JP7016078B2 - Control device - Google Patents

Description

The present invention relates to a control device, specifically, a control device that performs simple adaptive control on a controlled object to make an output follow a target value.

One of the inventors of the present invention has proposed a control device that performs simple adaptive control for a controlled object having wasted time (see, for example, Patent Document 1). This control device introduces a parallel feedforward compensator having a dead time for a controlled object having a dead time, and the parallel feedforward compensator is a transfer function that combines the controlled object and the parallel feedforward compensator. Is a device that provides compensation that satisfies the general strength and truth conditions.

International Publication No. 2013/187414

By the way, in a container crane, it is known that a rotary motion (skew motion) around a vertical axis is generated with respect to a container of a suspended load in a transport operation. In the control of the actuator for controlling this skew motion, in addition to the change in the motion characteristics due to the state of the suspended load and the response delay due to the dead time, there are input restrictions on the amplitude and rate of change of the input signal to the actuator. Therefore, in the device described in Patent Document 1 that does not consider the input restriction, the ideal input value based on the control law for the actuator and the actual input value are different. As a result, the output feedback control did not function effectively, resulting in deterioration of control performance and instability of the control system.

An object of the present invention is to provide a control device capable of performing robust simple adaptive control for a controlled object having a non-linear element such as an input restriction to quickly follow an output to a target value.

The control device of the present invention that achieves the above object is a control device that controls a control target having a non-linear element and a dynamic characteristic element, and includes a feedback controller and a parallel feed-forward compensator, and the feedback control is performed in the order of signal input. The instrument, the non-linear element, and the dynamic characteristic element are connected in series, and the parallel feedback compensator is connected in parallel to each of the controlled object and the dynamic characteristic element possessed by the controlled object. Two values, a value output from the feedback controller and a value output from the non-linear element, are input to the parallel feed forward compensator, and the parallel feed forward compensator controls the controlled object and the parallel feed forward. It is characterized in that the expansion system element including the compensator compensates to satisfy the general strength and truth condition, and the feedback controller performs feedback control to the expansion system element.

According to the present invention, by connecting a parallel feedforward compensator in parallel to each of a controlled object and a dynamic characteristic element of the controlled object, an expansion system element composed of a controlled object and a parallel feedforward compensator. Satisfies the general strength and truth conditions. Therefore, it is advantageous to guarantee the proximity stability of the adaptive output feedback control system for the expansion system element, and the output of the controlled object can be quickly followed to the target value by the robust adaptive output feedback control.

It is a block diagram which illustrates the embodiment of a control device. It is a block diagram which illustrates the basic concept of designing the parallel feedforward compensator of FIG. It is a block diagram which illustrates the nonlinear dynamics of the controlled object in a container crane. It is a numerical simulation result of the control device of the prior art which does not have a control device and a parallel feedforward compensator. It is a numerical simulation result of the control device which does not have a control device and a feedforward controller.

Hereinafter, embodiments of the control device will be described. In addition, "^" in this specification shall represent a superscript character for the character before it.

As illustrated in FIG. 1, the control device 1 is composed of a CPU that performs various information processing, an internal storage device that can read and write programs and information processing results used for performing the various information processing, and various interfaces. Hardware. The control device 1 includes a control target 10, an input unit 20, a feedback controller 30, a parallel feedforward compensator (PFC) 40, and a feedforward controller 50 as each functional element, and the control target 10 And an expansion system element 60 including a parallel feedforward compensator 40 is formed. Each functional element is stored in an internal storage device as a program, and is executed by the CPU in a timely manner. In addition to the program, each functional element may be configured by a programmable controller (PLC) that functions independently.

The controlled object (plant) 10 is a model in which an input value u (t) is input and an output value y (t) is output, and has a nonlinear element 11 and a dynamic characteristic element 12.

The nonlinear element 11 is a model in which an input value u (t) is input and an operation value f (u) is output, and the dynamics of the system cannot be completely captured in a linear manner. The nonlinear element 11 includes a model using a dynamic nonlinear estimator such as a sigmoid or a wavelet, an input restriction such as a gradient limit or saturation which is an exception in a linear model, and a static model such as a dead zone, unknown. An example is a model using an ordinary differential equation or a difference equation including parameters. Further, the nonlinear model 11 also includes a dead time (delay time) generated in the system. The nonlinear dynamics of the nonlinear element 11 are represented by f (.).

The dynamic characteristic element 12 is a model in which the operation value f (u) is input and the output value y (t) is output, and the dynamics of the system capture it linearly except for the non-linear element 11 of the controlled objects 10. It is a model to be. Examples of the dynamic characteristic element 12 include a first-order lag system and a second-order lag system. The transfer function of the dynamic characteristic element 12 is represented by G (s).

