JP2018163395A - Control method, control device and control program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To properly control an object to be controlled using an estimated value that is not necessarily converged to a true value.SOLUTION: This control method generates a gain matrix used for estimating an internal state of an object to be controlled based on the equation corresponding to the condition satisfied by the variable representing the internal state of the object to be controlled, and includes a process of controlling the object to be controlled based on the estimation result of the internal state of the object to be controlled generated by the observer using the generated gain matrix.SELECTED DRAWING: Figure 12

Description

  The present invention relates to a feedback control technique.

  A dynamic system is a system whose output depends not only on current inputs but also on past inputs. In particular, a dynamic system represented by a discrete-time linear state equation (1) and a linear output equation (2) as follows is called a discrete-time linear time-invariant system.

FIG. 1 shows a block diagram of the above discrete time linear time invariant system. X [k + 1] is obtained by adding Ax [k] and Bu [k]. Further, y [k] is obtained as Cx [k]. q ⁻¹ is an operator for reducing k of x [k] by 1.

  However, it is not always possible to directly observe the state of the dynamic system. If direct observation is not possible, the state is estimated from the observable output. For example, in feedback control, an internal state of an observation or control target (hereinafter referred to as a control target) is estimated based on an observable output, and an input is determined according to the estimated internal state.

  An apparatus that calculates the value of a state that converges over time for a linear system that is detectable is called an observer. The estimated value by the observer is guaranteed to converge to a true value when sufficient time has passed. In the conventional technique, an estimated value after a sufficient time that can be considered that the estimated value has converged to a true value has been used for control.

However, when the control target is not stable, the internal state may change and control may not be in time if waiting for the estimated value to converge to a true value. 2 and 3 show the relationship between time and state. 2, the vertical axis represents the value of the state x _1, the horizontal axis represents time. 3, the vertical axis represents the value of the state x _2, the horizontal axis represents time. True values are plotted with solid lines, and estimated values are plotted with broken lines. In both FIG. 2 and FIG. 3, since the state changes until the estimated value converges to a true value, an inappropriate state may occur before the control based on the estimated value after convergence is executed. There is sex. On the other hand, before the estimated value converges to the true value, the constraints that the true state satisfies (for example, linear equation relations) are not satisfied, and control based on the estimated value cannot be performed. There is.

In addition, for example, when the estimated value is converted so as to satisfy the same constraints as the true state by the projection operation and used for the control, it is necessary to perform conversion every time the estimated value is obtained, which increases the calculation time. Therefore, in an unstable situation (for example, a situation where there is no time margin for generating a value used for control), control based on an inaccurate value is performed, resulting in instability. May lead to control. FIG. 4 shows the relationship between the value of the state x ₁ and the time when the calculation time increases, and FIG. 5 shows the relationship between the value of the state x ₂ and the time when the calculation time increases. In both FIG. 4 and FIG. 5, the true value fluctuates in vibration, and the control is unstable.

JP-A-10-54279

R.F.Stengel, "Optimal Control and Estimation", Dover edition, Dover Publications, 1994. Gene F. Franklin, J. David Powell and Michael Workman, "Digital Control of Dynamic Systems", third edition, Ellis-Kagle Press, 1998. Mustapha Ait Rami, Fernand Tadeo and Uwe Helmke, "Positive observers for linear positive systems, and their implications", International Journal of Control, vol.84, no.4, pp.716-725, 2011.

  In one aspect, an object of the present invention is to provide a technique for appropriately controlling a control target using an estimated value that does not necessarily converge to a true value.

  According to an aspect of the present invention, there is provided a control method that generates a gain matrix used to estimate an internal state of a controlled object based on an equation corresponding to a condition satisfied by a variable that represents the internal state of the controlled object, and uses the generated gain matrix. Includes a process of controlling the control target based on the estimation result of the internal state of the control target generated by.

  In one aspect, the control target can be appropriately controlled using an estimated value that does not necessarily converge to a true value.

