Method and device for automatically designing control signals or control parameters robust to plant variations

Abstract

To provide an automatic control design technology that experiences a plurality of plant variation conditions, solves an optimization problem based on a plurality of predicted responses under the conditions, and enables robustness against plant variations.SOLUTION: A designing method for a control signal includes the steps of: collecting and storing in a memory positioning input / output data of a control system when an arbitrary control signal is given to the control system under multiple plant variation conditions; calculating a predicted output signal of the control system under multiple plant variation conditions from input / output data collected under multiple plant variation conditions; defining an evaluation function or constraints for the difference between the predicted output signal and a target output signal under multiple plant variation conditions; and determining the control signal by solving an optimization problem including the evaluation function or constraints.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to an automatic design method and an automatic design device for control signals or control parameters that are robust against plant variations. [Background technology]

[0002] Positioning mechanisms used in various industrial machines are required to achieve high speed and high accuracy in positioning control in pursuit of productivity. To achieve this, in addition to suppressing resonant vibration excited by high acceleration / deceleration driving, it is also essential to provide robust performance against plant fluctuations due to, for example, changes in the mass of the transported object or aging (Non-Patent Document 1). Furthermore, industrial positioning mechanisms often do not or cannot provide feedback (FB) on the information of the control amount to be actually controlled, and are controlled by semi-closed control, making it difficult to achieve both vibration suppression and high speed positioning with general FB control methods (Non-Patent Document 2).

[0003] To address this issue, model-based feedforward (FF) compensation using a precise plant model is an effective approach, and various robust FF compensation methods that consider plant fluctuations have been proposed based on this approach (Non-Patent Documents 3, 4, etc.), and their effectiveness is well known. However, most of the robust FF compensation methods require accurate estimation of plant fluctuation characteristics, identification of a precise plant model, and trial-and-error adjustment of design parameters, which often require a great deal of time and effort.

[0004] Patent Document 1 describes a control parameter adjustment method in which control parameters that determine a transfer function of a control device that receives a target value and applies an operating variable to a control object in an open loop to control the control object are adjusted so that the response of the control variable of the control object to a target value approaches a reference model, so that control parameters can be determined directly from a set of test data. The control parameter adjustment method includes a process of applying a test input signal sequence that changes over time to the control object and collecting a test output signal sequence that is the time change of the control variable, and a control parameter determination process of determining the control parameters so as to minimize an evaluation function obtained by subtracting the data sequence when the test output signal sequence is applied to the transfer function of the control device from the data sequence when the test input signal sequence is applied to the transfer function of the reference model.

[0005] Patent Document 2 describes that in a nonlinear system in which the control system has saturation nonlinearity, the least squares method can be applied to the nonlinear system in relation to the adjustment of the control parameters of the controller by data-driven control, and further, that anti-windup compensation that eliminates the saturation nonlinearity can be applied in the adjustment of the control parameters to which the least squares method is applied. Here, the techniques described in Patent Documents 1 and 2 cannot guarantee robustness under conditions other than data acquisition conditions.

[0006] Patent Document 3 describes a transportation method that reduces the burden on workers and enables more flexible operation by constructing a power assist system that takes into account higher-order vibrations targeted at general overhead cranes. Here, the technology described in Patent Document 3 requires a great deal of effort to estimate plant fluctuations.

[0007] Patent Document 4 describes a technique for adjusting the parameters of a controller while desirably maintaining the stability of a control system, in which a control input according to a transfer function having a variable parameter is calculated based on the deviation between a control output and a target value, and a set value of a variable parameter in a control device that controls a controlled object based on the control input is updated. This updating method includes a procedure for calculating a value of a variable parameter that minimizes an output value of an evaluation function based on time series data of observed control input and output, and a procedure for updating the set value of the variable parameter to the calculated value, and the evaluation function includes first and second function portions. It describes that the first function portion is configured to output the norm of the difference between the observed value of the control input or output and a reference value of the control input or output corresponding to the value of the variable parameter, and the second function portion is configured to increase the output value of the evaluation function corresponding to the norm of the difference as the transfer function changes from the initial function. [Prior art documents] [Patent documents]

[0008] [Patent Document 1] JP 2009-175917 A [Patent Document 2] Patent No. 7256327 [Patent Document 3] JP 2008-222392 A [Patent Document 4] JP 2017-68658 A [Non-patent literature]

