Controller optimization method

Abstract

The response index of the controlled object, such as the amount of overshoot and the settling time, is minimized by directly considering the response index, and the control parameters of the controller are optimized to design optimal control parameters. [Solution] By introducing the amount of overshoot and the settling time, which are in a mutually constrained relationship, as response indices of the controlled object into the terms of the unconstrained optimization evaluation function J, minimization that directly considers the response indices becomes possible. In a first aspect, one of the response indices is introduced into the objective function term, and the other response index is introduced into the constraint condition term, thereby introducing the response indices of the controlled object, which are in a mutually constrained relationship, into the terms of the unconstrained optimization evaluation function J. In a second aspect, the objective function is introduced into the terms of the unconstrained optimization evaluation function J as a weighted sum of two response indices, the amount of overshoot and the settling time, weighted by the coefficients (1-α) and α.

Description

[Technical Field]

[0001] The present invention relates to a method for optimizing a controller to determine optimal control parameters of the controller. [Background technology]

[0002] Digital controllers that control power supplies require advanced control performance to achieve fast response. To achieve this, digital controllers are designed using complex methods such as model predictive control. However, since PID control is a widely used control technology in industry, a control method based on PID control is desirable when controlling power supplies.

[0003] Data-driven methods such as data-driven control and data-driven simulation can be applied to PID controllers and are known as control methods that provide higher control performance than conventional methods using simple algorithms. Although these data-driven methods have the advantage of not requiring a model of the controlled object, they have several problems.

[0004] As a method for overcoming these problems, an output estimation technique using a data-driven simulation method based on convolution operations (CDDS) has been proposed (Non-Patent Document 1). Patent Document 1 discloses that an output estimation technique using the CDDS method is applied to the design of control parameters of a controller. In these data-driven control techniques, a controller is generally optimized by setting a model reference control problem. Patent Document 2 describes adjusting the control parameters of a controller using a performance index function with constraints that uses a reference model.

[0005] When designing a controller for controlling a controlled object such as a converter, it is required that response indices such as the amount of overshoot and settling time in the output response of the controlled object fall within set values.

[0006] Patent Document 3 describes optimizing a controller by solving an optimization problem that minimizes the evaluation function while the amount of overshoot is set as a constraint condition and the settling time is set as an evaluation function, with the amount of overshoot being equal to or less than an allowable value. The adjustment of the control parameter θ disclosed in Patent Documents 2 and 3 is performed by solving a constrained optimization problem using an inequality for the constraint condition of the amount of overshoot and an equation that is independent of the equation for the evaluation function.

[0007] Patent Document 4 discloses that, as a general optimization problem, a constrained optimization problem is converted into an unconstrained optimization problem and then optimized. [Prior art documents] [Patent documents]

[0008] [Patent Document 1] Patent No. 7540644 [Patent Document 2] Patent No. 7207474 [Patent Document 3] Patent Publication No. 2021-43573 [Patent Document 4] Japanese Patent Application Publication No. 2-71458 [Non-patent literature]

[0009] [Non-Patent Document 1] “Convolution-based data-driven simulation and controller design method,” IEEE Transactions on Industrial Electronics, vol.71, no.8, pp.9541-9550, 2024. Summary of the Invention [Problem to be solved by the invention]

[0010] In the conventional data-driven control method, which optimizes a controller by setting a model reference control problem, there is a problem that the response obtained by optimizing the controller depends on a reference model that is set in advance. In addition, in Patent Documents 2 and 3, the problem is handled by a constraint-condition evaluation function that consists of an evaluation part and an inequality constraint part.

[0011] In control optimization using a model reference control problem or a performance index with constraints, the objective function is optimized within the range of the constraints. This optimization cannot directly consider response indices such as the amount of overshoot or settling time of the controlled object (e.g., a converter), and so minimizes them indirectly.

[0012] Since minimization of such a response index cannot be directly considered, there is a problem that the time required for minimizing the response index and optimizing the control parameters is long. In order to minimize the response index and optimize the control parameters more quickly, a method for directly minimizing the response index is required.

[0013] In optimization problems, converting a constrained optimization problem into an unconstrained optimization problem and then performing optimization is known as a general optimization problem in Patent Document 4. However, solving an evaluation function suitable for an unconstrained optimization problem that directly considers the amount of overshoot, which is a response index of a controlled object such as a converter, and the settling time is not known.

[0014] Furthermore, there is no known suggestion of a method for applying the amount of overshoot and the settling time to an unconstrained optimization problem as a general optimization problem to construct a suitable evaluation function that directly takes the amount of overshoot and the settling time into consideration.

[0015] The present invention aims to minimize response indices that directly consider the response indices of the controlled object, such as the amount of overshoot and the settling time, and to optimize the control parameters of the controller to design optimal control parameters. [Means for solving the problem]

[0016] The present invention enables minimization that directly considers response indices by introducing the amount of overshoot and settling time, which are in a constrained relationship with each other, into the terms that make up the unconstrained optimization evaluation function J as response indices of the controlled object. When response indices are in a constrained relationship with each other, one response index cannot change independently of the other response index, but fluctuates toward minimization under the constraint of the other response index.

[0017] The present invention uses the amount of overshoot and the settling time as response indices for introducing response indices of controlled objects that are in a constraint relationship with each other into terms constituting the unconstrained optimization evaluation function J. The present invention has a first aspect and a second aspect for introducing the amount of overshoot and the settling time into terms of the unconstrained optimization evaluation function J.

[0018] The first mode of the optimization evaluation function J introduces one of the response indexes into the objective function term and the other response index into the constraint term, thereby introducing the response indexes of the controlled objects that are in a mutually constrained relationship into the unconstrained optimization evaluation function J term.

[0019] The second aspect of the optimization evaluation function J is to construct the objective function as a weighted sum of two response indices, the amount of overshoot and the settling time, weighted by the coefficients (1-α) and α. By weighting with (1-α) versus α, the response indices of the controlled objects that are in a mutually constrained relationship are introduced into the terms of the unconstrained optimization evaluation function J.

[0020] According to the first and second aspects, in the unconstrained optimization evaluation function J, the amount of overshoot and the settling time are terms within one evaluation function. Therefore, the response index of the controlled object can be minimized based on the evaluation value obtained by the evaluation function without being constrained by an inequality in the constraint condition.

[0021] The controller optimization method of the present invention is a controller optimization method for optimizing a control parameter θ of a controller that controls a controlled object, (P1) A data-driven simulation process that simulates and estimates the output based on a time-domain convolution operation using experimental data of the input and output of the controlled object, and obtains the estimated output value. (P2) A response index value acquisition process for determining a response index value related to the response of the controlled object using the estimated output value acquired in the data-driven simulation process (P3) An evaluation value calculation step in which an evaluation value is calculated by using an unconstrained optimization evaluation function J in which response indicators having mutually constraining relationships are introduced into terms within the function, and substituting the response indicator values ​​acquired in the response indicator value acquisition step (P2) into the terms of this unconstrained optimization evaluation function J. (P4) A process of minimizing the evaluation function value by repeating the data-driven simulation process (P1), the response index value acquisition process (P2), and the evaluation value calculation process (P3) while updating the control parameter θ of the controller. The process comprises the following steps.

