameters based on reflectance, equivalent dose, and temperature samples, variational Bayesian methods are used to estimate the posterior distribution of the temperature-related response parameters within a sliding sample window, and the uncertainty of the temperature-related response parameters is output for robust weighting in constrained optimization.

5. The method according to claim 1, characterized in that, When constructing the Prandtl-Ishlinskii hysteresis model, the hysteresis weights are constrained to be non-negative and the run thresholds are monotonically arranged according to the amplitude. The analytical inverse operator of the Prandtl-Ishlinskii hysteresis model is used to convert the target reflectance into an equivalent dose target.

6. The method according to claim 1, characterized in that, When the equivalent dose target and the estimated state vector are used as inputs, model predictive control is used to optimize the zero DC vector waveform in the rolling time domain, and a worst-case cost term is set for the uncertainty of the temperature-related response parameters and weighted in the optimization objective.

7. The method according to claim 1, characterized in that, When solving the constraint optimization to obtain the zero DC vector waveform, zero DC constraint, temperature uniformity constraint, energy constraint, hardware constraint and low frequency spectrum constraint are applied simultaneously, and a phase sequence template with phase sign symmetry is used to satisfy the zero DC constraint.

8. The method according to claim 1, characterized in that, After obtaining the charge bias estimate and optical reflectance after execution using the opposite polarity probe pulse, the reflectance deviation threshold and the charge bias estimate threshold are used to form a preset judgment condition. If the preset judgment condition is not met, an opposite polarity correction phase pair is injected and the opposite polarity correction phase pair satisfies the voltage-time integral of zero.

9. The method according to claim 1, characterized in that, When performing block and phase misalignment scheduling based on optical deviation and charge bias, the keyboard is constructed as a graph containing adjacency weights and thermal coupling weights. The block set, dose quota and phase misalignment amount are determined through optimal transmission, and refresh and correction tasks are arranged accordingly within the time window.

10. The method according to claim 1, characterized in that, The total equivalent charge of the entire plate is calculated as a convergence criterion for window-level comparison. When the total equivalent charge of the entire plate does not meet the descent condition, a global reset phase sequence with zero DC is triggered, and the refresh frequency and single dose of high-risk key domains are reduced. At the same time, based on the newly added reflectivity, equivalent dose and temperature samples, the temperature-related response parameters are updated online and written back to the filtering fusion and constraint optimization for subsequent state reconstruction and zero DC vector waveform synthesis.

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