The input unit 20 is a functional element that outputs the target value r (t). As the input unit 20, a user interface such as an operation lever, a mouse, and a keyboard is exemplified. Further, as the input unit 20, one that uses a sensing device or a timer to change the target value r (t) over time, and one that automatically inputs the target value r (t) based on the operation of the device. Illustrated.

The feedback controller 30 is arranged between the input unit 20 and the control target 10 with respect to the signal flow, and is connected in series with the control target 10. The feedback controller 30 is a simple adaptive control (SAC: Simple Adaptive control) by adaptive output feedback control for the expansion system element 60 in which the control target 10 and the parallel feedforward compensator 40 are combined.
It is a controller that performs Control). The feedback controller 30 has _{a deviation between the target value r (t) and the actual output value ya (t) output from the expansion system element 60 −e a (} t) (= r (t) _−ya (t)). ) Is input, and the target input value u _e (t) that makes the deviation −e _a (t) zero or approaches zero is output. The variable feedback gain of the feedback controller 30 is represented by k (t).

The parallel feedforward compensator 40 is a compensator connected in parallel to each of the dynamic characteristic element 12 of the controlled object 10 and the controlled object 10. In the parallel feedforward compensator 40, the control input value u _e (t) output from the feedback controller 30 is input, and the operation value f (u) output from the non-linear element 11 is input to the expansion system. The element 60 is a compensator for compensating to satisfy the condition of General Positive Positive Positive (ASPR).

Here, the approximate strong positive and real conditions are three conditions that the relative order of the expansion system element 60 is "0" or "1", the highest coefficient is positive, and the minimum phase system. Is.

The parallel feedforward compensator 40 is a compensator designed by utilizing the idea of the Smith Act. Further, since the transfer function G (s) of the dynamic characteristic element 12 is unknown in the parallel feedforward compensator 40, the nominal model G ₀ (s) of the dynamic characteristic element 12 is used instead of the transfer function in the Smith predictor. It is a compensator configured using.

The parallel feedforward compensator 40 has a first nominal section 41, a second nominal section 42, and a compensating section 43. The parallel feedforward compensator 40 has a compensation value y _f (compensation value y f) obtained by subtracting the value output from the first nominal unit 41 from the value obtained by adding the value output from the second nominal unit 42 and the value output from the compensation unit 43. t) is output.

The first nominal part 41 and the second nominal part 42 have a function similar to that of the Smith predictor, and the closed loop obtained by the adaptive output feedback is a linear closed loop for the expansion system element 60 without the nonlinear dynamics f (.). It is a functional element that bears the function of assuming that the unit and the nonlinear dynamics f (・) are connected in series. The first nominal portion 41 and the second nominal portion 42 are designed as a nominal model of the dynamic characteristic element 12, and the transfer function of the nominal model is represented by G ₀ (s). The operation value f (u) output from the nonlinear element 11 is input to the first nominal unit 41, and the control input value u _e (t) output from the feedback controller 30 is input to the second nominal unit 42. To.

Here, the Smith method is a method in which a model of a controlled object including a dead time is included in a feedback control loop, and the output after the dead time is predicted and controlled. That is, the Smith predictor is a compensator that makes it possible to put the waste time of the controlled object out of the feedback control and feedback control the controlled object of the first-order lag excluding the waste time.

The compensation unit 43 compensates the expansion system element 60 to satisfy the general strength and truth condition. The compensation unit 43 is designed so that the transfer function G ^ _a (s) of the merging element 44 including the second nominal unit 42 and the compensation unit 43 satisfies the general strength / positiveness condition, and the transfer function is F (s). expressed. The compensation unit 43 inputs the control input value _ue (t) output from the feedback controller 30.
The actual output value _ya (t) output from the expansion system element 60 including the control target 10 and the parallel feedforward compensator 40 is expressed by the following mathematical formula (1).

In the above formula (1), assuming that the approximation error of the transfer function G ₀ (s) of the nominal model is small with respect to the transfer function G (s) of the dynamic characteristic element 12, the actual output value _ya (t) is It can be regarded as the following formula (2). A small approximation error means that the error between the output values of G (s) [f (u)] and G ₀ (s) [f (u)] is small in the assumed frequency band, and G (s) -The H∞ norm of G ₀ (s) is small enough.