[0022] The evaluation function value minimization step (P4) can be performed using an optimization solver based on the direct optimization approach of the Nelder-Mead method.

[0023] The present invention enables minimization that directly considers response indices by constructing an unconstrained optimization evaluation function J by introducing response indices that are in a mutually constrained relationship into terms in the evaluation function.

[0024] [First aspect of unconstrained optimization evaluation function] In the first mode of introducing the overshoot amount and the settling time into the unconstrained optimization evaluation function J, one of the response indicators is introduced into the objective function term, and the other response indicator is introduced into the constraint term.

[0025] The unconstrained optimization evaluation function J is composed of an objective function that introduces either the overshoot amount or the settling time response index, and a barrier function that incorporates the other response index as a variable related to the constraint condition. This allows the response indexes of the controlled objects that are in a mutually constrained relationship to be introduced into the unconstrained optimization evaluation function J.

[0026] The first aspect includes first to fourth forms.

[0027] (1) First Form The first type of unconstrained optimization evaluation function J is an unconstrained optimization evaluation function J consisting of an objective function (Ts / T0) that introduces a response index of the settling time Ts and a barrier function B(θ) that introduces a response index of the amount of overshoot as a variable related to the constraint. barr 1. This unconstrained optimization evaluation function J barr The minimization of 1 is expressed by the following equation:

[0028]

number

[0029] (2) Second Form In the second form, the positive constant p that determines the constraint on the amount of overshoot in the first form is set to 2%. The settling time Ts is generally defined as the time it takes for the output value to settle within a range of ±2% or ±5% of the target output, and in the second form, the constant p for the amount of overshoot that corresponds to this settling time Ts is set to 2%.

[0030] (3) Third Form In the third embodiment, the constant p that determines the constraint on the amount of overshoot in the first embodiment is set in consideration of an estimation error included in the data-driven simulation process. The output obtained by the data-driven simulation (CDDS method), which simulates an output based on a convolution operation in the time domain and obtains an estimated output value, usually includes an estimation error.

[0031] When comparing the output obtained by the CDDS method with the amount of overshoot, the actual output value is the value obtained by the CDDS method plus an estimation error, so an error occurs in the comparison with the amount of overshoot. Therefore, the constant p for the amount of overshoot is set to p _set Considering the estimation error, the estimation constant p is set smaller by a margin m to compensate for this estimation error. _est =(p _set -m) is used.

[0032] The third form is a setting constant p that determines the constraint on the amount of overshoot in the first form. _set , and the settling time Ts _set Instead, we add a margin m to account for the estimation error and use the overshoot estimation constant p _est , and estimated settling time Ts _est is used.

[0033] Here, the margin m is the set constant p _set and the estimated constant p _est The difference of (p _set -p _est ) and the estimated constant p _est (p _set The estimated constant p is expressed as a constant p that determines the constraint on the amount of overshoot, with a margin m added. _est After the output voltage waveform of the response characteristic rises, the estimated constant p _est Exceeding the settling range [Vr-p _est ,Vr+p _est ] is the estimated settling time Ts _est It is expressed as:

[0034] Estimated constant p including margin m _est, and estimated settling time Ts _est By using this, the set constant p _set , and the settling time Ts _set is set.

[0035] (4) Fourth Form In the first form, the settling time Ts is introduced into the objective function, and the overshoot amount is incorporated into the barrier function that introduces it as a variable related to the constraint, while in the fourth form the relationship of the introduction of the response index is reversed. The unconstrained optimization evaluation function J in the fourth form is an unconstrained optimization evaluation function J that is composed of the objective function (Vp-Vr) / Vr that introduces the response index of the overshoot amount, and the barrier function B(θ) that introduces the response index of the settling time Ts as a variable related to the constraint. barr Let's say it's 4.

[0036] The constraint for the settling time Ts is 0≦Ts / T0≦Ts _set / T0, the fourth form of unconstrained optimization evaluation function J barr The minimization of 4 is expressed by the following equation.

[0037]

number

[0038] [Second aspect of unconstrained optimization evaluation function] In the second mode of the unconstrained optimization evaluation function, the objective function is constructed as a weighted sum of two response indices, the amount of overshoot and the settling time, weighted by the coefficients (1-α) and α. By weighting the amount of overshoot and the settling time by the coefficients (1-α) and α, the unconstrained optimization evaluation function J is constructed with a constraint relationship between the amount of overshoot and the settling time.

[0039] The unconstrained optimization evaluation function J in the second mode is an unconstrained optimization evaluation function J that is composed of an objective function expressed as a weighted sum of two response indices: the amount of overshoot weighted by the coefficients (1-α) and α, and the settling time. α (θ). The unconstrained optimization evaluation function J α The minimization of (θ) is expressed by the following equation:

[0040]

number

[0041] As described above, according to the controller optimization method of the present invention, it is possible to perform minimization taking into account the response indexes of the controlled object of the amount of overshoot and the settling time directly, and to design control parameters that are optimized for the controller. [Brief explanation of the drawings]

[0042] [Figure 1] FIG. 1 is a block diagram of a closed-loop control system 100. [Figure 2] 1 is a flowchart illustrating the outline of the process of optimizing a controller according to the present invention. [Figure 3]FIG. 2 is a schematic diagram for explaining a response of a controlled object. [Figure 4] FIG. 1 is a diagram illustrating an example of a DC-DC converter. [Figure 5] FIG. 10 is a diagram illustrating an example of the configuration of a controller that performs PI control in which an inductor current is added as a minor loop for feedback. [Figure 6] FIG. 2 is a diagram illustrating an example of the configuration of a controller that performs PID control in current mode control. [Figure 7] FIG. 1 is a diagram illustrating an example of the configuration of a controller using PI-D control in current mode control. [Figure 8] FIG. 1 is a diagram illustrating an example of the configuration of a controller for PI control including an anti-windup compensation term in current mode control. [Figure 9] 10 is a flowchart for explaining optimization based on an unconstrained optimization evaluation function J of the first form. [Figure 10] FIG. 3 is a schematic diagram for explaining a response of a controlled object in the first embodiment. [Figure 11] FIG. 10 is a diagram showing a barrier function B(θ) of the first embodiment. [Figure 12] FIG. 10 is a diagram illustrating minimization of settling time Ts in the first mode. [Figure 13] FIG. 10 is a schematic diagram for explaining a response of a controlled object in the second embodiment. [Figure 14] FIG. 10 is a diagram illustrating a second mode barrier function B(θ). [Figure 15] FIG. 10 is a diagram illustrating minimization of settling time Ts in the second mode. [Figure 16] FIG. 10 is a schematic diagram for explaining a response of a controlled object in the third embodiment. [Figure 17] FIG. 10 is a diagram showing a third mode barrier function B(θ). [Figure 18] Minimizing the settling time Ts in the third form. [Figure 19] FIG. 10 is a schematic diagram for explaining a response of a controlled object in a fourth embodiment. [Figure 20] FIG. 10 is a diagram showing a fourth form barrier function B(θ). [Figure 21] FIG. 10 is a diagram illustrating minimization of the amount of overshoot Os in the fourth mode. [Figure 22] FIG. 10 is a diagram illustrating minimization of the amount of overshoot Os in the fourth mode. [Figure 23] FIG. 10 is a diagram illustrating simultaneous optimization of the amount of overshoot and settling time according to the second embodiment. [Figure 24] FIG. 10 is a diagram illustrating an example of changes in the evaluation function value of the unconstrained optimization evaluation function. [Figure 25] FIG. 10 is a diagram illustrating a comparison of the amount of overshoot and the settling time between the method of the present invention and a conventional method. DETAILED DESCRIPTION OF THE INVENTION

