Method and apparatus for designing data-driven damping feedforward control

Abstract

In ERIT, it is necessary to set a reference model for generating a target command for an ideal response before FF control design, and if an appropriate reference model cannot be set, coupled vibration caused by a plurality of structures cannot be suppressed. Further, when the characteristics of the plant are partially or entirely unknown, it is practically impossible to provide an appropriate reference model. Therefore, an object of the present invention is to provide a design method and a design device for data-driven damping feedforward control that can eliminate the need to set a complicated reference model.SOLUTION: A feedforward control design method has a controller structure in which a plurality of feedforward controllers to be designed are provided, a denominator polynomial of each feedforward controller is common, and a numerator polynomial is a free parameter, and the free parameter is designed by solving an optimization problem for minimizing a deviation between a target command generated by one feedforward controller among the plurality of feedforward controllers and a predicted response.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to a design method and a design device for data-driven vibration suppression feedforward control. [Background technology]

[0002] In high-speed, high-precision positioning control of positioning mechanisms inherent in various industrial mechatronics, coupled vibrations of the positioning mechanism and the entire machine (for example, load resonance and machine stand vibration) can lead to deterioration of positioning accuracy.One control method for achieving high-speed, high-precision positioning while suppressing coupled vibrations is to install displacement or acceleration sensors in each structure that makes up the coupled vibration to create a fully closed loop.However, due to reasons such as the increased cost of adding sensors, restrictions on installation space, and the complexity of control design, this is often difficult to implement, and so semi-closed loop control is the mainstream in industry.

[0003] Model-based feedforward (FF) control is widely used as a vibration suppression control method within the framework of semi-closed control, but the problem is that precise system identification and control adjustment for the plant are required to achieve the desired control performance, which requires a great deal of effort.

[0004] Patent Document 1 describes a controller setting method for a two-degree-of-freedom control system that controls a plant using a feedback controller and an FF controller, in which the FF controller is set in a controller setting step by multiplying the model characteristics of a reference model that indicates the transfer function up to the plant's response to a target value, to which the same input signal as that of the FF controller is input, by the inverse characteristics of the transfer characteristics of a closed-loop system.

[0005] Non-Patent Document 1 describes ERIT (Estimated Response Iterative Tuning), which adjusts the FF controller so as to minimize the deviation between a predicted response calculated offline and an ideal response, as a data-driven design method for vibration suppression FF control for a coupled vibration system. [Prior art documents] [Patent documents]

[0006] [Patent Document 1] Japanese Patent Publication No. 2021-157429 [Non-patent literature]

[0007] [Non-Patent Document 1] Kaneko et al.: "A New Approach to Feedforward Controller Update in Two-Degree-of-Freedom Control Systems - Proposal of Estimated Response Iterative Tuning (ERIT) -", Transactions of the Society of Instrument and Control Engineers, Vol. 54, No. 12, pp. 857-864, 2018 Summary of the Invention [Problem to be solved by the invention]

[0008] In conventional technology, for example, ERIT, it is necessary to set a reference model that generates a target command corresponding to an ideal response before designing an FF controller. If an appropriate reference model cannot be set, there is a problem that coupled vibrations caused by multiple structures cannot be suppressed. Furthermore, if the characteristics of the plant are partially or entirely unknown, it is practically impossible to provide an appropriate reference model. Therefore, an object of the present invention is to solve the above problems and provide a design method and design device for data-driven vibration suppression FF control that does not require the setting of a complex reference model. [Means for solving the problem]

[0009] The present invention, which solves the above problems, is as follows. [1] This is a design method for an FF controller, which has multiple FF controllers to be designed, each of which has a common denominator polynomial and a controller structure in which the numerator polynomial has a free parameter, and which designs the free parameter by solving an optimization problem that minimizes the deviation between the target command generated by one of the multiple FF controllers and the predicted response. [2] This is a control device that has multiple FF controllers to be designed, each of which has a common denominator polynomial and a numerator polynomial with a controller structure called a free parameter. [3] A control device comprising the FF controller described in [2], further comprising a data-driven design algorithm executed using learning data including at least one of data on observable state quantities obtained from a predetermined plant controlled by the control device. [Effects of the Invention]

[0010] It is possible to suppress coupled vibrations, including structures for which data has not yet been acquired, and it provides superior control performance compared to conventional technologies, while eliminating the cost of installing sensors for acquiring learning data. Furthermore, because a reference model is not required, it is possible to eliminate the trial-and-error process of setting a reference model that was required to suppress coupled vibrations with conventional technologies, thereby reducing the time and effort required for control design. [Brief explanation of the drawings]

