A kind of photoelectric target tracking platform nonlinear friction compensation control device and method

Abstract

The application discloses a kind of photoelectric target tracking platform nonlinear friction compensation control device, method, it is related to photoelectric target tracking system technical field, solve the horizontal shaft system friction influence horizontal photoelectric target tracking platform is greatly influenced by shaft system friction, and the problem of low control precision, its technical scheme main point is: by setting high controller in the speed loop of traditional three closed loop, improve loop order, reduce the overall tracking error, while aiming at the problem of increasing control parameters brought by order increase, using multi-objective optimization algorithm to carry out parameter setting;Secondly, set friction compensator in acceleration loop to compensate friction, and for the nonlinear friction problem in control system, using nonlinear modeling operator to carry out high-order linearization to nonlinear friction, further reduce the tracking error caused by friction of system.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of photoelectric target tracking systems, in particular to a photoelectric target tracking platform nonlinear friction compensation control device and method. BACKGROUND

[0002] The photoelectric target tracking platform is a technical system for realizing real-time monitoring and tracking of a moving target and a moving track by using a photoelectric sensor. The photoelectric target tracking platform is widely applied to the fields of machine vision, automatic driving, unmanned aerial vehicles and robots. When the structure and caliber of the horizontal photoelectric tracking platform are too large, the device space is too large in actual application and installation, so the horizontal structure is adjusted to a 90-degree rotating horizontal structure. The horizontal structure does not have a deflection torque, so the friction of the shaft system and the nonlinearity are relatively easy to control. However, the rolling bearing of the horizontal photoelectric target tracking platform bears the gravity and also bears the asymmetric deflection torque relative to the bearing structure. Therefore, the horizontal photoelectric target tracking platform is greatly affected by the horizontal shaft system friction (i.e. nonlinear friction), and the traditional control method cannot be applied.

[0003] Therefore, the application provides a photoelectric target tracking platform nonlinear friction compensation control device and method to solve the above problems. SUMMARY

[0004] The application aims to provide a photoelectric target tracking platform nonlinear friction compensation control device and method to solve the problem that the horizontal photoelectric target tracking platform is greatly affected by the shaft system nonlinear friction and has low control precision. The application sets a high-type controller in the speed loop to improve the low-frequency tracking precision and reduce the friction error caused by the speed change. A nonlinear modeling operator friction compensator is set in the acceleration loop to feed forward compensate the nonlinear friction and reduce the turning error. The application reduces the influence of the nonlinear friction on the control precision and improves the control precision.

[0005] The application provides a photoelectric target tracking platform nonlinear friction compensation control device, which comprises a three-closed-loop control circuit. The three-closed-loop control circuit comprises, from inside to outside, an acceleration loop, a speed loop and a position loop. A high-type controller is arranged in the speed loop. The high-type controller comprises a speed controller and an additional controller, which are used to eliminate the friction error in the speed loop caused by the speed change. A friction compensator is arranged in the acceleration loop. The transfer function of the friction compensator is determined by the relationship model of the actual acceleration signal of the controlled system and the friction compensation amount signal, and the friction compensator is used to feed forward compensate the controlled system.

[0006] In a possible implementation, the three closed-loop control circuit comprises a position controller, a high controller, an acceleration controller, a friction compensator and a controlled system; the position controller, the high controller, the acceleration controller and the controlled system are sequentially connected in signal; the friction compensator calculates a friction compensation signal according to an actual acceleration signal of the controlled system, and feeds forward compensates an input of the controlled system; wherein an input of the position controller is a difference signal of a target position and an actual position of the controlled system, and an output of the position controller is a position control signal; an input of the high controller is a difference signal of the position control signal and an actual speed signal of the controlled system, and an output of the high controller is a speed control signal; an input of the acceleration controller is a difference signal of the speed control signal and the actual acceleration signal of the controlled system, and an output of the acceleration controller is an acceleration control signal; and an input of the controlled system is a signal obtained by superimposing the acceleration control signal and the friction compensation signal.

[0007] In a possible implementation, the actual speed signal of the controlled system is measured by a gyroscope, the actual position signal of the controlled system is measured by an encoder, and the actual acceleration signal of the controlled system is obtained by differentiating the actual speed signal of the controlled system.