[0009] [Non-Patent Document 1] M. Iwasaki, K. Seki, and Y. Maeda, “High-Precision Motion Control Techniques: A Promising Approach to Improving Motion Performance,” IEEE Ind. Electron. Mag., Vol. 6, No.1, pp. 32-40 (2012) [Non-Patent Document 2] Hori, Sawada, Zen: "Optimal Estimation Speed ​​of Disturbance Observer in Slow Resonance Ratio Control", IEEJ Transactions on Electrical Engineering, Vol. 117, No. 1, pp. 50-56 (1998) [Non-Patent Document 3] Hirata, Hasegawa, and Nonami: "Final State Control for Short Seek Control of Hard Disk Drives", IEEJ Transactions on Electrical Engineering, Vol. 125, No. 5, pp. 524-529 (2005) [Non-Patent Document 4] Kato, Maeda, Iwasaki, Hirai: "Design of Two-Degree-of-Freedom Robust Vibration Suppression Positioning Control System Using LMI", IEEJ Transactions on Electrical Engineering, Vol. 131, No. 1, pp.93-101 (2011) Summary of the Invention [Problem to be solved by the invention]

[0010] However, while the conventional technology can adjust a control signal or control parameter to optimize an objective function related to a predicted response under a single plant condition based on positioning input / output data acquired under that condition, the adjusted control signal or control parameter does not guarantee robustness under plant conditions other than the aforementioned condition. In order to provide robustness, there is a problem that it is necessary to estimate the uncertainty required for robust control design and adjust the setting parameters by trial and error. Therefore, the present invention aims to provide an automatic control design technology that enables robustness against plant fluctuations by acquiring input / output data under multiple plant fluctuation conditions and solving an optimization problem based on multiple predicted responses. [Means for solving the problem]

[0011] The present invention which solves the above problems is as follows. [1] A step of collecting positioning input / output data {r, y} of a control system when an arbitrary control signal r is given to the control system under a plurality of plant variable conditions and storing the data in a memory; The input / output data {r m ,y m}, m=1, 2, ..., M, the predicted output signal y^ of the control system under the multiple plant fluctuation conditions m and calculating The predicted output signal y^ under the multiple plant fluctuation conditions m and defining an evaluation function or constraint on the difference between the output signal and a target output signal; The control signal r is generated by solving an optimization problem including the evaluation function or the constraint condition. * determining The control signal design method is characterized by comprising the steps of: [2] A step of collecting input / output data {r, y} of a control system when an arbitrary control parameter ρ is given to a controller K(ρ) that receives a control signal r' and outputs a control signal r under a plurality of plant fluctuation conditions, and storing the data in a memory; The input / output data {r m ,y m}, m=1, 2, ..., M, the predicted output signal y^ of the control system under the multiple plant fluctuation conditions m and calculating The predicted output signal y^ under the multiple plant fluctuation conditions m and defining an evaluation function or constraint on the difference between the output signal and a target output signal; The control parameter ρ * determining The control parameter design method is characterized by comprising the steps of: [3] An automatic design apparatus comprising the memory for realizing the control signal design method described in [1] or the parameter design method described in [2], and a processor for processing each of the steps. Effect of the Invention

[0012] The automatic control design technology (automatic design method and automatic design device for control signals or control parameters) of the present invention can provide robustness against plant fluctuations, and can provide better control performance even when operating conditions change or the system deteriorates over time, as compared with conventional technology. It can also eliminate trial-and-error estimation of uncertainties and adjustment of setting parameters, reducing the time and effort required for control design and development costs. [Brief description of the drawings]

[0013] [Figure 1] FIG. 1 is a block diagram of a system for designing control signals according to the inventive technique. [Diagram 2] 1 is a block diagram of a system for designing control parameters according to the inventive technique. [Diagram 3] FIG. 1 is a block diagram of a two-degree-of-freedom positioning control system with model-based FF compensation. [Figure 4] 13A and 13B are diagrams showing frequency responses from a motor torque command u to (a) a table position yT and (b) a load position yL measured under plant conditions C1 to C5, respectively. [Diagram 5] 1A and 1B are diagrams each showing a conceptual diagram of a time response waveform of a position command r and a predicted value y^T of a table position. [Figure 6] 1A and 1B are diagrams showing the time response waveform and acceleration frequency spectrum of a position command r designed using the conventional technology and the technology of the present invention, respectively. [Figure 7] FIG. 13 shows time response waveforms of (a) the table position error Xr-yT and (b) the load position error Xr-yL measured in positioning experiments conducted under plant conditions C1 to C5 using r designed according to the inventive technology. [Figure 8] FIG. 13 shows time response waveforms of (a) the table position error Xr-yT and (b) the load position error Xr-yL measured in positioning experiments under plant conditions C1 to C5 using r designed according to the conventional technology. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0014] Hereinafter, an embodiment of the present invention will be described with reference to the drawings. The present invention is not limited to the following embodiment, and changes, modifications, and improvements can be made without departing from the scope of the invention.

