JP6838454B2 - Control method, control device and control program - Google Patents

Description

The present invention relates to a feedback control technique.

A dynamic system is one in which the output depends not only on the current input but also on the past input. In particular, the dynamic system represented by the Linear State Equation (1) and the Linear Output Equation (2) of discrete time as follows is called a linear time-invariant system of discrete time.

FIG. 1 shows a block diagram of the above-mentioned discrete-time linear time-invariant system. X [k + 1] can be obtained by adding Ax [k] and Bu [k]. Further, y [k] is obtained as Cx [k]. q ^-1 is an operator that reduces k of x [k] by 1.

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

For a detectable linear system, a device that calculates the value of a state that converges over time is called an observer. Observer estimates are guaranteed to converge to true values over time. In the conventional technique, the estimated value after a sufficient time that can be regarded as having converged to the true value is used for control.

However, when the controlled object is not stable and waiting for the estimated value to converge to the true value, the internal state may change and the control may not be in time. 2 and 3 show the relationship between time and state. In FIG. 2, the vertical axis _{represents the value of the state x 1} and the horizontal axis represents the time. In FIG. 3, the vertical axis _{represents the value of the state x 2} and the horizontal axis represents the time. True values are plotted with solid lines and estimates are plotted with dashed lines. In both FIGS. 2 and 3, the state changes before the estimated value converges to the true value, so an inappropriate state may occur before performing control based on the estimated value after convergence. There is sex. On the other hand, before the estimated value converges to the true value, the constraint that the true state satisfies (for example, the linear equation relation) is not satisfied, so that the control based on the estimated value cannot be performed. There is.

Further, for example, when the estimated value is converted so as to satisfy the same constraint as the true state by a projection operation and used for control, it is necessary to perform the conversion every time the estimated value is obtained, which causes an increase in calculation time. Therefore, in an unstable situation (for example, a situation where there is no time to generate a value to be used for control), control based on an inaccurate value is performed, and as a result, it is unstable. 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 FIGS. 4 and 5, the true value fluctuates oscillatingly, and the control becomes unstable.

Japanese Unexamined Patent Publication No. 10-54279

R.F.Stengel, "Optimal Control and Optimization", 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.

An object of the present invention is to provide a technique for appropriately controlling a controlled object by using an estimated value that does not necessarily converge to a true value in one aspect.

The control method according to one aspect generates a gain matrix used for estimating 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, and an observer using the generated gain matrix. Includes processing to control the control target based on the estimation result of the internal state of the control target generated by.

In one aspect, it is possible to appropriately control the controlled object by using an estimated value that does not necessarily converge to the true value.

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

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

It is assumed that the Linear State Equation (1) and the Linear Output Equation (2) are as shown above, and A, B, C, W and υ are known. The linear equation (3) means that the value of the state is on a plane in the state space (that is, the conservation law holds), as shown in FIG.

In general, the observer's estimate ^ x [k + 1] 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 can be obtained by solving, for example, an LMI (Linear Matrix Inequality) solvable problem. The LMI solvable problem is a problem for which an efficient numerical calculation method is known, and since a solver (for example, an SDP (SemiDefinite Program) solver) also exists, it is appropriate as an existence determination method and a construction method.

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

This equation indicates that the matrix on the left side is positive. Then, the gain matrix is calculated as ^{L = X -1 Y.} This makes it possible to obtain the estimated value ^ x [k + 1].

However, as described in the background technology section, the estimated values obtained by such a method may not satisfy the equation constraint. This means that, as shown in FIG. 8, the estimated value may not be on a plane in the state space. Further, if the conversion is performed so that the estimated value exists on a plane in the state space, the calculation time becomes 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-1) 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 on. Then, when such an observer exists, a method (condition C) based on an efficient numerical calculation method capable of concretely realizing such an observer (condition B) will be examined.