That is, the actual output value y _a (t) is represented by the transfer function G ^ _a (s) of the merged element 44. As described above, since the compensating unit 43 is designed so that the merging element 44 satisfies the approximate strength / truth condition, the transfer function G ^ _a (s) of the merging element 44 satisfies the approximate strength / truth condition. Therefore, the expansion system element 60 satisfies the general strength / positiveness condition.

FIG. 2 assumes that the nonlinear element 11 of the controlled object 10 includes a dead time (transfer function is e ^-Ts ), and pushes the dead time out of the closed loop of the feedback control based on the idea of the Smith Act. It explains what can be regarded as a function. Here, the non-linear dynamics obtained by removing the dead time from the non-linear element 11 is g (.), And the transfer function obtained by adding the dead time to the dynamic characteristic element 12 is G (s) e ^-Ts . Further, let P (s) be the transfer function of the Smith predictor 45.

Here, if the operation value g (u) is equal to the control input value u _e (t) (ue ₍ t) = g (u)), the transfer function P (s) of the Smith predictor 45 is It is designed as the following formula (3). In the following mathematical formula, it is assumed that G _a (s) = G (s) + F (s), and G _a (s) satisfies the general strength and truth condition.

When the Smith predictor 15 is designed according to the above formula (3), the actual output value y _a (t) is expressed by the following formula (4).

As shown in the above formula (4), when the operation value g (u) is equal to the control input value u _e (t), the waste time is regarded as being pushed out of the closed loop of the feedback control, and the waste time is considered to have been pushed out. It is equivalent to feedback control of the first-order lag dynamic characteristic element 12 excluding.

However, if the operation value g (u) is not equal to the control input value u _e (t), the output fp (t) of the Smith predictor 45 is as follows in consideration of the nonlinear dynamics g (·). It is designed to be the formula (5). Since the transfer function G (s) is unknown, the transfer function G _a (s) is also unknown. Therefore, assuming that the transfer function of the nominal model of the dynamic characteristic element 12 is G ₀ (s), instead of the transfer function G _a (s), the transfer function G ^ _a (s) of the merged element 44 is used as a known transfer function. = G ₀ (s) + F (s)) is used.

When the Smith predictor 45 is designed as in the above equation (5), the control input value u _e (t) is expressed by the following equation (6).

When the approximation error of G ₀ (s) is small, the above formula (6) is expressed as the following formula (7).

上記の数式（７）で示す制御入力値ｕ_e（ｔ）が印加されたとき、実出力値ｙ_a（ｔ）は、以下の数式（８）で表される。

When the control input value u _e (t) shown in the above formula (7) is applied, the actual output value _ya (t) is expressed by the following formula (8).

Therefore, when u _e (t) = g (u), it becomes the same as the mathematical formula (4), and it is considered that the dead time is pushed out of the closed loop of the feedback control, and the first-order delayed motion excluding the dead time. It is equivalent to feedback control of the characteristic element 12.

Rewriting the block diagram 2 having the above mathematical formula (5) as a compensator is equivalent to the block diagram of the enlarged system element 60 illustrated in FIG. In FIG. 1, C = k (t). Further, since the nonlinear dynamics f (.), The nonlinear dynamics g (.) And the waste time (e ^-Ts ) are equivalent, the waste time is included in the nonlinear element 11. On the other hand, when the dead time is included in the dynamic characteristic element 12, the dead time may be included in the first nominal portion 41 in the same manner.

As illustrated in FIG. 1, the feedforward controller 50 is applied inside the parallel feedforward compensator 40, is connected in parallel to the feedback controller 30, and is not applied to the parallel feedforward compensator 40. It is a controller configured as such. The feedforward controller 50 has an ideal input unit 51, an output error input unit 52, and an input removal unit 53, and the ideal input unit 51 and the output error input unit 52 are connected in parallel to each other.

The ideal input unit 51 inputs the state vector ω of the target value r (t) and outputs the ideal input value v ^* (t). For the ideal input value v ^* (t), the output value y (t) of the controlled object 10 achieves perfect follow-up to the target value r (t) using a radial basis function network (RBFN: Radial Basis Function Network). It is a numerical value calculated approximately as such.

When the unknown ideal input value is v _nn (t) and approximated using the radial basis function network, the unknown ideal input value v _nn (t) is expressed by the following formulas (9) to (12). .. Here, W is a weight vector, l is the number of nodes in the neural network, and μ _i and η _i are design parameters.

The radial basis function network is a neural network that develops a nonlinear function with a radial basis function, and is known to have no initial value dependence and to be processed at a high speed among many neural networks. Further, the radial basis function is a function having circular contour lines, and the value decreases monotonically with respect to the distance from the center point, and the Gaussian function is exemplified.