[0011] [Figure 1] FIG. 1 is a diagram showing a schematic diagram of a situation in which coupled vibration occurs in a servo device of a machine tool or processing machine that is configured by connecting multiple structures. [Figure 2] FIG. 1 is a diagram showing a control block diagram illustrating a data-driven design of an FF controller, which is one embodiment of the present invention. [Figure 3] 1A and 1B are diagrams showing the FF controller structure of the present invention and the prior art (ERIT), respectively. [Figure 4] FIG. 1 is a block diagram of a two-degree-of-freedom positioning control system having an FF controller according to the present invention. [Figure 5] FIG. 10 is a diagram showing frequency characteristics of a galvanometer scanner. [Figure 6] FIG. 10 is a diagram showing learning data used in designing an FF controller. [Figure 7] FIG. 10 is a diagram showing the frequency characteristics of Fr(z) of the FF controller. [Figure 8]FIG. 10 is a diagram showing the frequency characteristics of Fu(z) of the FF controller. [Figure 9] FIG. 10 is a diagram showing an FF control input waveform. [Figure 10] 1A and 1B are diagrams showing motor and mirror angular displacement response waveforms for (a) ERIT (conventional method) and (b) VF-DDC (method of the present invention), respectively. [Figure 11] 1A and 1B are diagrams showing motor-mirror angular displacement deviation waveforms, respectively, for (a) ERIT (conventional method) and (b) VF-DDC (method of the present invention). DETAILED DESCRIPTION OF THE INVENTION

[0012] Hereinafter, embodiments of the present invention will be described with reference to the drawings. The present invention is not limited to the following embodiments, and changes, modifications, and improvements can be made without departing from the scope of the invention.

[0013] As shown in Figure 1, in a servo device 1 for a machine tool / processing machine, the driving force acting on a table 2 generates vibrations due to a load 4 connected to the table 2, and the driving reaction force generates vibrations in the machine base 3 on which the table 2 is placed and vibrations due to ancillary equipment 5 connected to the machine base 3, resulting in coupled vibrations due to the multiple structures that make up the machine. Position information required for the table 2 to perform its task can be measured and collected by a position sensor 6. The connections between the machine base 3 and floor 7, the table 2 and load 4, and the machine base 3 and ancillary equipment 5 can be represented by a Voigt model.

[0014] As shown in Fig. 2, a control block diagram 11 representing a data-driven design of an FF controller according to one embodiment of the present invention includes an FF controller 12, a FB controller C 13, a plant P 14, a memory 15, and a data-driven control design algorithm 16. In the control block diagram 11, a command r is input to the FF controller 12, and a target command r is output from the FF controller 12. * and FF control input are output respectively. *The FF control input is input to the FB controller C13, and the FF control input is input to the plant P14. As shown in FIG. 3(a), there are, for example, two FF controllers 12. r (ρ r ) 12a and FF controller F u (ρ u ) 12b, and FF controller F r (ρ r )12a is the target command r * FF controller F u (ρ u )12b is FF control input u ff Here, the FF controller F r (ρ r ) 12a and FF controller F u (ρ u ) 12b, the denominator polynomials of the compensators are common, and the numerator polynomials have a controller structure in which the parameters are free. The number of FF controllers 12 is not limited to two, and can be two or more. In this case, the denominator polynomials of the compensators of the FF controllers are common, and the numerator polynomials have a controller structure in which the parameters are free.

[0015] As shown in FIG. 3(b), even in the prior art (ERIT), the FF controller F u (ρ u ) 22b is the FF controller F u (ρ u ) FF control input u as in 12b ff On the other hand, the FF controller T des Regarding 22a, before designing the FF control, a reference model is required to generate a target command based on the setting of ideal response characteristics. As a result, in situations where the coupled vibration phenomenon is unknown or there is a lot of uncertainty, it is practically difficult to set an effective ideal response characteristic. However, in the same figure (a), the FF controller F r (ρ r )12a, no normative model is required. More details on this will be explained later.

[0016] The output from the plant P14 is the observable y1 and the unobservable y2, ..., y N The observable y1 is sent to memory 15 together with command r and is input as learning data to data-driven control design algorithm 16. Then, parameters calculated by applying data-driven control design algorithm 16 based on the learning data are reflected in FF controller 12.