FIG. 1 is a block diagram of a discrete-time linear time-invariant system. FIG. 2 is a diagram illustrating the relationship between time and state. FIG. 3 is a diagram illustrating the relationship between time and state. FIG. 4 is a diagram illustrating the relationship between time and state. FIG. 5 is a diagram illustrating the relationship between time and state. FIG. 6 is a diagram illustrating planes and values in the state space. FIG. 7 is a block diagram of the observer. FIG. 8 is a diagram showing planes and values in the state space. FIG. 9 is a diagram illustrating an overview of the dynamic system according to the first embodiment. FIG. 10 is a functional block diagram of the control device. FIG. 11 is a functional block diagram of the control target apparatus. FIG. 12 is a diagram illustrating a processing flow of processing executed by the design unit. FIG. 13 is a diagram illustrating a processing flow of processing executed by the state estimation unit. FIG. 14 is a diagram illustrating a processing flow of processing executed by the communication unit. FIG. 15 is a diagram illustrating a processing flow of processing executed by the communication unit. FIG. 16 is a diagram illustrating an overview of a dynamic system according to the second embodiment. FIG. 17 is a functional block diagram of a computer.

[Embodiment 1]
In the present embodiment, a discrete-time linear time-invariant system that can be detected and whose state satisfies the following linear equation (3) is set as a control target.

  The linear state equation (1) and the linear output equation (2) are as shown above, and A, B, C, W and υ are known. As shown in FIG. 6, the linear equation (3) means that the value of the state is on a plane in the state space (that is, the conservation law is established).

  In general, the estimated value ^ x [k + 1] by the observer is expressed as follows.

  The block diagram of the observer is as shown in FIG.

  The matrix L is a gain matrix (also called an observer gain). The gain matrix is obtained, for example, by solving an LMI (Linear Matrix Inequality) solvable problem. The LMI solvable problem is a problem in which an efficient numerical calculation method is known, and a solver (for example, an SDP (SemiDefinite Program) solver) exists, and is therefore suitable as an existence determination method and a configuration method.

  First, a matrix X and a matrix Y are obtained by solving the following LMI solvable problem based on the inputted A, B, and C.

This expression indicates that the left-hand side matrix is positive definite. The gain matrix is calculated as L = X ⁻¹ Y. Thereby, an estimated value ^ x [k + 1] can be obtained.

  However, as described in the background section, the estimated value obtained by such a method may not satisfy the equality constraint. This means that the estimated value may not be on a plane in the state space, as shown in FIG. Further, if the conversion is performed so that the estimated value exists on a plane in the state space, the calculation time may be long and the control may become unstable.

  Therefore, in the following, the true value is satisfied with the passage of time while satisfying the same linear equation as the true value (Condition A-2) without increasing the amount of calculation as compared with a normal observer (Condition A-1). Consider a method for determining whether there is an observer (condition A-3) that calculates an estimated value that converges to. Then, when such an observer exists, a method (condition C) based on an efficient numerical calculation method that can specifically realize such an observer (condition B) is examined.

  With respect to the condition A-1, a necessary and sufficient condition for preventing the amount of calculation from increasing as compared with a normal observer is that the calculation formula has the same format as that of a normal observer. That is, the calculation formula of the present embodiment is in the form of formula (5).

  Regarding condition A-2, the necessary and sufficient conditions for the estimated value to satisfy the same linear equation as the true value are W ^ x [0] = υ and WL = 0. The proof is as follows. First, the following holds.

(Sufficient)
When WL = 0, the following holds:

  That is, since W ^ x [k] has the same initial value as Wx [k] and follows the same recurrence formula as Wx [k], the following holds.

(necessity)
Conversely, when WL ≠ 0, there is a case where the following expression does not hold.

  Therefore, since W ^ x [k] follows a recurrence formula different from Wx [k], formula (9) does not hold. This completes the proof of the necessary and sufficient conditions for Condition A-2.