[0043] In the controller optimization method of the present invention, experimental data is used during optimization to estimate the output by data-driven simulation, and the controller provided in the closed-loop control system is optimized. In the present invention, the output is estimated using data-driven simulation based on a convolution operation (Convolution-based Data-Driven Simulation, CDDS).

[0044] (closed loop control system) The present invention performs output estimation in a closed-loop control system to obtain an estimated output value y, and minimizes a response index of a controlled object of the closed-loop control system and optimizes control parameters of a controller using the obtained estimated output value y. Here, the amount of overshoot and settling time are considered as the response index of the controlled object.

[0045] The closed-loop control system will be described with reference to the block diagram of the closed-loop control system 100 shown in Figure 1. The closed-loop control system 100 inputs a reference signal r(k) to a controller C(θ), and converts the control signal obtained by the controller C(θ) into an input signal u(k) of the controlled object P(z). in (k), and the output signal y of the controlled object P(z) out(k) is fed back to the controller C(θ) and the control process is performed in discrete time. out (k) corresponds to the plant and plant output.

[0046] The flowchart in Figure 2 shows the outline of the process for optimizing a controller according to the present invention. In a closed-loop control system in which a control signal from the controller is input as a control input to a controlled object and the output of the controlled object is fed back to the controller, the optimization of the controller according to the present invention is carried out as follows: (P1) A data-driven simulation process that simulates and estimates the output based on a time-domain convolution operation using experimental data of the input and output of the controlled object, and obtains the estimated output value. (P2) A response index value acquisition process for determining a response index value related to the response of the controlled object using the estimated output value acquired in the data-driven simulation process (P3) An evaluation value calculation step in which response indicators that are in a mutually constrained relationship are introduced into terms in a function to construct an unconstrained optimization evaluation function J, and the response indicator values ​​acquired in the response indicator value acquisition step (P2) are substituted into the terms of this unconstrained optimization evaluation function J to calculate an evaluation value. (P4) A process of minimizing the evaluation function value by repeating the data-driven simulation process (P1), the response index value acquisition process (P2), and the evaluation value calculation process (P3) while updating the control parameter θ of the controller. The process comprises the following steps.

[0047] Below, (P1) to (P4) will be explained. (P1) Data-driven simulation process Convolution-based Data-Driven Simulation (CDDS) is a data-driven simulation method that estimates the output by performing a simulation using experimental data on the input and output of the control object P(z) in a discrete-time closed-loop control system. The experimental output data, experimental input data, and estimated output and input values ​​obtained by simulation are convolved in the time domain.

[0048] The convolution operation is performed in the time domain on the input / output experimental data (u0, y0) and the estimated input / output values ​​(u, y). The input / output experimental data (u0, y0) are the experimental input data (u0) and experimental output data (y0) obtained by actually experimenting with the controlled object. The estimated input / output values ​​(u, y) are the estimated input values ​​(u) and estimated output values ​​(y) at each sampling time obtained by simulating the controlled object P(z). The simulation using the convolution operation estimates the estimated output value (y) at the next sampling time of the controlled object P(z).

[0049] In the data-driven simulation, the experimental data used in the simulation of the controlled object P(z) are the experimental input data (u0) and experimental output data (y0) obtained in an experiment on the controlled object, and the input / output values ​​used in the simulation are the estimated input values ​​(u) and estimated output values ​​(y) obtained in a simulation of the controlled object (P). Neither the experimental data nor the input / output values ​​used in the calculation are related to the parameter θ of the controller C(θ).

[0050] Therefore, the output estimation method using the data-driven simulation process is a simulation using only the controlled object P(z) without the involvement of the controller C(θ). Because the involvement of the controller C(θ) is eliminated, the contribution of linearity / nonlinearity due to the controller C(θ) is eliminated. Even if the controller C(θ) has nonlinearity, it is possible to perform a convolution operation and estimate the output of the controlled object. Furthermore, it is possible to estimate the output of the controlled object regardless of the linearity / nonlinearity of the controller C(θ).

[0051] Furthermore, the time domain convolution calculation used in the output estimation method is expressed as an arithmetic expression that excludes the term of the controlled object P(z). Therefore, the output estimation can be simulated without involving not only the controller C(θ) but also the controlled object P(z).

[0052] In estimating the output, the following assumptions are made: the first assumption is that the control object P(z) is a linear time-invariant (LTI) system; the second assumption is that the state of the control object P(z) before the 0th sampling time k=0 of the experimental data can be ignored; and the third assumption is that the first experimental input data u0(0) of the experimental data is a non-zero value.

[0053] The first assumption is that the control object P(z) is a linear time-invariant (LTI) system. A linear time-invariant system is a linear system for which the principle of superposition holds, and the system properties do not change over time. By introducing the assumption of a linear time-invariant system into the control object P(z), the relationship between the control object P(z) and the input and output can be expressed in the form of a product in the frequency domain (z domain).

[0054] The experimental output data Y0(z) obtained by the experiment is expressed by Equation 4 as the product in the z domain of the controlled object P(z) and the experimental input data U0(z) obtained by the experiment.

[0055]

number

[0056] The estimated output value Y(z) simulated in the z domain is expressed by Equation 5 as the product in the z domain of the controlled object P(z) and the estimated input value U(z) simulated in the z domain.

[0057]

number

[0058] In the equations in the z domain expressed by Equations 4 and 5, the experimental input data U0(z) and experimental output data Y0(z) are obtained during the experiment, and the estimated input value U(z) is input during the simulation, so the estimated output value Y(z) is the only unknown.

[0059] The relationship between Equation 4 and Equation 5 is expressed by Equation 6 by canceling the term of the controlled object P(z).

[0060]

number

[0061] The second and third assumptions are introduced to obtain the estimated output value y(k) in the time domain from the estimated output value Y(z) in the z domain.

[0062] The second assumption, that the state of the controlled plant P(z) before the 0th sampling time k=0 of the experimental data can be ignored, guarantees the causality of the experimental data. This guarantees that the state of the controlled plant P(z) before the sampling time k=0 does not affect the experimental data after the sampling time k=0. Therefore, when the response of the controlled plant P(z) starts from the zero state or steady state, the experimental data obtained in the experiment of the controlled plant P(z) can be used for the estimated output value y(k) in the time domain.