[0008] The application also provides a nonlinear friction compensation control method for an optoelectronic target tracking platform, which is executed based on the above-mentioned nonlinear friction compensation control device for the optoelectronic target tracking platform. The method comprises: a high controller: taking phase margin and amplitude margin as constraint conditions, taking frequency domain bandwidth and time domain time multiplied by error absolute value integral as target functions, constructing a multi-objective optimization function of control parameters of the high controller, determining an initial range of the control parameters of the high controller through Routh criterion, and solving the multi-objective optimization function based on a multi-objective optimization algorithm to obtain optimal control parameters of the high controller; and a friction compensator: solving a relationship model of the actual acceleration signal of the controlled system and the friction compensation signal based on a nonlinear modeling operator, bringing the actual acceleration signal of the controlled system into the relationship model to calculate the friction compensation signal, and superimposing the friction compensation signal to an input of the controlled system for feed forward compensation.

[0009] In a possible implementation, a multi-objective optimization function of control parameters of the high controller is constructed by taking phase margin and amplitude margin as constraint conditions and taking frequency domain bandwidth and time domain time multiplied by error absolute value integral as target functions; the multi-objective optimization function is as follows:

[0010] ;

[0011] wherein, is a target function; is a frequency domain bandwidth target function; is a time domain time multiplied by error absolute value integral target function; is a frequency domain bandwidth index; is a time domain time multiplied by an error absolute value integral index; is a set of control parameters , the number of control parameters from to ; is a solution set space; is a constraint function; is a system amplitude margin, is a value of a system open loop transfer function at a gain crossing frequency , is an imaginary unit; is a system phase margin; is a phase angle of a system open loop transfer function at a phase crossing frequency ; is a variable, taking a value between a lower limit and an upper limit .

[0012] In a possible implementation, an initial range of the high type controller control parameters is determined by the Routh criterion, comprising:

[0013] According to a transfer function of the high type controller, a characteristic equation of the speed loop is constructed;

[0014] According to the characteristic equation of the speed loop, a Routh table is constructed;

[0015] Based on the Routh table and a stability condition of the Routh criterion, the initial range of the high type controller control parameters is solved.

[0016] In a possible implementation, when a two type speed loop is adopted, the transfer function of the high type controller is defined as:

[0017] ;

[0018] The closed loop characteristic equation of the speed loop is constructed as:

[0019] ;

[0020] According to the closed loop characteristic equation of the speed loop, the Routh table is constructed as:

[0021] ;

[0022] Based on the Routh table and a stability condition of the Routh criterion, the initial range of the high type controller control parameters is solved as:

[0023] ;

[0024] wherein, is a proportional gain of the high type controller, The time constant of the high-performance controller. For complex frequency variables, For the proportional gain of the high-performance controller, The time constant of the high-performance controller. For system coefficients, The total gain of the high-performance controller. The coefficients in the Routh table, These are intermediate variables used to calculate the stability conditions.

[0025] In one possible implementation, a relationship model between the actual acceleration signal and the friction compensation signal of the controlled system is solved based on a nonlinear modeling operator; including:

[0026] In the open-loop acceleration loop, a set of regular electrical signals is given as input and the output signals of the accelerometer are recorded to construct a dataset;

[0027] Define the vector function and lifting order of the nonlinear modeling operator to lift the dataset to a higher-dimensional space, and obtain the lifted dataset.

[0028] The estimation of nonlinear modeling operators is transformed into a minimization problem by using the extended mode dynamic decomposition method. Solving the minimization problem yields the estimation of the nonlinear modeling operators.

[0029] By decomposing the nonlinear modeling operator estimates, the state-space equation parameters of the accelerated controlled system in discrete linearized representation are obtained;

[0030] Based on the parameters of the state-space equations, a discrete linearized representation of the acceleration controlled system is constructed to reflect the relationship between the actual acceleration signal and the friction compensation signal of the controlled system.

[0031] In one possible implementation, the discrete linearized representation of the accelerated controlled system is:

[0032] ;

[0033] in, For time steps The output of the prediction system, For time steps The actual measured system output, For system output, For time steps System input, For system input, Estimating the nonlinear modeling operator. For rank change, For vector functions, These are the parameters of the state-space equations for the accelerated controlled system.

[0034] In one possible implementation, the transfer function of the friction compensator is:

[0035] ;

[0036] in, This is the transfer function form of the relationship model between the actual acceleration signal and the friction compensation signal of the controlled system. This represents the gain of the low-pass filter. The time constant of the low-pass filter. It is a complex frequency variable.