  Regarding condition A-3, the following is referred to as an error system.

  The convergence of the estimated value to a true value over time is referred to as “the error system is stable”. A necessary and sufficient condition (that is, a necessary and sufficient condition for the condition A-3) for the estimation value calculation method that makes the error system stable (that is, such a gain matrix exists) is expressed by Equation (6). ) Exists in the solution of the LMI solvable problem.

Regarding condition B, in order to realize an observer that stabilizes the error system, the gain matrix of equation (5) may be obtained as L = X ⁻¹ Y.

From the above, the following problem in which Equation (6), which is a necessary and sufficient condition for Condition A-3, and WL = 0, which is a necessary and sufficient condition for Condition A-2, are combined, and L = X ⁻¹ Y is substituted. If it can be solved, Condition A-1, Condition A-2, Condition A-3 and Condition B are satisfied.

  However, since Equation (12) is a nonlinear problem with a matrix as a variable, an efficient numerical calculation method cannot be applied, and the condition C is not satisfied.

  Therefore, in the present embodiment, a necessary condition for the estimated value to satisfy the linear equation is represented by an equation relating to the gain matrix, and using this equation, the condition A-1, the condition A-2, the condition A-3, and Condition B is reduced to an LMI solvable problem.

  First, a singular value decomposition (Singular Value Decomposition) is performed on the coefficient matrix W of the linear equation as follows. U and V are orthogonal matrices. Note that the singular value decomposition can be executed because the equation is limited to a linear equation rather than a general equation (f (x [k]) = 0).

  It is determined whether there is a gain matrix L that satisfies the following conditions (a) and (b). If there is, the gain matrix L is calculated.

The condition (a) is that the gain matrix L is expressed as follows using Λ∈R ^{(nr) × p} and the orthogonal matrix V.

  Condition (a) is a necessary and sufficient condition for WL = 0. See appendix for this proof. Thus, by expressing the necessary and sufficient condition of the condition (A-2) in the form of the expression (14), it becomes possible to reduce to the LMI solvable problem.

  Condition (b) is that it exists inside a circle having a radius of 1 centered at the origin in all eigenvalue complex planes of A-LC.

  When there is a gain matrix L that satisfies the conditions (a) and (b), the gain matrix L is calculated, and the observer is set to perform state estimation according to the equation (5) based on the calculated gain matrix L. Set. Hereinafter, the observer set in this way is referred to as a linear equation storage observer.

  The procedure for determining whether there is a gain matrix L satisfying the conditions (a) and (b) and calculating the gain matrix L when the gain matrix L exists is as follows.

  First, the following LMI solvable problem is solved.

  When Expression (15) is solvable (that is, when solutions X and Y exist), it is determined that there is a gain matrix L that satisfies the conditions (a) and (b). When Expression (15) is not solvable, it is determined that there is no gain matrix L that satisfies the conditions (a) and (b). When the equation (15) is solvable, the gain matrix L is calculated based on the following equation.

  The proof that the existence of the gain matrix L can be determined by the equation (15) and that the gain matrix can be calculated by the equation (16) is shown below.

  The necessary and sufficient condition for the error system expressed by Equation (11) to be stable (n → ∞, x [k] − ^ x [k] → 0) is that all eigenvalues of A-LC are complex planes. Exists within a circle of radius 1 centered at the origin, which is equivalent to the existence of a matrix P and a gain matrix L that satisfy the following matrix inequality (ie, Lyapunov inequality for discrete-time linear time-invariant systems): is there. For this point, see “Yoshio Sugawara,“ System Control by LMI ”, Morikita Publishing, 2012”.

  Substituting Equation (14), which is a condition equivalent to WL = 0, into this matrix inequality gives the following.