[0063] When the relational expression in the z domain expressed by Equation 6 is converted into a relational expression in the time domain, the following Equation 7 is obtained.

[0064]

number

[0065] The equation (7) is converted into a time domain signal expressed by the following equation (8) by a convolution operation.

[0066]

number

[0067] The subscript "0" of the input / output data (u0, y0) indicates that it is experimental data.

[0068] When the formula (8) is expanded with respect to the estimated output value y(k) at the sampling time k, the formula (9) is obtained.

[0069]

number

[0070] In equation (9), if the first experimental input data u0(0) is set to a value other than zero according to the third assumption, then equation (10) for the estimated output value y(k) in the time domain is obtained.

[0071]

number

[0072] Equation 10 shows that the estimated output value y(k) of the controlled object P(z) at sampling time k can be obtained from the experimental input / output data (u0, y0) of the controlled object P(z) and the estimated output value y(i) up to sampling time k-1.

[0073] The first term on the right side of equation 10 represents the convolution operation between the estimated input value u(i) and the experimental output data y0(k-1), the second term represents the convolution operation between the estimated output value y(i) and the experimental input data u0(k-1), and the third term represents the product of the estimated input value u(k) and the experimental output data y0(0).

[0074] The estimated output value y(k) in equation (10) does not include a term for the controlled object P(z), so a transfer function representing a plant model of the controlled object P(z) is not required. Therefore, setting a plant model for the controlled object P(z) is not required to estimate the estimated output value y(k).

[0075] (P2) Response index value acquisition process The response index value acquisition step is a step of obtaining a response index value relating to the response of the controlled object using the estimated output value acquired in the data-driven simulation step (P1).

[0076] Figure 3 is a schematic diagram for explaining the response of the controlled object, showing the rising state of the output voltage V. Vp is the peak voltage when the output voltage V rises, and Vr is the target voltage of the output voltage V. After reaching the peak voltage Vp, the output voltage V drops and gradually approaches the target voltage Vr.

[0077] The amount of overshoot Os and the settling time Ts are response indices that represent the response characteristics of the output voltage V. In Fig. 3, the amount of overshoot Os is the differential voltage (Vp-Vr) between the peak voltage Vp and the target voltage Vr.

[0078] In the following, the amount of overshoot will be explained using the overshoot amount Os of the differential voltage (Vp-Vr) and the overshoot amount p obtained by standardizing the differential voltage (Vp-Vr) by dividing it by the target voltage Vr, which is (Vp-Vr) / Vr.

[0079] The settling time Ts is defined as the time it takes for the output voltage V to settle within a predetermined range relative to the target voltage Vr, and is generally set within a range of ±2% or ±5%. This settling range is determined by a positive constant p that determines the constraint on the overshoot amount Os.

[0080] The shaded area in FIG. 3 indicates the range in which the output voltage V settles, and the settling time Ts indicates the time it takes for the output voltage V to settle within this range.

[0081] In the response index value acquisition step, the settling time Ts or the response index of the overshoot amount Os is calculated based on the estimated output value obtained in the data-driven simulation step (P1). The settling time Ts is the time from when the output voltage V rises to when it exceeds the voltage V ((1 + p) Vr in Figure 3) determined by the constant p that determines the constraint, falls within the settling range, and reaches a settled state, when the overshoot amount is used as a constraint.

[0082] (P3) Evaluation value calculation process The evaluation value calculation step is a step of calculating an evaluation value by substituting the response index value acquired in the response index value acquisition step (P2) into the term of the unconstrained optimization evaluation function J.

[0083] The unconstrained optimization evaluation function J of the present invention can be configured in the following two ways. (i) First mode: A mode consisting of objective function terms and constraint terms (ii) Second mode: A mode in which the objective function is configured as a weighted sum of the amount of overshoot and the settling time weighted by the coefficients (1-α) and α.

[0084] The optimization evaluation function J of these aspects is substituted with the values ​​acquired in the response index value acquisition step (P2) for the amount of overshoot and settling time of each term to calculate the evaluation value.

[0085] (P4) Evaluation function value minimization process The evaluation function value minimization process involves repeating the steps of data-driven simulation (P1), response index value acquisition (P2), and evaluation value calculation (P3) while updating the control parameter θ of the controller to minimize the evaluation value. The evaluation function value minimization process (P4) can be performed using an optimization solver based on the direct optimization approach of the Nelder-Mead method.

[0086] Below, we will explain the optimal control parameter design process using a DC-DC converter as the controlled object and PI control, PID control, and PI-D control as examples of closed-loop control systems.

[0087] (Control object) Figure 4 shows an example of a DC-DC converter. The DC-DC converter operates on an input voltage V in The inverter circuit is composed of an LC circuit consisting of a switch SW1 connected in series to a load R, a switch SW2 connected in parallel to the load R, an inductor L connected in series to the load R, and a capacitor C connected in parallel to the load R. The switches SW1 and SW2 are switched by a PWM signal from a controller C.

[0088] The controller inputs input data u to the DC-DC converter to be controlled, and controls the on / off of switches SW1 and SW2 using PWM signals to output the output voltage V c On the other hand, the output data y output from the DC-DC converter is the output voltage V of the capacitor C. c , and the inductor current i of inductor L L The controller feeds back the output data y to form a closed-loop control system.

[0089] (PI control) Figure 5 shows an example of the configuration of a controller that performs PI control by feeding back the inductor current as a minor loop. PI control performs proportional-integral control by inputting the difference between the target voltage Vr and the capacitor voltage output voltage Vc (e = (Vr - Vc)) into the proportional and integral terms, and also controls the inductor current i L is entered into the feedback term.

[0090] The proportional term, integral term, and feedback term of the controller are controlled by the control parameter θ, which is the proportional gain K P , integral gain K I , and feedback gain K L The outputs of these terms are added together to produce an output that is output as input data u for the controlled object. The input signal u converted into a PWM signal is input to the controlled object of the DC-DC converter, and the switching operation of the switching element of the DC-DC converter is controlled.

[0091] (PID control) Figure 6 shows an example of the configuration of a controller that performs PID control in current mode control. The proportional term, integral term, differential term, and feedback term of PID control are controlled by the control parameter θ, and the proportional gain K P , integral gain K I , differential gain K D , and feedback gain K L The sum output of these is output as input data u to be controlled.

[0092] Proportional Gain K P is the gain for the difference (Vr-Vc) between the target voltage Vr and the output voltage Vc, and the integral gain K I is the gain for the integral value of the difference (Vr-Vc) between the target voltage Vr and the output voltage Vc. D is the gain for the differential value of the difference (Vr-Vc) between the target voltage Vr and the output voltage Vc, and the feedback gain K L is the inductor current i L is the gain relative to

[0093] PID control performs proportional-integral-derivative control by inputting the difference between the target voltage Vr and the output voltage Vc (e = (Vr - Vc)) into the proportional, integral, and derivative terms, and also controls the inductor current i L The feedback signal is input to the feedback term.