[0017] The block diagram shown in FIG. 4 is a block diagram 21 of a two-degree-of-freedom positioning control system equipped with an FF controller according to the method of the present invention, which is used when coupled vibration occurs.

[0018] In the block diagram 21 of the two-degree-of-freedom positioning control system in FIG. 4, r is the position command, r * is the target trajectory, u ff is the FF control input, e is the motor trajectory tracking error, C(z) is the FB controller, F r (z,ρ r ) and F u (z,ρ u ) is the FF controller, ρ r and ρ u is the parameter vector to be designed.

[0019] Based on the command r, the FF controller F r (z,ρ r ) 22a and FF controller F u (z,ρ u )22b, the target trajectory r * and FF control input u ff are output respectively. Target trajectory r * is fed to the FB controller C(z) 23, and the output from the FB controller C(z) 23 is the transfer function P mot (z) and P mir On the other hand, the FF control input u ff is input directly into the plant, Plant24. As will be explained later, the transfer function P mot (z) and P mir (z) is the motor angular displacement y from the control input umot , mirror angular displacement y mir The transfer function is the motor angular displacement y mot is observable, but the mirror angular displacement y mir is a state quantity that cannot be observed (unobservable). [Example]

[0020] (Overview of Galvanometer Scanners and Problem Setting) <Galvano Scanner Overview> The galvanometer scanner, which is the object of control, is a positioning mechanism used in a laser drilling machine for printed circuit boards, and in order to achieve high productivity and processing quality, a response frequency on the order of kHz and a positioning accuracy on the order of μm are required. A galvanometer scanner is broadly composed of a servo motor, a galvanometer mirror, and an encoder that detects the motor angular displacement, and exhibits the characteristics of a typical load resonance system with the mirror as the load. The only observable state quantity available for control is the motor angular displacement, and this signal is fed back (FB) to perform semi-closed loop control of the mirror angular displacement. Considering that the poles of the transfer function from the motor to the mirror are theoretically identical, the motor angular displacement y can be calculated by mot , mirror angular displacement y mir Transfer function P mot (z), P mir (z) can be expressed by equation (1). (Number 1) JPEG2026028384000002.jpg1297

[0021] Figure 5 shows the frequency characteristics of the galvanometer scanner measured using the sine wave sweep method. The mirror angular displacement was measured using a PSD sensor, and this signal was used for evaluation purposes only. Figure 5 shows that both the motor and mirror have major vibration modes with resonance frequencies of approximately 3.0 kHz and 6.0 kHz, and that when driven at high acceleration and deceleration, this coupled vibration reduces positioning accuracy.

[0022] <Question setting> The design problem of the FF controller 22 in the block diagram 21 of the two-degree-of-freedom positioning control system is to control the motor angular displacement y motis used as learning data, and the control parameters ρ that satisfy the control specifications (settling time, settling accuracy) described later for both the motor and mirror are calculated. r , ρ u The goal is to design the system in a data-driven control framework. r (z)=1, F u The data is acquired by performing a positioning operation using a one-degree-of-freedom control system with (z) = 0. The characteristics of each FF controller when acquiring learning data are not limited to this.

[0023] <Data-driven design of vibration suppression FF control> (Conventional method (ERIT) and its problems) Conventional methods generally use an FF controller F to generate a position command trajectory. r (z,ρ r ) contains y mot Ideal response characteristic T des (z) is designed in advance, and then the FF controller F u (z,ρ u ) is designed by data-driven design. Therefore, in the conventional method, F r (z,ρ r )=T des (z) and F u (z,ρ u ) design parameter ρ u This becomes a design problem based on the optimization problem of equation (2).

[0024] (Number 2) JPEG2026028384000003.jpg3297 where T ed : predicted end time, y^ mot :y mot (Note that the "^" written consecutively after y is written that way for convenience, where it should have been written above y, and the same applies to alphabets other than y.) In what follows, we will show a specific formulation example of the optimization problem of equation (2), and theoretically demonstrate that conventional methods cannot suppress coupled vibration of the mirror angular displacement (load side). First, when there is a SISO LTI system F with input x(t) and output y(t), for t=0, 1, ... , Ted x(t) and y(t) in are expressed as in equation (3).