[0015] In this invention, in a problem of high-speed, high-precision positioning control of a positioning mechanism with plant fluctuations, a position command is designed within the framework of a data-driven control method (Kaneko, Nakamura, Ikezaki: “A New Approach to Updating Feedforward Controllers in Two-Degree-of-Freedom Control Systems - Proposal of Estimated Response Iterative Tuning (ERIT) -”, Transactions of the Society of Computational Control Engineers, Vol. 54, No. 12, pp. 857-864 (2018); Z. Zhang and W. Yin, “Data-Driven Feedforward Control on Active Vibration Isolation System,” Proc. 17th Int. Conf. Control, Automation and Systems, pp. 562-567 (2017)) using positioning input / output data (hereinafter referred to as empirical data) obtained in advance during plant fluctuations, thereby improving the robust vibration control performance compared to when designed using empirical data obtained under a single plant condition. In the following, we will describe the theoretical development of the invented technology and demonstrate its effectiveness through high-speed, high-precision positioning experiments of a load resonance table positioning mechanism accompanied by changes in load mass.

[0016] <Positioning control system> A block diagram of a two-degree-of-freedom positioning control system with model-based FF compensation used in an embodiment of the present invention is shown in FIG. FFr , C FFu : Model-based FF compensator, C FB :FB controller, P T : Dynamics of the table as the driving point, P L : Dynamics of the load mechanism that is the control point, r: Target value X r Position command, y T : table position, y L: load position, u: motor torque command, f: friction occurring in guides and bearings, f ~ In this embodiment, the output data available for position command design is the table position y T Only at load position y L Note that is only observed for evaluation purposes. In addition, the " ~ " is written that way for convenience when it should have been written above the f, and the same goes for the subsequent "^" and "￣".

[0017] The motor torque command u and table position y measured under plant conditions C1 to C5 with different load masses T , load position y L The frequency response up to 100 Hz is shown in Fig. 4. The gain and resonance frequency of the rigid body mode change with the change in the load mass.

[0018] In this invention, on the premise that the above-mentioned two-degree-of-freedom positioning control system has already been configured within the framework of a model-based control design method, we consider data-driven design of the position command r that achieves good positioning performance even under plant fluctuations.

[0019] [Data-driven design method for robust vibration suppression position command] <Summary of invention technology> The proposed data-driven position command design predicts the table position response under plant fluctuation conditions and designs a position command that optimizes the vibration suppression performance of the predicted response in order to provide robust performance against plant fluctuations. Its characteristic is that the position command r and table position y obtained under M plant conditions are T The data set is used as empirical data and the following equation Y T0 The key point is to store it as follows: (Number 1) JPEG2025027716000002.jpg36121 Here, r0, y T0m, m=1,2,...,M are the position command and table position data obtained under each plant condition defined later, and the subscript 0 is added to represent empirical data. The r to be designed is the set Y T0 The vibration control performance is achieved under the plant fluctuation conditions included in the above and similar fluctuation conditions.

[0020] Empirical data is obtained during preliminary operation or actual operation, and does not require the cumbersome estimation of plant fluctuations, which is performed in general control design methods based on robust control theory. When preliminary operation is performed, empirical data is obtained when plant fluctuations occur accidentally or intentionally. When empirical data is obtained during actual operation, for example, table position deviation X r -y T The positioning input / output data when the maximum absolute value of exceeds a predetermined value is stored as empirical data, or the empirical data is acquired at random timing.