Regarding condition A-1, the necessary and sufficient condition for the calculation amount not to increase as compared with the normal observer is that the calculation formula has the same format as the normal observer. That is, the calculation formula of the present embodiment is in the form of the formula (5).

For 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.

(Sufficiency)
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)
On the contrary, when WL ≠ 0, the following equation may not hold.

Therefore, since W ^ x [k] follows a recurrence formula different from Wx [k], the 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 called an error system.

The fact that the estimated value converges to the true value with the passage of time is called "the error system is stable". The necessary and sufficient condition (that is, the necessary and sufficient condition of condition A-3) for the existence of the calculation method of the estimated value that stabilizes the error system (that is, the existence of such a gain matrix) is given by the equation (6). ) Is that there is a solution to the LMI solvable problem.

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

From the above, the following problem is solved by combining equation (6), which is a necessary and sufficient condition of condition A-3, with WL = 0, which is a necessary and sufficient condition of condition A-2, ^{and substituting L = X -1 Y.} If it can be solved, the conditions A-1, A-2, A-3 and B are satisfied.

However, since Eq. (12) is a non-linear 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, the necessary conditions for the estimated value to satisfy the linear equation are expressed by an equation related to the gain matrix, and these equations are used to express conditions A-1, condition A-2, condition A-3, and conditions A-3. Condition B is reduced to the LMI solvable problem.

First, the coefficient matrix W of the linear equation is singular value decomposed (Singular Value Decomposition) as follows. U and V are orthogonal matrices. It should be noted that the singular value decomposition can be executed because it is limited to the linear equation instead of the general equation (f (x [k]) = 0).

It is determined whether or not a gain matrix L that satisfies the following conditions (a) and (b) exists, and if so, 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.

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

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

When the gain matrix L satisfying the condition (a) and the condition (b) exists, the observer calculates the gain matrix L and estimates the state according to the equation (5) based on the calculated gain matrix L. Set. In the following, the observer set in this way is referred to as a linear equation preservation observer.

The procedure for determining whether or not the gain matrix L satisfying the condition (a) and the condition (b) exists and calculating the gain matrix L when the gain matrix L exists is as follows.

First, the following LMI solvable problem is solved.

When the equation (15) is solvable (that is, when the solutions X and Y exist), it is determined that the gain matrix L satisfying the condition (a) and the condition (b) exists. If the equation (15) is not solvable, it is determined that there is no gain matrix L that satisfies the condition (a) and the condition (b). If 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 represented by the equation (11) to be stable (n → ∞, x [k] − ^ x [k] → 0) is that all the eigenvalues of A-LC are in the complex plane. It exists in a circle with a radius of 1 centered on the origin, which is equivalent to the existence of a matrix P and a gain matrix L that satisfy the following matrix inequality (that is, the Riapnov inequality for a discrete-time linear time-invariant system). is there. For this point, refer to "Yoshio Ebihara," 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 that satisfy this matrix inequality is a necessary and sufficient condition for the existence of the gain matrix L of the form of the equation (14) that stabilizes the error system. ^{When VV T} = I is inserted into the first equation and ^{arranged, and V T} is applied from the left on 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 that satisfy this equation is a necessary and sufficient condition for the existence of the gain matrix L of the form of the equation (14) that stabilizes the error system.

Here, if X: = ^VT PV, it becomes as follows.

The existence of the matrix X and the matrix Λ that satisfy this equation is a necessary and sufficient condition for the existence of the gain matrix L of the form of the equation (14) that stabilizes the error system.

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 "Atsumi Ohara," Control System Design by Matrix Inequality Approach ", Corona Publishing Co., Ltd., 2016".

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

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

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

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

FIG. 9 shows an outline of the dynamic system of 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 the program into the memory 2501 in FIG. 17 and executing it by the 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 the memory 2501 or the 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 controlled 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. It 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. Further, the communication unit 105 transmits the input to the control target device 3 to the control target device 3.