[0037] Compared with the prior art, this application has the following advantages: First, by setting a high-order controller in the velocity loop of the traditional three-closed-loop system, the loop order is improved, reducing the overall tracking error. At the same time, to address the problem of increased control parameters due to the increased order, a multi-objective optimization algorithm is used to tune the parameters. Second, a friction compensator is set in the acceleration loop to compensate for friction. Furthermore, for the nonlinear friction problem in the control system, a nonlinear modeling operator is used to linearize the nonlinear friction to a higher order, further reducing the tracking error caused by friction. Attached Figure Description

[0038] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and form part of this application, do not constitute a limitation thereof. In the drawings:

[0039] Figure 1 A schematic diagram of the nonlinear friction compensation control device for the photoelectric target tracking platform provided in the embodiments of this application;

[0040] Figure 2 A flowchart of a nonlinear friction compensation control method for an optoelectronic target tracking platform provided in an embodiment of this application;

[0041] Figure 3 The position tracking effect comparison diagram provided in the embodiments of this application is shown in the figure. Figure 3 (a) in the figure is the position tracking response curve. Figure 3 (b) in the figure is the position tracking error curve. Detailed Implementation

[0042] In the following, the terms “comprising” or “may include” as used in the various embodiments of this application indicate the presence of the claimed function, operation, or element, and do not limit the addition of one or more functions, operations, or elements. Furthermore, as used in the various embodiments of this application, the terms “comprising,” “having,” and their cognates are intended only to indicate a specific feature, number, step, operation, element, component, or combination of the foregoing, and should not be construed as primarily excluding the presence of one or more other features, numbers, steps, operations, elements, components, or combinations of the foregoing, or the possibility of adding one or more combinations of the foregoing.

[0043] The terminology used in the various embodiments of this application is for the purpose of describing particular embodiments only and is not intended to limit the various embodiments of this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the various embodiments of this application pertain. The terms (such as those defined in a generally used dictionary) are to be interpreted as having the same meaning as in the context of the relevant technical field and are not to be interpreted as having an idealized or overly formal meaning, unless clearly defined in the various embodiments of this application.

[0044] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the embodiments and accompanying drawings. The illustrative embodiments and descriptions of this application are only for explaining this application and are not intended to limit this application.

[0045] First, the application scenario of this application is explained: This application targets a horizontal photoelectric target tracking platform, aiming to reduce the adverse effects of nonlinear friction in the horizontal shaft system on the platform's control accuracy. As a cantilever shaft system structure, the horizontal shaft system must withstand overturning moments and radial loads. The bearing rollers experience significant and uneven stress, resulting in large and dynamically changing frictional torques, thus affecting the platform's tracking control accuracy. To address this issue, this application proposes a nonlinear friction compensation control device and method for a photoelectric target tracking platform. By optimizing the servo control technology of the friction shaft system, the tracking control accuracy of the platform is improved, ensuring high-precision target tracking under complex working conditions.

[0046] Please see Figure 1 As shown, Figure 1This is a schematic diagram of a nonlinear friction compensation control device for a photoelectric target tracking platform provided in an embodiment of this application. The device includes a three-loop control system, which, from the inside out, consists of an acceleration loop, a velocity loop, and a position loop. The velocity loop includes a high-performance controller, comprising a speed controller and an auxiliary controller, used to eliminate friction errors caused by velocity variations in the velocity loop. The acceleration loop includes a friction compensator, the transfer function of which is determined by a relationship model between the actual acceleration signal of the controlled system and the friction compensation signal, used for feedforward compensation of the controlled system.

[0047] The improvement of this application lies in setting a high-performance controller in the velocity loop, which adds more integrators to the feedback control loop. The added integrators can better describe the high-frequency characteristics, eliminate friction errors caused by speed changes in the velocity loop, and improve the overall tracking accuracy. A friction compensator is set in the acceleration loop to compensate for the nonlinear friction of the system, reduce the turning error caused by nonlinear friction, and further improve the tracking positioning accuracy and tracking performance.

[0048] It should be noted that for horizontal photoelectric target tracking platforms, nonlinear friction of the horizontal shaft system reduces system stability and tracking accuracy, causing unevenness in low-speed motion, specifically manifested as a turning error. That is, when the tracking signal changes direction, the error is significantly greater than that during stable tracking; this error is called the turning error (or commutation error).

[0049] In one possible implementation, a three-closed-loop control loop includes: a position controller Cp, a high-level controller, an acceleration controller Ca, a friction compensator F, and a controlled system Ga. The position controller Cp, the high-level controller (including a speed controller Cv and an auxiliary controller Cadd), the acceleration controller Ca, and the controlled system Ga are sequentially connected by signals. The friction compensator F calculates the friction compensation signal uk based on the actual acceleration signal a of the controlled system and performs feedforward compensation on the input of the controlled system Ga. The input of the position controller Cp is the differential signal between the target position r and the actual position P of the controlled system, and its output is the position control signal up. The input of the high-level controller is the differential signal between the position control signal up and the actual velocity signal v of the controlled system, and its output is the velocity control signal uv. The input of the acceleration controller Ca is the differential signal between the velocity control signal uv and the actual acceleration signal a of the controlled system, and its output is the acceleration control signal ua. The input of the controlled system is the superposition of the acceleration control signal ua and the friction compensation signal uk (a disturbance signal d can also be added).