The existence of the matrix P and the matrix Λ satisfying this matrix inequality is a necessary and sufficient condition for the existence of the gain matrix L in the form of the equation (14) that makes the error system stable. When VV ^T = I is inserted into the first equation and rearranged, and V ^T is applied from the left side of both sides of the second equation and V is applied from the right, the result is as follows.

  The existence of the matrix P and the matrix Λ satisfying this expression is a necessary and sufficient condition for the existence of the gain matrix L in the form of the expression (14) that makes the error system stable.

Here, when X: = V ^T PV is set, it becomes as follows.

  The existence of the matrix X and the matrix Λ satisfying this expression is a necessary and sufficient condition for the existence of the gain matrix L in the form of the expression (14) that makes the error system stable.

  This equation is also a Lyapunov inequality for a discrete-time linear time-invariant system and is equivalent to the following equation. For this point, refer to “Satomi Ohara,“ Control System Design Using Matrix Inequalities Approach ”, Corona, 2016”.

  Therefore, the existence of the matrix X and the matrix Λ satisfying this expression is a necessary and sufficient condition for the existence of the gain matrix L in the form of Expression (14) that stabilizes the error system.

  Furthermore, if Y: = XΛ, the following linear matrix inequality can be obtained.

  Therefore, there exists a gain matrix L in the form of equation (14) that stabilizes the error system only when this linear matrix inequality has a solution X> 0 and a solution Y. A specific gain matrix L is obtained from the definition of Y as shown in Expression (16).

  Hereinafter, specific modes of the present embodiment based on the above discussion will be described.

  FIG. 9 shows an outline of the dynamic system according to the first embodiment. The control device 1 and the control target device 3 controlled by the control device 1 are connected to a network 2 such as a LAN (Local Area Network) or the Internet.

  The control device 1 is, for example, a personal computer, a server, or a microcontroller. FIG. 10 shows a functional block diagram of the control device 1. The control device 1 includes a design unit 101, a state estimation unit 103 that executes processing as an observer, a communication unit 105, an output data storage unit 111, an estimated value storage unit 113, and a work data storage unit 115. .

  The design unit 101, the state estimation unit 103, and the communication unit 105 are realized by loading a program into the memory 2501 in FIG. 17 and executing it by a CPU (Central Processing Unit) 2503. The output data storage unit 111, the estimated value storage unit 113, and the work data storage unit 115 are provided on a memory 2501 or an HDD (Hard Disk Drive) 2505 in FIG.

  The design unit 101 calculates the gain matrix L based on the parameters stored in the work data storage unit 115 and stores the calculated gain matrix in the work data storage unit 115. The state estimation unit 103 calculates an estimated value of the state of the control target device 3 based on the data stored in the work data storage unit 115 and the data stored in the output data storage unit 111, and estimates the calculated estimated value The value is stored in the value storage unit 113. The communication unit 105 receives the output of the control target device 3 from the control target device 3 and stores the received output in the output data storage unit 111. In addition, the communication unit 105 transmits an input to the control target device 3 to the control target device 3.

  In FIG. 11, the functional block diagram of the control object apparatus 3 is shown. The control target device 3 includes a sensor 301 that is a physical sensor, a controlled unit 302, and a communication unit 303.

  The sensor 301 measures an observable output y. The operation of the controlled unit 302 is controlled according to the input u received from the control device 1. The communication unit 303 receives the input u from the control device 1. In addition, the communication unit 303 transmits the output y measured by the sensor 301 to the control device 1.

  For example, when the control target device 3 is a vehicle, the controlled unit 302 is, for example, a motor, the input u is the rotation speed of the motor, the output y is, for example, position information of the control target device 3, and the state x is, for example, a position It is a combination of information and speed information of the control target device 3. For example, when the control target device 3 is a plurality of water storage tanks, the controlled unit 302 is a pump that adjusts the amount of water in the plurality of water storage tanks, for example. Yes, the output y is, for example, the amount of water in one of the plurality of storage tanks, and the state x is the amount of water in each of the plurality of storage tanks, for example. However, the embodiment is not limited to such an example. For example, dynamic systems such as electric circuits, chemical plants, blast furnaces, air conditioners, robots, servers, server rooms, and data centers may be targeted.