[0021] <Design theory> To explain the design theory of the robust vibration suppression position command, the command r(t) and the predicted value y^ of the table position are T A conceptual diagram of the time response waveform of (t) is shown in Figure 5. In the inventive technology, in order to achieve high-speed, high-precision positioning even under plant fluctuations, r(t) is designed taking into consideration the following i) to iii). i) r(t) is a finite time t=N rs Target value X r Settling to. ii) r(t) is the transient response period 0≦t≦N rs It has a smooth trajectory at iii) Predicted response y^ under M plant conditions Tm (t), m=1,2,.. .,M, N s ≦t≦N deviation X r -y^ Tm (t) is minimized. The designed r(t) is the transient response period (0≦t≦N rs ) and settling interval (N rs +1≦t≦N) is distinguished and defined as follows: (Number 2) JPEG2025027716000003.jpg40106 In the following theoretical development, the actual design variable is r t Hereinafter, the formulation of the constrained optimization problem with the equality constraint of (i) and the objective functions of (ii) and (iii) and its solution method will be described.

[0022] <Formulation of (i)> The constraint condition for finite-time tuning to the target value is formulated by the following equation using r rs ) = X r as r t is used. (Equation 3) JPEG2025027716000004.jpg2297 <Formulation of (ii)> In order to obtain a smooth position command trajectory, the sum of squares of the second-order difference values of r(t) is used as the objective function as follows. (Equation 4) JPEG2025027716000005.jpg1997

[0023] Here, q is the shift operator, and it is assumed that r(-1) = r(-2) = 0. Equation (5) can be formulated by the following equation using r t is used. (Equation 5) JPEG2025027716000006.jpg1497 Here, H 2di ff ∈ R(N rs +2) × (N rs +1), Qa ∈ R(N rs +1) × (N rs +1) are second-order difference matrices.

[0024] <Formulation of (iii)> As the objective function related to robust vibration control, the sum of squared deviations of the predicted value ŷ Tm (t) of y Tm (t) under M plant conditions from the target value X r is used as follows. (Number 6) JPEG2025027716000007.jpg2097 Now, from r to y in Figure 3 T Considering the transfer characteristics up to y^ Tm (t) is defined as follows: (Number 7) JPEG2025027716000008.jpg2097 In order to simplify the theoretical development, we assume that friction compensation is ideal in Fig. 3 (i.e., f ~ =f), note that the effect of friction is ignored. System G m Assuming that the initial state of is zero, y^ at t=0,1,...,N Tm (t) can be expressed as follows: (Number 8) JPEG2025027716000009.jpg65111 Here, the matrix G m A in m , B m , C m , D m is G m This is the coefficient matrix when (q) is expressed in state space. y^ Tm P Tm Without a precise model of (q), accurate predictions cannot be calculated. Therefore, in this design example, we use the empirical data set Y in equation (1) based on the method described in the literature (Z. Zhang and W. Yin, “Data-Driven Feedforward Control on Active Vibration Isolation System,” Proc. 17th Int. Conf. Control, Automation and Systems, pp. 562-567 (2017)). T0 Command r0(t) and table position y T0m (t) G of the following formula ~ m So, G in equation (8) m Replace with.

[0025] (Number 9) JPEG2025027716000010.jpg97111 In this case, y^ in equation (8) Tm is t It can be calculated as a function of (Number 10) JPEG2025027716000011.jpg1597 Here, G ~ tm ∈R(N+1)×(N rs +1), and in the above transformation, the following relational expression is used taking into account condition i). (Number 11) JPEG2025027716000012.jpg39111 From equation (10), the objective function J in equation (6) e is t This can be formulated as a quadratic form of JPEG2025027716000013.jpg95111

[0026] In this embodiment, G in the formula (9) ~ m is calculated using empirical data obtained under the same operating conditions (e.g., the same moving distance) as those for designing the command r, but it may be calculated using empirical data obtained under different operating conditions. That is, G ~ m The conditions for obtaining empirical data to calculate and the predicted response y^ to design r Tm The operating conditions under which (t) is calculated do not necessarily have to be the same.