FIG. 11 shows a functional block diagram of the controlled device 3. The controlled target device 3 includes a sensor 301 which is a physical sensor, a controlled unit 302, and a communication unit 303.

The sensor 301 measures the 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. Further, the communication unit 303 transmits the output y measured by the sensor 301 to the control device 1.

For example, when the controlled 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, the position information of the controlled target device 3, and the state x is, for example, the position. It is a combination of the information and the speed information of the control target device 3. Further, for example, when the controlled device 3 is a plurality of water storage tanks, the controlled unit 302 is, for example, a pump that adjusts the amount of water in the plurality of water storage tanks, and the input u is the amount of water transported between the plurality of water storage tanks. Yes, the output y is, for example, the amount of water in any of the plurality of water storage tanks, and the state x is, for example, the amount of water in each of the plurality of water storage tanks. 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.

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

The design unit 101 receives the input of the parameters (here, the matrices A, B, C and W of the equation (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 the parameters stored in advance in the storage area.

The design unit 101 executes a process of obtaining solutions X and Y of the LMI solvable problem represented by the equation (15) using the parameters stored in the work data storage unit 115 in step S1 (step S3).

The design unit 101 determines in step S3 whether a solution exists (step S5). When the solution does not exist (step S5: No route), the design unit 101 executes the following processing. Specifically, the design unit 101 sets the state estimation unit 103 to calculate the estimated value by a normal method (step S7). And the process ends. The usual method is, for example, a process of obtaining an estimated value by a normal observer and then converting the estimated value so as to satisfy the equation constraint. Since the process of step S7 is not the main process of the present embodiment, detailed description thereof will be 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 the equation (16) using the obtained solutions X and Y (step S9).

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

By executing the above processing, the state estimation unit 103 can use the gain matrix L capable of calculating the estimated value satisfying the equation constraint.

The process executed by the state estimation unit 103 of the control device 1 will be described with reference to FIG.

The state estimation unit 103 reads out 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 the input u of the previous time (step S17).

The state estimation unit 103 uses the parameter and gain matrix read in step S13, the inputs u and output y acquired in step S17, and the calculated or initialized estimated value ^ x to ^ 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 the process end instruction is received (step S21: Yes route), the process ends, and when the process end instruction is not accepted (step S21: No route), the process returns to step S17.

As described above, in the case of the linear equation preservation observer of the present embodiment, since the estimated value is guaranteed to satisfy the equation constraint, the controlled object is controlled by using the estimated value that does not necessarily converge to the true value. Will be able to control.

A process executed by the communication unit 105 of the control device 1 will be described with reference to FIGS. 14 and 15.

First, the process of transmitting the input u by the communication unit 105 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, the 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). And the process ends.

Next, the process of receiving the output y by the communication unit 105 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). And the process ends.

By executing the above processing, the control target device 3 can be appropriately controlled.

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

Although one embodiment of the present invention has been described above, the present invention is not limited thereto. For example, the functional block configuration 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, it is possible to change the order of processing if the processing result does not change. Further, it may be executed in parallel.

Further, 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 the proof that the 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 following equation.

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

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

This is the end of the appendix.

The control device 1, the design device 4, and the state estimation device 5 described above are computer devices, and as shown in FIG. 17, the memory 2501, the CPU 2503, the hard disk drive (HDD) 2505, and the display device 2509 The display control unit 2507 to be connected, the drive device 2513 for the removable disk 2511, the input device 2515, and the communication control unit 2517 for connecting to the network are connected by a bus 2519. The operating system (OS: Operating System) and the 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 contents of the application program to perform a predetermined operation. Further, the data in the process of processing is mainly stored in the memory 2501, but may be stored in the HDD 2505. In the embodiment of the present invention, the application program for performing the above-described processing is stored and distributed on the computer-readable removable disk 2511 and installed from the drive device 2513 to the HDD 2505. It may be installed on the HDD 2505 via a network such as the Internet and a communication control unit 2517. Such a computer device realizes various functions as described above by organically collaborating with the hardware such as the CPU 2503 and the memory 2501 described above and the program such as the OS and the application program. ..