[0050] Furthermore, the actual velocity signal v of the controlled system is measured by the gyroscope, the actual position signal p of the controlled system is measured by the encoder, and the actual acceleration signal a of the controlled system is obtained by differentiating the actual velocity signal of the controlled system.

[0051] Specifically, in Figure 1 The relationship between the actual acceleration signal *a*, the actual velocity signal *v*, and the actual position signal *p* of the controlled system is presented using an integrator (1 / s). In the experiment, the actual velocity signal *v* is measured using a gyroscope, and the actual position signal *p* is measured using an encoder. Because accelerometers are noisy and expensive, this application uses the derivative of the actual velocity signal *v* to obtain the actual acceleration signal *a*.

[0052] It should be noted that the device provided in this application improves the low-frequency tracking accuracy of the platform by setting a high-performance controller in the velocity loop and achieves friction feedforward compensation by setting a friction compensator in the acceleration loop. However, although the high-performance system formed by introducing a high-performance controller has higher accuracy and faster response speed, its design is more difficult in practical applications because the high-performance controller requires more parameter adjustment and calculation capabilities. The design of the high-performance controller mainly has two problems: first, with the increase of integrators, the parameter adjustment of the high-performance controller becomes more complex; second, adding an integral element will lead to integral saturation, and when the saturation time is too long, overshoot and instability will occur, reducing the system stability margin. In addition, the friction compensator requires the construction of an accurate acceleration-friction model to perform accurate friction feedforward compensation; however, the friction of horizontal shaft systems is nonlinear, and its modeling is difficult.

[0053] Therefore, this application also provides a nonlinear friction compensation control method for an optoelectronic target tracking platform, for Figure 1 The nonlinear friction compensation control device of the photoelectric target tracking platform shown has been optimized.

[0054] Please see Figure 2 As shown, Figure 2 A flowchart illustrating the nonlinear friction compensation control method for an optoelectronic target tracking platform provided in this application embodiment. The method is based on... Figure 1The nonlinear friction compensation control device of the photoelectric target tracking platform shown includes: a high-performance controller: using phase margin and amplitude margin as constraints, and frequency domain bandwidth and time domain time multiplied by the absolute value of error as objective functions, a multi-objective optimization function for the control parameters of the high-performance controller is constructed. The initial range of the control parameters of the high-performance controller is determined by the Routh criterion. The multi-objective optimization function is solved based on the multi-objective optimization algorithm to obtain the optimal control parameters of the high-performance controller; a friction compensator: based on a nonlinear modeling operator, a relationship model between the actual acceleration signal of the controlled system and the friction compensation signal is solved. The actual acceleration signal of the controlled system is substituted into the relationship model to calculate the friction compensation signal. The friction compensation signal is superimposed on the input of the controlled system for feedforward compensation.

[0055] Specifically, a high-performance controller is used to improve the low-frequency tracking accuracy of the system. A multi-objective optimization function is constructed by considering the system stability margin, frequency domain bandwidth, and time domain time multiplied by the absolute value of the error. The initial search range is narrowed according to the Routh criterion, and the optimal control parameters of the high-performance controller are obtained by solving the multi-objective optimization problem. The optimal control parameters improve the dynamic response performance and error attenuation capability of the system while satisfying the system stability and performance indicators. A friction compensator is used to perform feedforward compensation for the nonlinear friction of the shaft system. The relationship model between acceleration and friction compensation is solved by a nonlinear modeling operator. The friction compensation is predicted by the relationship model and then fedforward compensation is performed to reduce the impact of nonlinear friction of the horizontal shaft system on the system tracking accuracy and reduce the turning error of the system under low-speed motion.

[0056] The improvement of this application lies in that it solves for the optimal control parameters of the high-performance controller through a multi-objective optimization function, and combines the Routh criterion to narrow the initial search range, thereby accelerating the solution speed of control parameters and improving the overall control accuracy of the system; it also solves for the relationship model between acceleration and friction compensation by a nonlinear modeling operator, thereby determining the transfer function of the friction compensator and improving the accuracy of friction feedforward compensation.