[0027] <optimal solution r t * Calculation formula> From equations (3), (5), and (12), taking into account i) to iii), t The optimization problem for is (Number 13) JPEG2025027716000014.jpg2197 Here, w is the weighting coefficient. The optimal solution r of Eq. (13) t * can be calculated using the Lagrange undetermined constant method as follows: (Number 14) JPEG2025027716000015.jpg1797

[0028] <Design of robust vibration suppression position command> The empirical data used for design based on the <design theory> is the r, y T (Sample period T s = 0.5 ms). The r value of the invented technology was 0.0715 s, which is the target value X r = N to reach 20 mm rs = 142, and in order to set the evaluation interval of the predicted position deviation in iii) to 0.1 to 0.2 s, N s = 200, N = 400. The weight w in equation (14) was determined by trial and error to be w = 0.005, taking into consideration the balance between the smoothness of the position command trajectory and the robust vibration suppression performance. On the other hand, in the conventional technology to be compared, r was designed using empirical data for only one condition (M = 1) of the plant condition C1. N rs , N s , the value of N is the same as in the case of the invented technology. Figure 6 shows the time response waveform and acceleration frequency spectrum of r(t) designed using the conventional technology and the invented technology. As can be seen from Figure 6(a), while the invented technology reaches the target value in 0.0715 s, the same as the conventional technology, a different trajectory is designed in the transient response section from the conventional technology. Also, Figure 6(b) shows that both commands have reduced spectra in the frequency band around 28 Hz where vibration response occurs, which will be described later.

[0029] <Results of positioning experiment> Position error response waveform X of table and load measured by performing positioning experiments under plant conditions C1 to C5 using r(t) designed by the invented technology r -yT , X r -y L Figure 7 shows the position error response waveform X of the table and load measured in positioning experiments under plant conditions C1 to C5 using r(t) designed by the conventional technology. r -y T , X r -y L The results are shown in Figure 8. Compared to the conventional technology, the inventive technology suppresses the vibration response around 28Hz during settling for both the table and the load, clearly demonstrating the improvement in robust vibration suppression performance achieved by the inventive technology. In addition, the response characteristics have improved even under inexperienced plant conditions C2 and C4, confirming that effective command design is possible even under inexperienced conditions if empirical data can be appropriately acquired. In order to quantitatively evaluate robust performance, y T (t) and y L (t) The average at each time y T (t), y L (t), the maximum absolute deviation max|y￣ T (t)-y Tm (t)|, max|y￣ L (t)-y Lm (t)| is listed in Table 1 as the amount of response variation. Note that the bold numbers in the table for both methods indicate the maximum value under all conditions. The invented technology reduced response variation more than the conventional technology under all conditions, and when viewed under conditions with the maximum amount of response variation, a large reduction effect was obtained, with the table reducing by -45.5% at C3 and the load reducing by -50.3% at C5. The effectiveness of the proposed data-driven robust vibration suppression position command design method was verified by the above experimental evaluation. (Table 1) JPEG2025027716000016.jpg4397 [Industrial Applicability]

[0030] It can be used for control design of positioning mechanisms in industrial and logistics machinery, and the data that can be acquired includes the position, speed, acceleration, and force of the positioning mechanism. In addition to positioning mechanisms, it can also handle the control design of control devices for temperature, air volume, etc.

Claims

1. a step of collecting positioning input / output data {r, y} of a control system when an arbitrary control signal r is given to the control system under a plurality of plant variable conditions and storing the data in a memory; The input / output data {r ｍ , y ｍ }, m=1, 2, . . . , M, the predicted output signal y^ of the control system under the multiple plant fluctuation conditions is calculated. ｍ and calculating The predicted output signal ŷ under the multiple plant fluctuation conditions ｍ and defining an evaluation function or constraint on the difference between the output signal and a target output signal; The control signal r is generated by solving an optimization problem including the evaluation function or the constraint condition. ＊ determining A control signal design method comprising the steps of:

2. a step of collecting input / output data {r, y} of a control system when an arbitrary control parameter ρ is applied to a controller K(ρ) that receives a control signal r′ and outputs a control signal r under a plurality of plant fluctuation conditions, and storing the data in a memory; The input / output data {r ｍ , y ｍ }, m=1, 2, . . . , M, the predicted output signal y^ of the control system under the multiple plant fluctuation conditions is calculated. ｍ and calculating The predicted output signal ŷ under the multiple plant fluctuation conditions ｍ and defining an evaluation function or constraint on the difference between the output signal and a target output signal; The control parameter ρ ＊ determining A control parameter design method comprising the steps of:

3. 10. An automatic design device comprising: the memory for implementing the control signal design method according to claim 1 or the parameter design method according to claim 2; and a processor for carrying out processing of each of the steps.

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