[0094] (PI-D control) Figure 7 shows an example of the configuration of a controller using PI-D control in current mode control. PI-D control performs proportional-integral control by inputting the difference between the target voltage Vr and the output voltage Vc (e = (Vr - Vc)) into the proportional and integral terms, performs differential control by inputting the output voltage Vc into the differential term, and also controls the inductor current i L is entered into the feedback term.

[0095] The proportional, integral, derivative, and feedback terms of the controller are controlled by the control parameters θ, and the proportional gain K P , integral gain K I , differential gain K D , and feedback gain K L The sum output of these is output as input data u to be controlled.

[0096] Proportional Gain K P is the gain for the difference (Vr-Vc) between the target voltage Vr and the output voltage Vc, and the integral gain K Iis the gain for the integral value of the difference (Vr-Vc) between the target voltage Vr and the output voltage Vc. D is the output voltage V c is the gain for the differential value of L is the inductor current i L is the gain relative to

[0097] (Controller including anti-windup compensation term) In PI control, PID control, and PI-D control, the nonlinearity of the digital control system is compensated for by adding an anti-windup compensation term. Figure 8 shows an example of the configuration of a PI control controller that includes an anti-windup compensation term in current mode control.

[0098] The input data u is a PWM command input u that has nonlinearity due to saturation elements. r The command input u r The signal obtained by subtracting the input data u from is the feedback signal u of the anti-windup compensation that compensates for nonlinearity due to saturation. A The feedback signal u is fed back to the controller. A is the anti-windup gain K A In Fig. 8, a delay term 1 / z due to a unit step delay is introduced between the nonlinear element 4 and the controlled object 3.

[0099] The proportional term, integral term, feedback term, and anti-windup compensation term of the controller are controlled by the control parameters θ, which are proportional gain K P , integral gain K I , feedback gain K L , and anti-windup gain K A The outputs of these terms are added together to produce an output that is output as input data u for the controlled object. The input signal u converted into a PWM signal is input to the controlled object of the DC-DC converter, and the switching operation of the switching element of the DC-DC converter is controlled.

[0100] [Aspects of unconstrained optimization evaluation functions] The unconstrained optimization evaluation function of the present invention allows minimization by directly considering the response indexes of the controlled objects that are in a mutually constrained relationship, without requiring inequalities in the constraint conditions, by introducing the response indexes into the function.

[0101] The following describes first and second aspects of the unconstrained optimization evaluation function J of the present invention. For the first aspect, four example aspects, namely, first to fourth forms, are shown.

[0102] [First aspect] The first mode of the unconstrained optimization evaluation function J is a mode in which response indicators of controlled objects that are mutually constrained are introduced into the function, and one of the response indicators, the overshoot amount or the settling time, is introduced into the objective function term, and the other is introduced into the constraint term. A barrier function is used as the constraint term, and the other response indicator is incorporated as a variable related to the constraint condition.

[0103] The first aspect comprises first to fourth forms. In the first to third forms, an unconstrained optimization evaluation function J is configured by an objective function incorporating a settling time Ts and a barrier function B(θ) incorporating the amount of overshoot as a variable related to the constraint condition.

[0104] The fourth form is a form in which the relationship between the settling time Ts and the amount of overshoot is the inverse of that of the first to third forms, and an unconstrained optimization evaluation function J is constructed by introducing the amount of overshoot into the objective function and introducing a variable related to the settling time Ts as a constraint condition into the barrier function B(θ).

[0105] The direct optimization approach can be applied as a design approach for the optimal control parameter design process. The direct optimization approach is an optimization approach that uses an evaluation function to directly optimize the control parameter θ of the controller, and uses the estimated output value y obtained in the data-driven simulation process, and applies a heuristic algorithm as an optimization solver to find the control parameters that minimize the evaluation function, thereby designing the optimal control parameters of the controller.

[0106] Applying heuristic algorithms such as the Nelder-Mead method, the evaluation function is minimized to obtain the optimal control parameter θ * The Nelder-Mead algorithm, also known as the simplex algorithm or the amoeba algorithm, is a nonlinear optimization method that searches for the minimum value of a multidimensional nonlinear function by expanding, shrinking, and moving a polygonal search area.

[0107] (1) First Form Optimization based on the unconstrained optimization evaluation function J of the first embodiment will be described using the flowchart in Fig. 9. Note that (S1) to (S9) below indicate the steps of the flowchart.

[0108] (S1) Setting response indices The first mode is a mode in which the settling time Ts is minimized with the amount of overshoot as a constraint, and the unconstrained optimization evaluation function J comprises an objective function that introduces the settling time Ts and a barrier function B(θ) that introduces the amount of overshoot as a variable related to the constraint. Here, a set constant p _set Set.

[0109] Fig. 10 is a schematic diagram for explaining the response of the controlled object in the first mode, showing the rising state of the output voltage V. In Fig. 10, Vp indicates the peak voltage when the output voltage V rises, and Vr indicates the target voltage of the output voltage V. The response characteristics shown in Fig. 10 show that the output voltage V reaches the peak voltage Vp when it rises, and then drops and approaches the target voltage Vr.

[0110] The overshoot amount Os and the settling time Ts are set as response indices that represent the response characteristics of the output voltage V. In FIG. 10, the overshoot amount Os is the differential voltage (Vp-Vr) between the peak voltage Vp and the target voltage Vr. The settling time Ts is defined as the time it takes for the output voltage V to settle within a predetermined range with respect to the target voltage Vr, and is the time it takes for the output voltage V to settle within this predetermined range. The shaded area in FIG. 10 indicates the voltage range in which the output voltage V is settled.

[0111] positive set constant p _set is a constant that determines the constraint on the overshoot amount Os, and is normalized by dividing the differential voltage (Vp-Vr) by the target voltage Vr, and determines the voltage range of settling and the settling time Ts. Here, the setting constant p _set It is defined as follows.

[0112] positive set constant p _set Therefore, the voltage range in which the output voltage V settles is (1+p _set )·Vr and (1-p _set ) Vr. The settling time Ts is the time when the output voltage V is (1+p _set )·Vr and (1-p _set )·Vr voltage range, and is a positive set constant p _set can be defined as a constraint.

[0113] (S2) Initial values ​​of control parameters In the direct optimization approach to design optimal control parameters, the Nelder-Mead method minimizes the target function using (n+1) initial value vectors for design variable n. Therefore, the initial values ​​of the control parameters of the controller used in designing the optimal control parameters are determined. The initial values ​​of the control parameters can be found using the pole placement method.

[0114] When performing PI control, the controller uses the control parameter θ as the proportional gain K P , integral gain K I , and feedback gain K L In the Nelder-Mead method, four initial values ​​θ1(K P1 ,K I1 ,K L1 ),θ2(K P2 ,K I2 ,K L2 ),θ3(K P3 ,K I3 ,K L3 ), and θ4(K P4 ,K I4 ,K L4 ) to set the

[0115] (S3) Output estimation using CDDS Next, for the initial values ​​θ1 to θ4 of the control parameters set in the previous step, an estimated output value y(k) is calculated using a data-driven simulation method, and the evaluation function J(θ) is calculated using the calculated estimated output value y(k) and the reference value r(k).