[0025] (Number 3) JPEG2026028384000004.jpg649 where: (Number 4) JPEG2026028384000005.jpg5597

[0026] (4) A in the formula F , B F , C F , D F is the coefficient matrix when F is expressed in state space. At this time, the motor angular displacement y mot (t), t=0, 1…, T ed y mot When expressed as a vector, it becomes equation (5). (Number 5) JPEG2026028384000006.jpg697 where P mot , C, T des , F u (ρ u ) are P mot (z), C(z), T des (z), F u (z,ρ u ) is the matrix corresponding to P mot Since we assume that we do not have a model for P mot In this paper, we estimate the equation (5) using the mathematical formula that does not include . 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, Autom. and Syst., pp. 562-567(2017)), we use the training data r0, y obtained by a one-degree-of-freedom control system without FF control. mot0 and the position command r, the y^ in the two-degree-of-freedom control system is expressed by equation (6).mot Predict. (Number 6) JPEG2026028384000007.jpg1897

[0027] where: (Number 7) JPEG2026028384000008.jpg7997

[0028] From the above, the predicted response y^ by equation (6) mot By using this, the parameter ρ u In particular, the FF controller F u (z,ρ u ) to ρ u When a linear parameter structure is assumed for , equation (2) can be solved by the least squares method, and this method has been used in many previous research cases. Next, we consider the response characteristics when an FF controller designed using a conventional method is applied to a coupled vibration system. The optimal parameter ρ that ideally makes the trajectory tracking error e=0 is u opt If obtained, the FF controller F u is expressed as equation (8).

[0029] (Number 8) JPEG2026028384000009.jpg1397 At this time, the motor angular displacement y mot , mirror angular displacement y mir can be expressed by equation (9). (Number 9) JPEG2026028384000010.jpg2397

[0030] From equation (9), the motor side is T des (z) is the target trajectory r * While the mirror perfectly follows the motor, the zero point (anti-resonance) on the motor side becomes a response pole, causing a vibration response. des (z)N motOne approach would be to provide a characteristic that offsets the undesirable pole in (z), but this is difficult to achieve in a data-driven design method that does not assume the implementation of system identification, as it makes the design difficult to predict. In this sense, it is clear that conventional methods do not guarantee the suppression of unobservable state variables in coupled vibration systems.

[0031] <Method of the present invention> Considering the problems with the conventional methods, we have designed a vibration suppression data-driven control (VF-DDC) as the method of the present invention, which also guarantees the suppression of unobservable state quantities of coupled vibration systems. The requirement for a vibration suppression FF controller for coupled vibration systems is that it is possible to perform arbitrary pole placement in the transfer characteristics of both the motor angular displacement and the mirror angular displacement. One method is to use the transfer function of the controlled object (in this case, the P mot A controller structure based on the coprime factorization expression of (z) is given. (Number 10) JPEG2026028384000011.jpg2297 Here, Q(z) is a transfer function (generally a low-pass filter) that stabilizes and propagates the FF controller. When the FF controller has the structure of Equation (10), y mot , y mir can be expressed by equation (11). JPEG2026028384000012.jpg1997

[0032] From equation (11), it is possible to arbitrarily specify the response poles of both the motor and the mirror by Q(z), and it is clear that if the controller structure of equation (10) can be realized, it is possible to control the vibration of not only the motor but also the unobservable mirror. Therefore, the method of the present invention does not use the ideal response characteristic T des (z) is not pre-set, and F r (z,ρ r ) and F u (z,ρ u ) are considered as design targets, and we consider a design problem aiming to realize the response characteristics of equation (11). In the method of the present invention, the FF controller is designed with the design parameter ρ r , ρ u is defined as equation (12) using F r (z,ρ r) and F u (z,ρ u ) is common to Q(z). JPEG2026028384000013.jpg2996 where: JPEG2026028384000014.jpg5097

[0033] Next, we formulate an optimization problem to design the parameter ρ. First, we consider the target trajectory r * Generate F r (z,ρ r ) is the steady state * = r, we impose the equality constraint of Eq. (14). (Number 14) JPEG2026028384000015.jpg2297 Next, noting that the trajectory tracking error becomes e = 0 when equation (10) is realized, we set the predicted response y^ as the objective function. mot The trajectory tracking error r * -y^ mot The predicted trajectory tracking error can be expressed as a vector in the same way as in equation (6) by taking into account the two-degree-of-freedom control system shown in Figure 4, and is given by equation (15). (Number 15) JPEG2026028384000016.jpg4697 where Φ rm , Φ um、m =0, 1, ..., M is Eq. (16). (Number 16) JPEG2026028384000017.jpg1697 Note that G^ in equation (15) is equation (7), as in the conventional method. From the above, using equations (14) and (15), ρ can be calculated by Lagrange's undetermined multiplier method as a solution to the constrained optimization problem of equation (17).