  Processing executed by the design unit 101 of the control device 1 will be described with reference to FIG.

  The design unit 101 accepts input of parameters (here, matrices A, B, C, and W of Expression (15)) (FIG. 12: step S1) and stores them in the work data storage unit 115. In step S1, the design unit 101 may read out parameters stored in advance in the storage area.

  The design unit 101 uses the parameters stored in the work data storage unit 115 in step S1 to execute processing for obtaining the solutions X and Y of the LMI solvable problem represented by the equation (15) (step S3).

  The design unit 101 determines whether a solution exists in step S3 (step S5). When there is no solution (step S5: No route), the design unit 101 executes the following processing. Specifically, the design unit 101 performs setting so that the state estimation unit 103 calculates an estimated value by a normal method (step S7). Then, the process ends. The normal method is, for example, a process of converting the estimated value so as to satisfy the equality constraint after obtaining the estimated value with a normal observer. Since the process of step S7 is not the main process of the present embodiment, detailed description thereof is omitted.

  On the other hand, when a solution exists (step S5: Yes route), the design unit 101 executes the following processing. Specifically, the design unit 101 calculates the gain matrix L by Expression (16) using the obtained solutions X and Y (Step S9).

  The design unit 101 stores the gain matrix L calculated in step S9 in an area for setting the state estimation unit 103 in the work data storage unit 115 (step S11). Then, the process ends.

  By executing the processing as described above, the state estimation unit 103 can use a gain matrix L that can calculate an estimated value that satisfies the equality constraint.

  The process which the state estimation part 103 of the control apparatus 1 performs is demonstrated using FIG.

  The state estimation unit 103 reads the parameters input in step S1 and stored in the work data storage unit 115 and the gain matrix L stored in the work data storage unit 115 in step S11 (FIG. 13: step S13).

  The state estimation unit 103 initializes the estimated value ^ x (step S15).

  The state estimation unit 103 acquires the output y of the previous time from the output data storage unit 111 and acquires the input u of the previous time (step S17).

  The state estimation unit 103 uses the parameters and gain matrix read in step S13, the input u and output y acquired in step S17, and the estimated value ^ x calculated or initialized, and ^ x ← The estimated value ^ x is updated by A ^ x + Bu + L (y-C ^ x) (step S19). The state estimation unit 103 stores the updated estimated value ^ x in the estimated value storage unit 113.

  The state estimation unit 103 determines whether to end the process (step S21). For example, when a process end instruction is received (step S21: Yes route), the process ends. When a process end instruction is not received (step S21: No route), the process returns to step S17.

  As described above, with the linear equation storage observer according to the present embodiment, the estimated value is guaranteed to satisfy the equality constraint, and therefore, the control target is not necessarily calculated using the estimated value that does not converge to the true value. Will be able to control.

  The process which the communication part 105 of the control apparatus 1 performs is demonstrated using FIG.14 and FIG.15.

  First, a process in which the communication unit 105 transmits the input u will be described. The communication unit 105 acquires the input u (FIG. 14: step S31). The input u is calculated by the design unit 101 based on the estimated value ^ x when the estimated value ^ x has already been calculated. If the estimated value ^ x has not been calculated, an initial value is set as the input u.

  The communication unit 105 transmits the input u acquired in step S31 to the control target device 3 (step S33). Then, the process ends.

  Next, processing in which the communication unit 105 receives the output y will be described. The communication unit 105 receives the output y from the control target device 3 (FIG. 15: Step S41).

  The communication unit 105 stores the output y received in step S41 in the output data storage unit 111 (step S43). Then, the process ends.

  If the process as described above is executed, the control target apparatus 3 can be appropriately controlled.