[0116] The estimated output value is obtained by simulating the output based on a data-driven simulation using time-domain convolution (CDDS) with experimental data of the input and output of the controlled object. The estimated output value by CDDS can be calculated based on Equation 10 using the estimated output value y(k) of the controlled object P(z) at sampling time k, the experimental input / output data (u0, y0) of the controlled object P(z), and the estimated output value y(i) up to sampling time k-1.

[0117] (S4) Calculation of response index value Based on the estimated output value at each time point k obtained by output estimation in S3, the amount of overshoot (Vp-Vr) / Vr, which is a response index related to the response of the controlled object, and the value of the settling time Ts are calculated.

[0118] (S5) Unconstrained optimization evaluation function J The first type of unconstrained optimization evaluation function J is composed of an objective function (Ts / T0) that introduces a response index of the settling time Ts, and a barrier function B(θ) that uses the response index of the overshoot amount as a variable related to the constraint. Here, the first type of unconstrained optimization evaluation function J is defined as J barr 1, and the optimization evaluation function J barr Let me explain 1.

[0119] Unconstrained optimization evaluation function J barr The minimization of the control parameter θ of 1 is expressed by the following equation (11).

[0120]

number

[0121] In the formula (11), J barr 1: Unconstrained optimization evaluation function θ: control parameter Vp: Peak voltage at rise Vr: target voltage (Vp-Vr) / Vr: Amount of overshoot p: A positive constant that determines the constraint on the amount of overshoot Ts:Settling time T0: Circuit specific constant Ts / T0: Objective function B(θ): Barrier function μ: any constant is.

[0122] The barrier function B(θ) is shown in Figure 11. The barrier function B(θ) is a function in which the value of B(θ) diffuses when the overshoot amount (Vp-Vr) / Vr asymptotically approaches the positive constant p that determines the constraint. In addition to the function shown in Equation 11, the barrier function B(θ) can also be expressed using the logarithmic function -log(px).

[0123] (S6, S7) Unconstrained optimization evaluation function J barr Minimizing 1 Next, the unconstrained optimization evaluation function J barr Minimize 1. Unconstrained optimization evaluation function J barr The minimization of 1 is carried out by gradually changing the value of the constant μ of the barrier function B(θ) to a smaller value while updating the control parameter θ and calculating the unconstrained optimization evaluation function J in S5. barr The value of 1 is calculated, and steps S3 to S5 are repeated to minimize the calculated value.

[0124] The control parameter θ can be updated using an optimization solver that employs the Nelder-Mead direct optimization approach with a heuristic algorithm.

[0125] The control parameter θ is changed by the Nelder-Mead method, and the previous step is repeated to obtain the evaluation function J barr This is repeated until 1(θ) is minimized, and the optimal control parameter θ is obtained. The control parameter θ obtained by optimization is called the optimal control parameter θ * (K P * ,K I * ,K L * )

[0126] The determination of whether the calculated value is minimized or not can be made based on any determination criterion. Examples of the determination criterion include determining whether the number of turning operations S3 to S7 has reached a set number, determining whether the unconstrained optimization evaluation function J barr The calculated value of 1 is compared with the previous calculated value, and it is determined whether the difference is less than the set value. barrIt is possible to use a determination as to whether the calculated value of 1 is equal to the set value or not.

[0127] (S8) Calculation of settling time Ts Unconstrained optimization evaluation function J barr The value of the settling time Ts is found by minimizing the objective function Ts / T0 by 1.

[0128] Fig. 12 shows a schematic diagram of minimization of the settling time Ts in the first mode. In Fig. 12, the solid line indicates the response characteristics before minimization, and the dashed line and the dashed line indicate the response characteristics during and after minimization. A positive constant p that determines the constraint on the amount of overshoot is set as a set constant p _set When this is the case, the settling time Ts is reduced from the settling time Ts1 before minimization to settling times Ts2 and Ts3 by minimization.

[0129] The settling time Ts2 is (1+p _set )·Vr, and the settling time Ts3 is the time when the output voltage reaches the voltage range below (1-p _set )·Vr or higher.

[0130] (S9) Calculation of control parameter θ Unconstrained optimization evaluation function J barr The control parameter θ is calculated when 1 is minimized. By updating the control parameter θ in the minimization step S7, the control parameter θ approaches the optimal parameter. barr The control parameter θ obtained by minimizing 1 is calculated as the optimal control parameter.

[0131] (2) Second Form The second form is a positive setting constant p that determines the constraint on the set overshoot amount in the first form. _set is set to 2%. Generally, the settling time Ts is defined as the time it takes for the output value to settle within a range of ±2% or ±5% of the target output. The second form is to set the overshoot amount setting constant p _set Set 2% as the

[0132] 13 is a schematic diagram for explaining the response of the controlled object in the second embodiment. In the second embodiment, the setting constant p _set This shows an example where the positive setting constant p _set By setting this constant to 2%, the voltage range in which the output voltage V settles is determined to be between 1.02Vr and 0.98Vr, with the target voltage Vr in between. The settling time Ts is the time it takes for the output voltage V to fall within the voltage range of 1.02Vr and 0.98Vr, with the set constant 2% as a constraint.

[0133] The minimization of the settling time Ts and the control parameters in the first mode is achieved by using a positive set constant p _set This is done by setting the value at 2%.

[0134] The second form of unconstrained optimization evaluation function J is J barr 2. Unconstrained optimization evaluation function J barr The minimization of the control parameter θ in 2 is expressed by the following equation (12) in which the constant p of the barrier function B(θ) in equation (11) is replaced by 0.02.

[0135]

number

[0136] 14 shows the barrier function B(θ). The barrier function B(θ) is a positive set constant p that determines the constraint on the overshoot amount (Vp-Vr) / Vr. _set As the function approaches 2%, the value of B(θ) spreads.

[0137] Fig. 15 shows a schematic diagram of minimization of the settling time Ts in the second mode. In Fig. 15, the solid line indicates the response characteristics before minimization, and the dashed line and the dashed line indicate the response characteristics during and after minimization. A positive setting constant p that determines the constraint on the amount of overshoot is_set When is set to 2%, the settling time Ts is reduced by minimization from the settling time Ts1 (2%) before minimization to settling times Ts2 (2%) and Ts3 (2%).

[0138] Settling times Ts1 (2%) and Ts2 (2%) indicate the points at which the output voltage reaches a voltage range of 1.02 Vr or less, and settling time Ts3 (2%) indicates the point at which the output voltage reaches a voltage range of 0.98 Vr or more.

[0139] (3) Third Form In data-driven simulation (CDDS method), which obtains estimated output values ​​based on convolution operations in the time domain, the output may contain estimation errors. In the third mode, the constant p that determines the constraint on the amount of overshoot is set taking into account the estimation errors included in the data-driven simulation process.