[0034] JPEG2026028384000018.jpg2297

[0035] As with the conventional method, we clarify the response characteristics of the coupled vibration system obtained by applying the FF controller designed by the method of the present invention. opt When this is obtained, equation (18) holds. (Number 18) JPEG2026028384000019.jpg1397

[0036] Equation (18) is rearranged as the ratio of the FF controller to obtain equation (19). JPEG2026028384000020.jpg1997 From equation (19), it can be seen that the method of the present invention attempts to match the model with the controlled object using two FF controllers. If the order M of the FF controller is set higher than the order of the controlled object, ideally, F r (z,ρ r opt ), F u (z,ρ u opt ) are N mot (z), D(z) and the redundant polynomial. red When expressed as (z), y mot , y mir is expressed as equation (20). (Number 20) JPEG2026028384000021.jpg1697 From equation (20), the method of the present invention can ideally specify the response poles of both the motor and mirror arbitrarily using Q(z), just like equation (11). From the above, the method of the present invention is theoretically capable of suppressing unobservable state variables in a coupled vibration system, as shown in equation (20), and is expected to solve the problems of conventional methods.

[0037] (Experimental evaluation using a galvanometer scanner) <Experimental conditions> The target control specification is stroke Y rIn the point-to-point positioning operation of =6.6 mrad, it is specified that the settling accuracy of both the motor and mirror must be within ±13.2 μrad (μm order in terms of laser irradiation position) within a settling time of 1.00 ms. The positioning operation is performed by a two-degree-of-freedom control system (control period is T s =20μs), and the FB controller C(z) was a cascade connection of a PID compensator and a two-stage second-order IIR filter. The FB controller parameters were designed based on the method described in the literature (E. Kuroda, Y. Maeda, and M. Iwasaki, “Autonomous Parameter Design for Cascade-Structure Feedback Controller Based on Cooperative Optimization Method,” IEEJ J. Ind. App., Vol. 10, No. 4, pp. 457-468 (2021)) taking into consideration the expansion of the control band and robust stabilization of the first and second vibration modes. The position command r was an S-curve command that reached the target position in 0.2ms. Note that when acquiring the learning data, a one-degree-of-freedom control system was used as shown in paragraph

[0017] (Fig. 4) and paragraph

[0022] , and the target position arrival time of the S-curve command given at that time was set to 1.00ms. The r0 and y acquired as learning data mot0 This is shown in Figure 6. The acquired learning data is stored in the memory of the control device.

[0038] Next, regarding the design of the FF controller, as an example of the method of the present invention, the order of the FF controller is M=20, and Q(z) that defines the response is a low-pass filter shown in equation (21). (Number 21) JPEG2026028384000022.jpg2097 Here, the filter order is M to make the FF controller proper. Q = 20, and the cutoff frequency is r * ω is set so that it reaches the target position within the target settling time. Q = 2π 9763 rad / s. The predicted end time is T ed =500(T ed Ts was set to 10 ms). On the other hand, in the conventional method, on the premise that the coupled vibration characteristics of the galvanometer scanner are unknown, the ideal response characteristic T des (z) used the low-pass filter shown in Equation (22). (Equation 22) JPEG2026028384000023.jpg1797 Here, the filter order and the cut-off frequency are M des = 20 and ω des = 2π·6390 rad / s, respectively. Also, the FF controller F u (z) was given a FIR structure controller with an order of M = 200 as shown in Equation (23). JPEG2026028384000024.jpg1797 Although the order is higher compared to the method of the present invention, this is because in the FIR structure controller where parameter design is possible by the least squares method, it aims to realize the controller characteristics of Equation (8) as much as possible. The prediction end time was set to the same T ed = 500 as the method of the present invention.