When the above formulas (9) to (12) hold, the ideal weight that satisfies the following formula (13) with a certain compact set (ω ∈ Ω ω ⊂ R ^q ) for a sufficiently large number of nodes l. W ^* exists.

Therefore, the ideal input value v ^* (t) is composed of the following mathematical formula (14). Since the ideal weight W ^* is unknown, the estimated value W ^ (t) of the ideal weight is used.

The ideal input unit 51 may be configured by a neural network other than the radial basis function network (for example, a convolutional neural network or a recursive neural network) or the reciprocal of an approximate system (inverse function). However, the ideal input unit 51 preferably uses a neural network rather than the reciprocal of the approximate system, and more preferably uses a radial basis function network among various neural networks. By using a neural network, it is not necessary to obtain a new system that occurs when the reciprocal of the approximate system is adopted, and the labor required for the system can be reduced and the accuracy can be improved. Further, the neural network radial basis function network has a simple structure as compared with other neural networks of unknown weight vector × known basis function. Therefore, by using the radial basis function network for the ideal input unit 51, the time required for the calculation that occurs when another neural network is used can be shortened, and adjustment by many experiments and tests can be omitted.

The output error input unit 52 inputs the target value r (t) and outputs the correction value V (t). The correction value V (t) is expressed by the following mathematical formula (15) based on the output error e (t) that actually occurs when the target value r (t) is input. Here, 1 / K _n is set as the nominal value of the target value r (t) in the steady state.

The output error input unit 52 is a functional element that corrects the error of the target value r (t) in the steady state by the integral term of the normalized error. By providing the output error input unit 52, when the target value r (t) fluctuates greatly, the tracking cannot be made in time only by the ideal input value v ^* (t) output from the ideal input value 51 by the nonlinear element 11. It will be advantageous to eliminate the problem.
The characteristic equation in the simple adaptive control of the control device 1 is expressed by the following equation (16).

Further, k (t) and W ^ (t) of the above equation (16) are integral parameter adjustment rules (adaptive adjustment rules) including sigma correction terms represented by the following equations (17) and (18). Obtained by.

As described above, the control device 1 connects the parallel feedforward compensator 40 in parallel to each of the nonlinear element 11 and the dynamic characteristic element 12 of the controlled object 10 in parallel to feed the dynamic characteristic element 12 in parallel. The expansion system element 60 including the forward compensator 40 satisfies the general strength and truth condition. Therefore, it is advantageous to guarantee the proximity stability of the adaptive output feedback control system composed of the mathematical formulas (16) to (18) for the expansion system element 60, and the actual output value y is obtained by the robust adaptive output feedback control. It is possible to quickly make _a (t) follow the target value r (t).

Further, the control device 1 applies the feedforward controller 50 to the inside of the parallel feedforward compensator 40, so that the actual output value y _a (t) even when the uncertainty of the control target 10 and the variation in the characteristic change are large. ) Can completely follow the target value r (t).

Specifically, the result of performing simple adaptive control by the control device 1 for the control of the actuator related to the skew motion in the container crane is shown.

Here, the transfer function G (s) of the dynamic characteristic element 12 with the actuator related to the skew motion as the control target 10 is expressed by the following mathematical formula (19). K ₁ is the gain, ω is the skew angle frequency, and ζ is the attenuation factor. In the verification, K ₁ = 0.0098, ω = 0.4, and ζ = 0.01 are given, and the true value is unknown. However, it is assumed that the nominal values shown below are known and given. Further, the transfer function G ₀ (s) of the nominal model of the dynamic characteristic element 12 is expressed by the following mathematical formula (20). It should be noted that Kn = 0.01, ωn = 0.5, and ζn = 1 are given as the nominal values.

The nonlinear dynamics f (.) Of the nonlinear element 11 whose control target 10 is the actuator related to the skew motion is shown in FIG. Note that τ is the time constant of the actuator, T is the wasted time, K _J is the static gain, and K _px and K _pv are the feedback gains. It is assumed that τ, T, and K _J are known, and K _px and K _pv are adjusted to appropriate values in advance by experiments and tests. In the verification, τ = 0.1, T = 0.5, K _J = 0.5, K _px = 21.9296, and K _pv = 0.0981 are given. Further, the upper and lower limit values of saturation are set to ± 100, and the upper and lower limit values of the rate of change are set to ± 200.