[Embodiment 2]
In the first embodiment, the control device 1 executes both the process for obtaining the gain matrix L and the process for obtaining the estimated value. In the second embodiment, both processes are executed in separate apparatuses. Specifically, as shown in FIG. 16, the design device 4 connected to the network 2 executes a process of obtaining the gain matrix L, and the state estimation device 5 connected to the network 2 performs a process of calculating the estimated value. Run. Even in such a system form, the control target apparatus 3 can be appropriately controlled.

  Although one embodiment of the present invention has been described above, the present invention is not limited to this. For example, the functional block configurations of the control device 1 and the control target device 3 described above may not match the actual program module configuration.

  Also in the processing flow, if the processing result does not change, the processing order can be changed. Further, it may be executed in parallel.

  The control device 1, the design device 4, and the state estimation device 5 may be connected to the network 2 by wire.

[Appendix]
This appendix shows proof that condition (a) is a necessary and sufficient condition for WL = 0.

  The following holds.

  Therefore, the following holds.

  Since U is an orthogonal matrix, this equation is further equivalent to:

The product of the underlined part of Expression (25) and V ^T L is 0 only when V ^T L is expressed as follows using Λ∈R ^{(nr) × p} .

  Since V is an orthogonal matrix, this is equivalent to equation (14).

  This completes the appendix.

  Note that the control device 1, the design device 4, and the state estimation device 5 described above are computer devices. As shown in FIG. 17, the memory 2501, the CPU 2503, the hard disk drive (HDD) 2505, and the display device 2509 are included. A display control unit 2507 to be connected, a drive device 2513 for the removable disk 2511, an input device 2515, and a communication control unit 2517 for connecting to a network are connected by a bus 2519. An operating system (OS) and an application program for executing the processing in this embodiment are stored in the HDD 2505, and are read from the HDD 2505 to the memory 2501 when executed by the CPU 2503. The CPU 2503 controls the display control unit 2507, the communication control unit 2517, and the drive device 2513 according to the processing content of the application program, and performs a predetermined operation. Further, data in the middle of processing is mainly stored in the memory 2501, but may be stored in the HDD 2505. In the embodiment of the present invention, an application program for performing the above-described processing is stored in a computer-readable removable disk 2511 and distributed, and installed in the HDD 2505 from the drive device 2513. In some cases, the HDD 2505 may be installed via a network such as the Internet and the communication control unit 2517. Such a computer apparatus realizes various functions as described above by organically cooperating hardware such as the CPU 2503 and the memory 2501 described above and programs such as the OS and application programs. .

  The embodiment of the present invention described above is summarized as follows.

  The control method according to the first aspect of the present embodiment generates (A) a gain matrix used for estimation of the internal state of the controlled object based on an equation corresponding to a condition satisfied by a variable representing the internal state of the controlled object. (B) includes processing for controlling the control target based on the estimation result of the internal state of the control target generated by the observer using the generated gain matrix.

  If the gain matrix based on the above equation is used, the estimation result satisfies the condition. Therefore, the control target can be appropriately controlled using the estimation result that does not necessarily converge to the true value.

  Further, the above equation may include a gain matrix and an orthogonal matrix included in a result of singular value decomposition with respect to an equality-constrained coefficient matrix satisfied by a variable representing the internal state of the control target. If such an equation is used, an LMI solvable problem can be applied.

  Further, in the process of generating the gain matrix, (a1) it is determined whether there is a solution of an LMI (Linear Matrix Inequality) solvable problem based on the input data, and (a2) a solution of the LMI solvable problem is present The gain matrix may be generated using the solution of the LMI solvable problem and the equation.