The embodiments of the present invention described above can be summarized as follows.

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

If the gain matrix based on the above equation is used, the estimation result satisfies the condition, so that the control target can be appropriately controlled by 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 the result of singular value decomposition for the coefficient matrix of the equation constraint satisfied by the variable representing the internal state of the controlled object. By using such an equation, the 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 the LMI (Linear Matrix Inequality) solvable problem based on the input data, and (a2) there is a solution of the LMI solvable problem. , 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 a gain matrix used for estimating the internal state of the controlled object based on (C) an equation corresponding to a condition satisfied by a variable representing the internal state of the controlled object. The generation unit (the design unit 101 in the embodiment is an example of the generation unit) and the observer using the gain matrix generated by the (D) generation unit (the state estimation unit 103 in the embodiment is an example of the observer). ), Based on the estimation result of the internal state of the controlled object, has a control unit (the communication unit 105 in the embodiment is an example of the control unit) that controls the controlled object.

A program for causing a computer to execute the processing by 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. Stored in storage. The intermediate processing result is temporarily stored in a storage device such as a main memory.

The following additional notes will be further disclosed with respect to the embodiments including the above embodiments.

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

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

(Appendix 3)
In the process of generating the gain matrix,
Determine if there is a solution to the LMI (Linear Matrix Inequality) solvable problem based on the input data.
If a solution to the LMI solvable problem exists, 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)
The computer
Based on the equation corresponding to the condition satisfied by the variable representing the internal state of the controlled object, a gain matrix used for estimating the internal state of the controlled object is generated.
The control target is controlled based on the estimation result of the internal state of the control target generated by the observer using the generated gain matrix.
A control method that executes processing.

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

1 Control device 2 Network 3 Control target device 4 Design device 5 State estimation device 101 Design unit 103 State estimation unit 105 Communication unit 111 Output data storage unit 113 Estimated value storage unit 115 Work data storage unit 301 Sensor 302 Controlled unit 303 Communication unit

Claims (3)

On the computer
LMI (LMI) based on the coefficient matrix included in the linear state equation and linear output equation of the controlled object and the orthogonal matrix included in the result of singularity decomposition for the coefficient matrix of the linear equation constraint satisfied by the variable representing the internal state of the controlled object. Linear Matrix Inequality) Determines if a solution to the solvable problem exists and
When the solution of the LMI solvable problem exists, a gain matrix used for estimating the internal state of the controlled object is generated from the solution of the LMI solvable problem.
The control target is controlled based on the estimation result of the internal state of the control target generated by the observer using the generated gain matrix.
A control program that executes processing. The computer
LMI (LMI) based on the coefficient matrix included in the linear state equation and linear output equation of the controlled object and the orthogonal matrix included in the result of singularity decomposition for the coefficient matrix of the linear equation constraint satisfied by the variable representing the internal state of the controlled object. Linear Matrix Inequality) Determines if a solution to the solvable problem exists and
When the solution of the LMI solvable problem exists, a gain matrix used for estimating the internal state of the controlled object is generated from the solution of the LMI solvable problem.
The control target is controlled based on the estimation result of the internal state of the control target generated by the observer using the generated gain matrix.
A control method that executes processing. LMI (LMI) based on the coefficient matrix included in the linear state equation and linear output equation of the controlled object and the orthogonal matrix included in the result of singularity decomposition for the coefficient matrix of the linear equation constraint satisfied by the variable representing the internal state of the controlled object. Linear Matrix Inequality) Determines if there is a solution to the solvable problem, and if there is a solution to the LMI solvable problem, it is used to estimate the internal state of the controlled object from the solution of the LMI solvable problem. A generator that generates a gain matrix and
A control unit that controls the control target based on an estimation result of an internal state of the control target generated by an observer using the gain matrix generated by the generation unit.
Control device with.

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