The transfer function F (s) of the compensation unit 43 is expressed by the following mathematical formula (21). It is assumed that the compensation value y _f (t), which is the output of the parallel feedforward compensator 40, converges to "zero" when the control target 10 is in the steady state. In the verification, α ₁ = 0.1, β ₁ = 0.002, β ₂ = 0.001, a = 0.1, and b = 1.

The parallel feedforward compensator 40 can reduce the error between the output value _y (t) and the actual output value ya (t) by reducing β ₁ and β ₂ as in the above verification. However, if β ₁ and β ₂ are made too small, robustness may be reduced due to the influence of noise. Therefore, the parallel feedforward compensator 40 can eliminate the influence of the parallel feedforward compensator 40 in the steady state by adding a proper filter (bs / (s + a)) including a differential term.

As design parameters in the above formulas (17) and (18), γ = 1.0 × 105, σ = 1.0 × ^{10 -3} , Γ = 1.0 × 10 ² , σω = 1.0 × 10 ^-2 , S (ω) = r (t), α = 2.

FIG. 4 shows _a simulation in which the target value r (t) is constant and the initial value is given to the actual output value ya (t), and the solid line and the dotted line are the results of the control device 1 of the embodiment. Is shown, and the alternate long and short dash line shows the results (Y (t), F (u)) by the conventional control device without the parallel feed-forward compensator 40. In the simple adaptive control of the control device 1, the actual output value ya (t) follows the target value r (t) and converges over time. On the other hand, in the control device of the prior art, the output value Y (t) does not follow the target value r (t) and does not converge.

FIG. 5 shows a simulation in which an initial value is given to the target value r (t), the solid line and the dotted line show the result by the control device 1 of the embodiment, and the alternate long and short dash line has the feed forward controller 50. The result (y _b (t)) by the control device 1 is shown. Here, K ₁ = 0.0147 is given so that the gain K ₁ of the controlled object 10 includes an error of 50%, and the control device 1 having no feedforward controller 50 has a fixed gain instead. Only 1/0.01 is applied. Even if the value of the gain K ₁ of the controlled object 10 and the value of the nominal value K _n of the nominal model G0 (s) deviate significantly, the actual output value y _a (t) is swift in the simple adaptive control of the control device 1. Follows the target value r (t). On the other hand, in the control device 1 without the feedforward controller 50, the time required for tracking is long.

In the above-described embodiment, the actuator that controls the skew rotation motion generated in the suspended load of the container crane is exemplified as the control target 10, but the control target is not limited to the present embodiment.

In the above-described embodiment, an example including the feedforward controller 50 connected in parallel to the feedback controller 30 has been described, but even if the feedforward controller 50 is not provided, the actual output value _ya (actual output value ya) ( If it can be expected that the time required to follow t) to the target value r (t) is short, the feedforward controller 50 may not be provided.

1 Control device 10 Control target 11 Non-linear element 12 Dynamic characteristic element 30 Feedback controller 40 Parallel feedforward compensator 60 Expansion system element

Claims (3)

In a control device that controls a controlled object having a non-linear element and a dynamic characteristic element,
A feedback controller and a parallel feedforward compensator are provided, and the feedback controller, the nonlinear element, and the dynamic characteristic element are connected in series in the order of signal input, and the parallel feedforward compensator is the controlled object and the control target. It is connected in parallel to each of the dynamic characteristic elements of the controlled object, and is connected in parallel.
Two values, a value output from the feedback controller and a value output from the non-linear element, are input to the parallel feedforward compensator, and the parallel feedforward compensator controls the controlled object and the parallel feed. The expansion system element including the forward compensator compensates to satisfy the general strength and truth conditions.
A control device characterized in that the feedback controller is configured to perform feedback control on the expansion system element. The parallel feedforward compensator has a first nominal section, a second nominal section, and a compensating section.
The first nominal part and the second nominal part are designed based on the nominal model of the dynamic characteristic element, and the compensating part is a general strong positive condition that the merged element including the compensating part and the second nominal part is a general condition. Designed to meet,
The value output from the non-linear element is input to the first nominal unit, and the value output from the feedback controller is input to the second nominal unit and the compensation unit.
The control according to claim 1, wherein a value obtained by subtracting a value output from the first nominal unit from a value obtained by adding a value output from the second nominal unit and a value output from the compensation unit is output. Device. A feedforward controller connected in parallel to the feedback controller is provided.
The value input to the nonlinear element is a value obtained by adding the value output from the feedback controller and the value output from the feedforward controller.
The value output from the nonlinear element and input to the parallel feedforward compensator is a value obtained by subtracting the value output from the feedforward controller between the nonlinear element and the parallel feedforward compensator. The control device according to claim 1 or 2.

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