[0140] When comparing the output obtained by the CDDS method with the amount of overshoot, the actual output value is the sum of the output obtained by the CDDS method and the estimated error due to the error caused by the CDDS method. The third form uses a setting constant p _set , and settling time Ts(p _set ) is replaced by an estimation constant p that takes into account a margin m to mitigate the estimation error. _est =(p _set -m), and estimated settling time Ts _est Set.

[0141] 16 is a schematic diagram for explaining the response of the controlled object in the third embodiment. In the third embodiment, a set constant p _set and the estimated constant p, which is the output included in the CDDS method minus a margin m to take into account the estimation error. _est where the estimated constant p _est (p _set The solid line in Figure 16 indicates the constant p _set The dashed line shows the output voltage V when the constant p is set to the estimated constant p _estThe figure shows the output voltage V when the

[0142] Setting constant p _set Instead of the estimated constant p _est By using this, the voltage range in which the output voltage V settles is [Vr-p _est ,Vr+p _est The settling time Ts is determined by the voltage range of the estimated constant p _est The output voltage V is Vr-p _est and Vr+p _est This is the time it takes for the voltage to reach the specified range. _set If the margin m is set to 1.1%, the estimated constant p _est is set to 0.9%.

[0143] The minimization of the settling time Ts and the control parameters in the third mode is achieved by replacing the positive constant p with the estimated constant p in the procedure of the first mode shown in the flowchart of FIG. _est This is done by setting

[0144] The third form of unconstrained optimization evaluation function J is J barr 3. Unconstrained optimization evaluation function J barr The minimization of the control parameter θ in 3 is performed by estimating the constant p of the barrier function B(θ) in Equation 11 as the constant p _est This is expressed by the following equation 13, where

[0145]

number

[0146] 17(a) and (b) show the barrier function B(θ). In FIG. 17(a), the constant p is set as the constant p _set The barrier function is shown, and the overshoot amount (Vp-Vr / Vr) is a positive constant p _setOn the other hand, in Figure 17(b), the value of B(θ) is spread out as the constant p is estimated. _est The barrier function is shown using the overshoot (Vp-Vr) / Vr, which is a positive estimated constant p _est As the value of B(θ) approaches asymptotically, the value of B(θ) spreads.

[0147] Fig. 18 shows a schematic diagram of minimizing the settling time Ts in the third mode, where (a) of Fig. 18 shows the response characteristics before minimization, and (b) of Fig. 18 shows the response characteristics after minimization.

[0148] In the response characteristics before minimization in Figure 18(a), the estimated constant p _est and the set constant p _set The settling time is Ts1, which is restricted by the amount of overshoot determined by the solid line and the dashed line. _set Response characteristics and estimated constant p _est The response characteristics are shown in the figure. The settling time Ts at this time is _set and the estimated constant p _est In either case, the settling time is Ts1.

[0149] On the other hand, in the response characteristics after minimization in Figure 18(b), the estimated constant p _est and the set constant p _set The settling time is Ts2, which is restricted by the amount of overshoot determined by the solid line and the dashed line. _set Response characteristics and estimated constant p _est The response characteristics are shown in the figure. The settling time Ts at this time is _set and the estimated constant p _est In either case, the settling time is Ts2.

[0150] Comparing the settling time Ts1 in Figure 18(a) with the settling time Ts2 in Figure 18(b), the settling time is reduced from Ts1 to Ts2 by minimizing the overshoot amount as a constraint. The arrow in the figure indicates the reduction in the settling time Ts.

[0151] (4) Fourth Form In the fourth form, the relationship between the response indices introduced in the first to third forms is reversed, the amount of overshoot is introduced into the objective function, and the settling time Ts is incorporated into the barrier function as a variable related to the constraint. In the fourth form, the amount of overshoot p is minimized using the settling time Ts as a constraint.

[0152] 19 is a schematic diagram for explaining the response of the controlled object in the fourth embodiment. In the fourth embodiment, the settling time Ts _set Set the settling time Ts _set In FIG. 19, the output voltage of the solid and dashed lines is _set The figure shows the response characteristics before and after the setting when the constraint is set as follows.

[0153] The minimization of the overshoot amount Os and the control parameters in the fourth embodiment are performed by the evaluation function J in S5 shown in the flowchart of FIG. barr Optimization evaluation function J barr 4. The optimization evaluation function J barr 4 is an optimization evaluation function that introduces the amount of overshoot into the objective function and incorporates the settling time Ts into the barrier function as a variable related to the constraint condition. barr 4 is composed of an objective function (Vp-Vr) / Vr that introduces a response index of the amount of overshoot, and a barrier function B(θ) that uses a response index of the settling time Ts as a variable related to the constraint.

[0154] The fourth form of unconstrained optimization evaluation function J barr The minimization of 4 is expressed by the following equation 14. Note that the constraint condition for the settling time Ts is 0≦Ts / T0≦Ts _set It is expressed as / T0.

[0155]

number

[0156] Figure 20 shows the barrier function B(θ). Figure 20 shows the barrier function with the set settling time Ts _set as a constraint condition, and the value of B(θ) spreads as the settling time Ts approaches the set settling time Ts _set that determines the constraint.

[0157] Figures 21 and 22 schematically show the minimization of the overshoot amount Os in the fourth form. The solid line in Figure 21 shows the response characteristic before minimization, and the dashed line shows the response characteristic during minimization. For the set settling time Ts _set the overshoot amount Os is reduced from the overshoot amount Os1 before minimization to the overshoot amount Os2 by minimization.

[0158] <00​​​​​​​​​​​​In the second mode, the objective function is the weighted sum of two response indices, the amount of overshoot and the settling time, weighted by the coefficients (1-α) and α. By weighting the amount of overshoot and the settling time by the ratio of (1-α) to α, the response indices of the controlled object, which are in a mutually constrained relationship, are introduced into the term of the unconstrained optimization evaluation function J, and the amount of overshoot and the settling time are simultaneously optimized.

[0160] The second aspect of the unconstrained optimization evaluation function J α In (θ), the coefficient α is an arbitrary constant that satisfies 0<α<1, and the objective function is the weighted sum obtained by weighting the overshoot amount and the settling time, which are in a mutually constrained relationship, using this coefficient α.

[0161] Unconstrained optimization evaluation function J α (θ) is expressed as the sum of a term weighted by multiplying the overshoot amount (Vp-Vr) / Vr by a coefficient (1-α) and a term weighted by multiplying the settling time by a coefficient α, and J α The minimization of (θ) is expressed by the following equation (15).

[0162]

number

[0163] In addition, the unconstrained optimization evaluation function J α (θ) may be composed of a weighted sum of a term weighted by multiplying the overshoot amount (Vp-Vr) / Vr by α and a term weighted by multiplying the settling time by (1-α).

[0164] Fig. 23 shows a schematic diagram of simultaneous optimization of the amount of overshoot and settling time according to the second aspect. The solid line in Fig. 23 shows the response before optimization, and the dashed line in Fig. 23 shows the response after optimization.