  The control device according to the second aspect of the present embodiment generates (C) a gain matrix used for estimation of the internal state of the controlled object based on an equation corresponding to a condition satisfied by a variable representing the internal state of the controlled object Generating unit (design unit 101 in the embodiment is an example of a generating unit) and (D) an observer using a gain matrix generated by the generating unit (state estimating unit 103 in the embodiment is an example of an observer) ) Generated based on the estimation result of the internal state of the control target, the control unit for controlling the control target (communication unit 105 in the embodiment is an example of the control unit).

  A program for causing a computer to execute the processing according to the above method can be created, and the program can be a computer-readable storage medium such as a flexible disk, a CD-ROM, a magneto-optical disk, a semiconductor memory, or a hard disk, or It is stored in a storage device. The intermediate processing result is temporarily stored in a storage device such as a main memory.

  The following supplementary notes are further disclosed with respect to the embodiments including the above examples.

(Appendix 1)
On the computer,
Based on an equation corresponding to a condition satisfied by a variable representing the internal state of the controlled object, a gain matrix used to estimate the internal state of the controlled object is generated,
Controlling the control target based on the estimation result of the internal state of the control target generated by an observer using the generated gain matrix;
A control program that executes processing.

(Appendix 2)
The equation includes the gain matrix and an orthogonal matrix included in a result of singular value decomposition on a coefficient matrix of an equality constraint satisfied by a variable representing an internal state of the controlled object.
The control program according to attachment 1.

(Appendix 3)
In the process of generating the gain matrix,
Determine whether there is a solution to an LMI (Linear Matrix Inequality) solvable problem based on the input data,
If there is a solution of the LMI solvable problem, the gain matrix is generated using the solution of the LMI solvable problem and the equation.
The control program according to appendix 1 or 2.

(Appendix 4)
Computer
Based on an equation corresponding to a condition satisfied by a variable representing the internal state of the controlled object, a gain matrix used to estimate the internal state of the controlled object is generated,
Controlling the control target based on the estimation result of the internal state of the control target generated by an observer using the generated gain matrix;
A control method for executing processing.

(Appendix 5)
A generating unit that generates a gain matrix used for estimation of the internal state of the controlled object, based on an equation corresponding to a condition satisfied by a variable representing the internal state of the controlled object;
A control unit for controlling the control target based on an estimation result of the internal state of the control target generated by an observer using the gain matrix generated by the generation unit;
Control device.

DESCRIPTION OF SYMBOLS 1 Control apparatus 2 Network 3 Control object apparatus 4 Design apparatus 5 State estimation apparatus 101 Design part 103 State estimation part 105 Communication part 111 Output data storage part 113 Estimated value storage part 115 Work data storage part 301 Sensor 302 Controlled part 303 Communication part

Claims (5)

On the computer,
Based on an equation corresponding to a condition satisfied by a variable representing the internal state of the controlled object, a gain matrix used to estimate the internal state of the controlled object is generated,
Controlling the control target based on the estimation result of the internal state of the control target generated by an observer using the generated gain matrix;
A control program that executes processing. The equation includes the gain matrix and an orthogonal matrix included in a result of singular value decomposition on a coefficient matrix of an equality constraint satisfied by a variable representing an internal state of the controlled object.
The control program according to claim 1. In the process of generating the gain matrix,
Determine whether there is a solution to an LMI (Linear Matrix Inequality) solvable problem based on the input data,
If there is a solution of the LMI solvable problem, the gain matrix is generated using the solution of the LMI solvable problem and the equation.
The control program according to claim 1 or 2. Computer
Based on an equation corresponding to a condition satisfied by a variable representing the internal state of the controlled object, a gain matrix used to estimate the internal state of the controlled object is generated,
Controlling the control target based on the estimation result of the internal state of the control target generated by an observer using the generated gain matrix;
A control method for executing processing. A generating unit that generates a gain matrix used for estimation of the internal state of the controlled object, based on an equation corresponding to a condition satisfied by a variable representing the internal state of the controlled object;
A control unit for controlling the control target based on an estimation result of the internal state of the control target generated by an observer using the gain matrix generated by the generation unit;
Control device.

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