[0057] Regarding high-order controllers: While high-order systems offer higher precision and faster response times, their design and implementation are more challenging in practical applications due to the greater parameter tuning and computational demands. This necessitates a comprehensive consideration of the control system's complexity and performance requirements. To address this issue, this application constructs a multi-objective optimization function for parameter tuning of the high-order controller. Constraints on the control parameters are imposed using step response indices, bandwidth, and stability margins to improve system performance without compromising system stability.

[0058] In one possible implementation, a multi-objective optimization function for the control parameters of the high-performance controller is constructed, using phase margin and gain margin as constraints, and frequency domain bandwidth, time domain time multiplied by the integral of the absolute value of the error as objective functions; the multi-objective optimization function is:

[0059] ;

[0060] in, The objective function is... The objective function is the frequency domain bandwidth. The objective function is the integral of time multiplied by the absolute value of the error in the time domain. This refers to the frequency domain bandwidth indicator. The integral index is the time domain time multiplied by the absolute value of the error. For control parameters The set of control parameters numbered from arrive ; For the solution set space; For constraint functions; For the system gain margin, The system's open-loop transfer function at the gain crossover frequency The value at that location, The imaginary unit; This refers to the system phase margin; For the system open-loop transfer function at the phase crossing frequency Phase angle at; As a variable, its value is within the lower limit. and upper limit between.

[0061] Specifically, the bandwidth of a closed-loop system is a crucial indicator of its signal tracking capability; a wider bandwidth indicates a broader usable tracking frequency band. Meanwhile, time-domain metrics such as overshoot, steady-state error, and response time characterize the system's stability and response speed. Therefore, this application considers bandwidth in the frequency domain. The integral index of time multiplied by the absolute value of error in the time domain The explicit expressions for the two indicators are shown below:

[0062] ;

[0063] ;

[0064] in, This refers to the frequency domain bandwidth indicator. This is the frequency at which the gain drops to −3 dB; For the closed-loop transfer function of the system The magnitude of the system frequency response when the gain drops to −3 dB. The imaginary unit, Angular frequency; The integral of time multiplied by the absolute value of the error; Let be the error function. For time.

[0065] Meanwhile, in order to ensure system stability, the system's gain margin is... and phase margin The calculations are performed to establish the constraints. The formula is shown below:

[0066] ;

[0067] ;

[0068] in, For the system open-loop transfer function Gain Crossover Frequency The value at that location, For the system open-loop transfer function Gain Crossover Frequency Phase angle at that point, It is an integer. For the system open-loop transfer function Phase crossing frequency Phase angle at that point, For the system open-loop transfer function Phase crossing frequency The value at that location.

[0069] In summary, based on phase margin and gain margin As a constraint, frequency domain bandwidth Integral of time in the time domain multiplied by the absolute value of the error As the objective function, the parameter tuning problem of the high-performance controller is modeled as a multi-objective optimization problem.

[0070] To improve the search efficiency of solving multi-objective optimization problems and ensure the validity of search results, this application also narrows the initial search range of the control parameters of the high-performance controller.

[0071] In one possible implementation, the initial range of the control parameters of the high-performance controller is determined by the Routh criterion, including: constructing the characteristic equation of the speed loop based on the transfer function of the high-performance controller;

[0072] Based on the characteristic equation of the velocity loop, construct the Routh table; based on the stability conditions of the Routh table and the Routh criterion, solve for the initial range of the control parameters of the high-performance controller.

[0073] Specifically, the high-performance controller of this application is applied in a speed loop. Taking the calculation of a high-performance controller for a type-II speed loop system as an example, the Routh criterion is used to determine the initial search range of the control parameters. Assume the transfer function of the high-performance controller in the type-II speed loop system is:

[0074] ;

[0075] Therefore, the closed-loop characteristic equation for constructing the velocity loop is:

[0076] ;

[0077] The Routh table is constructed based on the closed-loop characteristic equation of the velocity loop as follows:

[0078] ;

[0079] Due to the existence of control parameters in high-performance controllers Therefore, based on the Routh table and the stability condition of the Routh criterion, the initial range of the control parameters of the high-performance controller can be obtained as follows:

[0080] ;

[0081] in, For the proportional gain of the high-performance controller, The time constant of the high-performance controller. For complex frequency variables, For the proportional gain of the high-performance controller, The time constant of the high-performance controller. For system coefficients, The total gain of the high-performance controller. The coefficients in the Routh table, These are intermediate variables used to calculate the stability conditions.