[0165] Before optimization, the settling time and overshoot of the characteristic point P1 of the response are Ts1 and Os1, respectively. After optimization, the settling time and overshoot of the characteristic point P2 of the response are Ts2 and Os2, respectively.

[0166] Unconstrained optimization evaluation function J α Due to (θ), the characteristic point of the response after optimization changes from P1 to P2, and the response indices of the settling time and the amount of overshoot are both reduced.

[0167] (Comparative Example of the Present Invention and the Conventional Method) Table 1 shows the specifications of the step-down DC-DC converter used in the experiment.

[0168] [Table 1]

[0169] For the above step-down DC-DC converter, the initial value of the control parameter θ of the controller is set to θ=[K P K I K L ]=[0.006366 31.73 -0.008369] is obtained.

[0170] The above value is used as the initial value of the control parameter θ to obtain an experimental value, and optimization is performed. An example of the change in the evaluation function value of the unconstrained optimization evaluation function obtained through optimization is shown in Figure 24. In Figure 24, the horizontal axis shows the number of iterations, and the vertical axis shows the optimization evaluation function value.

[0171] Table 2 shows the control parameter θ obtained by optimization [K P K I K L ] is shown in comparison with the conventional method and the method of the present invention.

[0172] [Table 2]

[0173] Table 3 and Fig. 25 show a comparison between the method according to the third aspect of the present invention and the conventional method with respect to the amount of overshoot and settling time. In Fig. 25, the dashed line shows the output voltage using the conventional method, and the solid line shows the output voltage using the method of the present invention. Here, in the third aspect of the present invention, the setting constant p for the amount of overshoot is set to 2%, the estimation constant p is set to 0.9%, and a settling time of 2% is shown.

[0174] [Table 3]

[0175] According to Table 3 and Figure 25, the experiment shows a tendency for the amount of overshoot to be larger than that in the simulation, but the setting constant p _set 2%, and the estimated constant p _est is set to 0.9%, and by setting the amount of overshoot during simulation to be within 0.9%, the amount of overshoot in the experimental results is within 2%.

[0176] This shows that the method of the present invention can shorten the settling time by 2% compared to the conventional technique by sacrificing the amount of overshoot. Experimental results show that the response speed is improved by (226.9 - 211.8) / 226.9 - 6.655% compared to the conventional method. [Industrial Applicability]

[0177] The controller optimization method of the present invention can be applied to minimizing the response index of a power supply device using a DC-DC converter and to designing the control parameter θ of the controller of the power supply device. [Explanation of symbols]

[0178] B(θ) barrier function J Evaluation Function J barr 1. J barr 2. J barr 3. J barr 4. J α Unconstrained optimization evaluation function θ control parameter p is a positive constant that determines the constraint on the amount of overshoot p _set Setting constants p _est Estimated Constant T0 Circuit specific constant Ts / T0 objective function Ts settling time Ts _set Setting settling time Ts _est Estimated settling time m margin Vp Peak voltage Vr target voltage (Vp-Vr) / Vr Overshoot amount α is any constant that satisfies 0<α<1 μ any constant 100 Closed-loop control system C(θ) controller P(z) Control target r(k) reference signal u in (k) Input signal y out (k) Output signal

Claims

1. A controller optimization method for optimizing a control parameter θ of a controller that controls a controlled object, comprising: a data-driven simulation step (P1) of simulating an output based on a time-domain convolution operation using experimental data of input and output of the controlled object to obtain an estimated output value; a response index value acquisition step (P2) of calculating a response index value related to the response of the controlled object using the estimated output value acquired in the data-driven simulation step; an evaluation value calculation step (P3) of constructing an unconstrained optimization evaluation function J by introducing response indicators that are in a constraint relationship with each other into terms within a function, and calculating an evaluation value by substituting the response index value acquired in the response index value acquisition step into the term of the unconstrained optimization evaluation function J; an evaluation function value minimization step (P4) for minimizing the evaluation value by repeating the data-driven simulation step (P1), the response index value acquisition step (P2), and the evaluation value calculation step (P3) while updating a control parameter θ of the controller; and Equipped with Controller optimization methods.

2. The unconstrained optimization evaluation function J is composed of an objective function incorporating one of the response indicators of the overshoot amount and the settling time, and a barrier function incorporating the other response indicator as a variable related to the constraint condition. The method of claim 1 .

3. The unconstrained optimization evaluation function J is an unconstrained optimization evaluation function J that is composed of an objective function (Ts / T0) that introduces a response index of the settling time Ts and a barrier function B(θ) that uses a response index of the overshoot amount as a variable related to the constraint condition. ｂａｒｒ 1, The unconstrained optimization evaluation function J ｂａｒｒ The minimization of 1 is expressed by the following equation: The method of claim 2 . [0016] 【number】 J ｂａｒｒ 1: Unconstrained optimization evaluation function θ: control parameter Vp: Peak voltage at rise Vr: target voltage (Vp-Vr) / Vr: amount of overshoot p: a positive constant that determines the constraint on the amount of overshoot Ts: settling time T0: Circuit-specific constant B(θ): Barrier function μ: arbitrary constant Ts / T0: Objective function

4. The constant p that determines the constraint on the amount of overshoot is an estimation constant p that determines the constraint on the amount of overshoot taking into account the estimation error included in the data-driven simulation process. ＿ｅｓｔ and The estimated constant p ＿ｅｓｔ is a setting constant p which is a constant that determines the constraint on the amount of overshoot when the estimation error is not taken into consideration. ＿ｓｅｔ is set smaller by the margin m due to the estimation error (p ＿ｓｅｔ -m), The method of claim 2 .

5. The unconstrained optimization evaluation function J is an unconstrained optimization evaluation function J consisting of an objective function (Vp-Vr) / Vr that introduces a response index of the overshoot amount and a barrier function B(θ) that uses a response index of the settling time Ts as a variable related to the constraint condition. ｂａｒｒ 4, and the unconstrained optimization evaluation function J ｂａｒｒ The minimization of 4 is expressed by the following equation: The method of claim 2 . [Equation 17] 【number】 J ｂａｒｒ 4: Unconstrained optimization evaluation function θ: control parameter Ts: settling time Ts ＿ｓｅｔ Set the set time T0: Circuit-specific constant (Vp-Vr) / Vr: amount of overshoot B(θ): Barrier function μ: arbitrary constant

6. The unconstrained optimization evaluation function J is an unconstrained optimization evaluation function J that is composed of an objective function expressed as a weighted sum of two response indices, the amount of overshoot and the settling time, weighted by the coefficients (1-α) and α. α (θ), The unconstrained optimization evaluation function J α The minimization of (θ) is expressed by the following equation: The method of claim 1 . [Equation 18] θ: control parameter J α : Unconstrained optimization evaluation function Vp: Peak voltage at rise Vr: target voltage Ts: settling time T0: Circuit-specific constant α: any constant satisfying 0<α<1

7. The evaluation function value minimization step (P4) is performed using an optimization solver based on the direct optimization approach of the Nelder-Mead method. A method for optimizing a controller according to any one of claims 1 to 6.

Images