[0039] <Design Results of FF Controller> Under the above design conditions, using the position command r0 stored in the memory as learning data and the motor angular displacement y, which is an observable state quantity of the plant, and the position command r at the time of designing the FF controller, a data-driven control design algorithm was executed by the processor on the control device, and the FF controller parameter ρ was calculated. mot0 Using the position command r0 stored in the memory as learning data and the motor angular displacement y, which is an observable state quantity of the plant, and the position command r at the time of designing the FF controller, a data-driven control design algorithm was executed by the processor on the control device, and the FF controller parameter ρ was calculated. The FF controllers F r (z) and F u (z) designed by the conventional method and the method of the present invention are shown in FIGS. 7 and 8, respectively. In both figures, the vertical dotted line indicates the first- and second-order resonance frequencies in P mot (z), and the vertical broken line indicates the first-order anti-resonance frequency. Also, the FF control input u u when applying the designed F ff (z) is shown in FIG. 9. The method of the present invention is at around the first-order anti-resonance frequency in F r (z), and in F uIn (z), the frequency characteristic reduces the gain near the primary and secondary resonance frequencies. This means that the characteristic is close to that of equation (20).

[0040] In contrast, the conventional method is F r (z) is F r (z)=T des Since it is (z), no shaping has been done for vibration control, and F u (z) has the characteristic of increasing the gain near the first anti-resonance frequency. ff Even in the conventional method, vibrations at approximately 2.5 kHz, which is near the first anti-resonance frequency, are clearly observed, and vibration excitation on the mirror side is expected.

[0041] <Positioning experiment results> When positioning is performed by a two-degree-of-freedom control system using the designed FF controller, mot , y mir The deviation Y r -y mot , Y r -y mir This is shown in Figure 11. As can be seen from the figure, with the conventional method, residual vibrations due to the primary vibration mode occur near the settling positions for both the motor and mirror, which greatly exceed the target settling accuracy of ±13.2 μrad, as indicated by the horizontal dotted line, and the vibrations on the mirror side, which is an unobservable state quantity, are more pronounced than on the motor side.

[0042] This is the anti-resonance frequency on the motor side, as explained in the theory in paragraphs

[0023] to

[0030] , and it is clear that the conventional method cannot suppress the continuous vibration. In contrast, the method of the present invention suppresses the residual vibration of both the motor and the mirror, and achieves positioning control that satisfies the target control specifications. The deviation Y of 1.00 to 10.00 ms in both methods r -y mot , Y r -y mir The RMS and settling time of the method of the present invention are shown in Table 1. Compared to the conventional method, the deviation RMS of the method of the present invention was reduced by 97.7% on the motor side and 99.3% on the mirror side, and the settling time was reduced by 89.4% on the motor side and 92.5% on the mirror side, verifying its effectiveness. (Table 1) JPEG2026028384000025.jpg21120

[0043] This paper describes a data-driven vibration suppression FF control design method (VF-DDC) for semi-closed controlled coupled vibration systems. This method is capable of suppressing not only observable state variables but also unobservable state variables in coupled vibration systems, and its design theory has been clarified by comparing it with the conventional method, ERIT. Furthermore, the method has been applied to the problem of high-speed, high-precision positioning control of a galvano scanner with load resonance characteristics, and the effectiveness of this method has been demonstrated through actual experiments. [Industrial Applicability]

[0044] As development costs continue to decrease, demand for data-driven design technology is expected to increase in the future market. For example, this technology can be used in the control design of servo devices in industrial and logistics machinery. [Explanation of symbols]

[0045] 1: Servo devices for machine tools and processing machines 2: Table 3: Machine stand 4: Load 5: Ancillary facilities 6: Position sensor 7:Floor 11, 21: Control block diagram 12, 22: FF controller 23:FB controller 12a, 22a: FF controller F r (ρ r ) 12b, 22b: FF controller F u (ρ u ) 13:FB controller C 14, 24: Plant 15: Memory 16: Data-driven control design algorithms r: Command (position command) r * :Target command (target trajectory) y1: Observable output y2, …, y N : Unobservable (unobservable) output u ff :FF control input e: Motor trajectory tracking error C(z): FB controller ρ r , ρ u :parameter vector P mir (z), P mot (z): Transfer function y mir : Mirror angle displacement y mot :Motor angular displacement

Claims

1. A method for designing a feedforward controller, comprising: a plurality of feedforward controllers to be designed; each of the feedforward controllers has a common denominator polynomial; and each of the numerator polynomials has a controller structure called a free parameter; and the free parameter is designed by solving an optimization problem that minimizes the deviation between a target command generated by one of the plurality of feedforward controllers and a predicted response.

2. A control device comprising a plurality of feedforward controllers to be designed, each of which has a controller structure in which the denominator polynomial of the feedforward controllers is common and the numerator polynomial is a free parameter.

3. The control device according to claim 2 , further comprising a data-driven design algorithm executed using learning data including at least one of data on observable state quantities acquired from a predetermined plant controlled by the control device.

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