[0082] Based on the above arguments and calculations, the initial search range of control parameters that satisfy the stability conditions for the Type II system can be obtained. The initial search ranges for the Type I and Type III systems are also determined following the same procedure.

[0083] Finally, the obtained initial range is substituted into a multi-objective optimization algorithm to solve the multi-objective optimization function, thus obtaining the optimal control parameters for the high-performance controller. Multi-objective optimization algorithms can include Particle Swarm Optimization (MOPSO), Non-Dominated Sorting Genetic Algorithm (NSGA II), and Multi-Objective Grey Wolf Optimization (MOGWO), among others.

[0084] Understandably, the key aspect of this application lies in constructing a multi-objective optimization function to tune the control parameters of the high-performance controller. Solving this multi-objective optimization function can employ existing multi-objective optimization algorithms and is not the focus of this application. To obtain the initial range of the high-performance controller's control parameters and improve algorithm search efficiency, this application constructs sufficient conditions for system closed-loop stability using the Routh criterion. Simultaneously, considering that the stability margin of the control system decreases in certain frequency bands as the number of integrators increases, affecting system stability, in practical engineering applications, the system's phase margin should be greater than or equal to 45°, and the gain margin should be greater than 6dB, which are used as constraints during optimization. For the objective function, the closed-loop bandwidth in the frequency domain is selected. and time-domain step response As an evaluation metric, a multi-objective optimization problem for tuning the control parameters of a high-performance controller is thus constructed.

[0085] Regarding the friction compensator: This application is based on solving the relationship model between the actual acceleration signal and the friction compensation signal of the controlled system using a nonlinear modeling operator. The transfer function of the friction compensator is designed according to the relationship model. The actual acceleration signal of the controlled system is substituted into the friction compensator to calculate the friction compensation signal. The friction compensation signal is then superimposed on the input of the controlled system for feedforward compensation.

[0086] In one possible implementation, a relationship model between the actual acceleration signal and the friction compensation signal of the controlled system is solved based on a nonlinear modeling operator; this includes: providing a set of regular electrical signals as input in the open-loop acceleration loop. And record the output signal of the accelerometer. Build dataset ,in, These are the time series numbers of the dataset, from 1 to... , To record the total number; define a vector function for the nonlinear modeling operator. The lifting order is used to lift the dataset to a higher-dimensional space, resulting in the lifted dataset. The estimation of the nonlinear modeling operator is transformed into a minimization problem by using the extended mode dynamic decomposition method. Solving the minimization problem yields the estimate of the nonlinear modeling operator. Decomposition of nonlinear modeling operator estimates The state-space equation parameters of the accelerated controlled system in discrete linearized representation are obtained. , Based on state-space equation parameters , A discrete linearized representation of the controlled acceleration system is constructed to reflect the relationship between the actual acceleration signal and the friction compensation signal of the controlled system.

[0087] Furthermore, the discrete linearized representation of the accelerated controlled system is:

[0088] ;

[0089] in, For time steps The output of the prediction system, For time steps The actual measured system output, For system output, For time steps System input, For system input, Estimating the nonlinear modeling operator. For rank change, For vector functions, These are the parameters of the state-space equations for the accelerated controlled system.

[0090] Specifically, through the parameters of the state-space equations of the accelerated controlled system This allows for the estimation of nonlinear systems through nonlinear modeling operators. Transforming it into an approximately linear system, we construct a discrete linearized representation of the accelerated controlled system, reflecting the coefficient input. (Friction compensation signal) and system output The relationship between (the actual acceleration signal of the controlled system) and (the actual acceleration signal of the controlled system).

[0091] It should be noted that the discrete linearized representation of the accelerated controlled system described above is a state-space model, which needs to be transformed into a transfer function form through Laplace transform. Laplace transform is well-known to those skilled in the art and will not be described in detail here.

[0092] Please see Figure 1 As shown, when the friction compensator Designed as the transfer function of the controlled system The reciprocal of, that is At this point, the acceleration loop can theoretically achieve zero error; this design method relies on accurate modeling of the controlled system. In this application, nonlinear modeling operators are used to model and predict the nonlinear characteristics of the controlled system, and then the friction compensator F is designed. However, in practical applications, The reciprocal of the denominator has a lower order than the numerator, which is a physically unrealizable model and requires an additional low-pass filter to be used.

[0093] Therefore, in one possible implementation, the transfer function of the friction compensator is:

[0094] ;

[0095] in, This is the transfer function form of the relationship model between the actual acceleration signal and the friction compensation signal of the controlled system. This represents the gain of the low-pass filter. The time constant of the low-pass filter. It is a complex frequency variable.

[0096] Please see Figure 3 As shown, Figure 3 The image shows a comparison of position tracking performance provided in the embodiments of this application. This application also provides specific experimental examples to verify the effectiveness of the nonlinear friction compensation control device and method for the photoelectric target tracking platform. The specific implementation steps are as follows:

[0097] (1) A set of regular electrical signals is given as input in the open-loop acceleration loop of the photoelectric target tracking platform. And record the output signal of the accelerometer at this time. This constitutes the dataset: ;

[0098] in, These are the time series numbers of the dataset, from 1 to... , It is the total number of records;

[0099] (2) Define the vector function of the nonlinear modeling operator With an improvement order of 7, the dataset is improved to a higher dimensional space, resulting in the improved dataset. ;

[0100] (3) Solve for the fitted nonlinear modeling operator to obtain the discretized representation of the accelerated controlled object as shown in the following equation:

[0101] ;

[0102] (4) The transfer function of the designed acceleration ring friction compensator is shown in the following equation:

[0103] ;

[0104] (5) With the acceleration loop closed, the velocity loop transfer function of the controlled system obtained by frequency sweep is as follows:

[0105] ;

[0106] Among them, gain time constant ,coefficient ,coefficient ,coefficient , It is a complex frequency variable;

[0107] (6) Using the method of this application, a high-speed loop controller was designed. By constructing and solving an optimization problem, the parameters of the Type II high-speed controller were obtained as follows:

[0108] .

[0109] The nonlinear friction compensation control device for the photoelectric target tracking platform was designed using the above parameters.

[0110] Position tracking experiments were conducted on a horizontal experimental platform using the aforementioned designed nonlinear friction compensation control device for the photoelectric target tracking platform, as well as the original three-closed-loop control device with a height-less controller and a friction-less compensator. A sinusoidal signal with a test amplitude of 1° and a frequency of 0.1Hz was selected as the reference signal for the tracking experiment. The experimental results showed... Figure 3 The image shows a comparison of the position tracking results. Figure 3 (a) in the figure is the position tracking response curve. Figure 3 (b) in the figure is the position tracking error curve, where the target position changes at a rate of 1 degree per second. Compared with the original three-loop device, this application can effectively improve tracking accuracy and reduce turning error caused by changes in friction torque.

[0111] It should be noted that the ideas in this application can also be extended to other control systems with strong nonlinearity, such as torque control of robotic arms and stability control of power distribution networks.

[0112] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A nonlinear friction compensation control method for a photoelectric target tracking platform, characterized in that, The method is executed based on a nonlinear friction compensation control device for an optoelectronic target tracking platform, the control device comprising: The three closed-loop control loops, from the inside out, consist of an acceleration loop, a velocity loop, and a position loop. The speed loop is equipped with a high-type controller, which includes a speed controller and an additional controller, to eliminate frictional errors caused by speed changes in the speed loop; A friction compensator is installed in the acceleration loop. The transfer function of the friction compensator is determined by the relationship model between the actual acceleration signal of the controlled system and the friction compensation signal, and is used to perform feedforward compensation on the controlled system. The control method includes: High-performance controller: Using phase margin and gain margin as constraints, and frequency domain bandwidth and time domain time multiplied by the absolute value of error integral as objective functions, a multi-objective optimization function for the control parameters of the high-performance controller is constructed. The initial range of the control parameters of the high-performance controller is determined by the Routh criterion. The optimal control parameters of the high-performance controller are obtained by solving the multi-objective optimization function based on the multi-objective optimization algorithm. Friction Compensator: A set of regular electrical signals is given as input in the open-loop acceleration loop, and the output signal of the accelerometer is recorded to construct a dataset. The vector function and lifting order of the nonlinear modeling operator are defined to lift the dataset to a high-dimensional space, resulting in the lifted dataset. The estimation of the nonlinear modeling operator is transformed into a minimization problem by using the extended mode dynamic decomposition method. Solving the minimization problem yields the nonlinear modeling operator estimate. The nonlinear modeling operator estimate is decomposed to obtain the state-space equation parameters of the acceleration controlled system in discrete linear representation. Based on the state-space equation parameters, a discrete linear representation of the acceleration controlled system is constructed to reflect the relationship between the actual acceleration signal and the friction compensation signal of the controlled system. The actual acceleration signal of the controlled system is substituted into the relationship model to calculate the friction compensation signal. The friction compensation signal is then superimposed on the input of the controlled system for feedforward compensation. The discrete linearized representation of the controlled acceleration system is as follows: Among them, y t+1 For the prediction system output at time step t+1, y t Let y be the measured system output at time step t, and i_u be the system output. t Let i_u be the system input at time step t. For the nonlinear modeling operator estimate, T is the rank transformation and ψ is the vector function. These are the parameters of the state-space equations for the accelerated controlled system.

2. The nonlinear friction compensation control method for a photoelectric target tracking platform according to claim 1, characterized in that, The three closed-loop control circuits include: Position controllers, high-performance controllers, acceleration controllers, friction compensators, and controlled systems; The position controller, high-type controller, acceleration controller, and controlled system are sequentially connected by signals. The friction compensator calculates the friction compensation signal based on the actual acceleration signal of the controlled system and performs feedforward compensation on the input of the controlled system. The position controller receives a differential signal between the target position and the actual position of the controlled system, and outputs a position control signal. The high-speed controller receives a differential signal between the position control signal and the actual velocity signal of the controlled system, and outputs a velocity control signal. The acceleration controller receives a differential signal between the velocity control signal and the actual acceleration signal of the controlled system, and outputs an acceleration control signal. The controlled system receives a signal obtained by superimposing the acceleration control signal and the friction compensation signal.

3. The nonlinear friction compensation control method for a photoelectric target tracking platform according to claim 2, characterized in that, The actual velocity signal of the controlled system is measured by the gyroscope, the actual position signal of the controlled system is measured by the encoder, and the actual acceleration signal of the controlled system is obtained by differentiating the actual velocity signal of the controlled system.

4. The nonlinear friction compensation control method for a photoelectric target tracking platform according to claim 1, characterized in that, Using phase margin and gain margin as constraints, and frequency domain bandwidth and time domain time multiplied by the absolute value of the error as objective functions, a multi-objective optimization function for the control parameters of the high-performance controller is constructed; the multi-objective optimization function is as follows: Where Func(X) is the objective function; func1(X) is the frequency domain bandwidth objective function; func2(X) is the time domain time multiplied by the absolute value of the error objective function; bandwidth is the frequency domain bandwidth index; ITAE is the time domain time multiplied by the absolute value of the error index; For control parameter T i The set, where the control parameter numbers i range from n1 to n r Ω is the solution space; st is the constraint function; G M For the system gain margin, G K (jω g () represents the system's open-loop transfer function at the gain crossover frequency ω. g The value at point P, where j is the imaginary unit; M For the system phase margin; ∠G K (jω c () represents the open-loop transfer function of the system at the phase crossover frequency ω. c Phase angle at T; i Let T be a variable, and let its value be within the lower limit T. i_min and upper limit T i_max between.

5. The nonlinear friction compensation control method for a photoelectric target tracking platform according to claim 1, characterized in that, The initial range of control parameters for a high-performance controller is determined using the Routh criterion, including: Based on the transfer function of the high-performance controller, the characteristic equation of the velocity loop is constructed; Construct a Routh table based on the characteristic equation of the velocity loop; Based on the stability conditions of the Routh table and Routh criterion, the initial range of the control parameters of the high-performance controller is solved.

6. The nonlinear friction compensation control method for a photoelectric target tracking platform according to claim 5, characterized in that, When using a type-two speed loop, the transfer function of the high-speed controller is defined as follows: The closed-loop characteristic equation for the velocity loop is as follows: k gv (T gv s+1)k cvII (T cvII1 s+1)(T cvII2 s+1)+s(a gv s 2 +b gv s+c gv )s(T cvII3 s+1)=0; The Routh table is constructed based on the closed-loop characteristic equation of the velocity loop as follows: Based on the stability conditions of the Routh table and the Routh criterion, the initial range of the control parameters of the high-performance controller is solved as follows: Where, k cvII For the proportional gain of the high-performance controller, T cvII1 T cvII2 T cvII3 Here, s is the time constant of the high-frequency controller, and k is the complex frequency variable. gv For the proportional gain of the high-performance controller, T gv a is the time constant of the high-performance controller. gv b gv c gv K represents the system coefficients. II denoted as the total gain of the high-performance controller, a0, a1, a2, a3, a4, and a5 are coefficients in the Routh table, and b1, b2, and c1 are intermediate variables used to calculate the stability conditions.

7. The nonlinear friction compensation control method for a photoelectric target tracking platform according to claim 1, characterized in that, The transfer function of the friction compensator is: Where Ga is the transfer function form of the relationship model between the actual acceleration signal and the friction compensation signal of the controlled system, and K... F T is the gain of the low-pass filter. F is the time constant of the low-pass filter, and s is a complex frequency variable.

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