JP2020030797A - Controller designing device and designing method - Google Patents

Abstract

To improve control performance and safety of a controller.SOLUTION: A state equation is set, expressing a closed loop system composed of: an enlargement system plant P including a state feedback controller K, a control target G, and a nominal plant model G; and a Robust disturbance feedback controller L. On the basis of the state equation, an optimization problem based on a linear matrix inequality is formulated, and the optimal robust disturbance feedback controller L is designed.SELECTED DRAWING: Figure 5

Description

  The present invention relates to a technique for designing a control device.

  Some control devices include, for example, a feedback controller that guarantees improvement in followability to a target value, and a robust disturbance feedback controller that compensates for disturbances and model errors.

  Related technologies include, for example, Patent Documents 1 to 4.

Kiyoshi OHISHI and Kouhei OHNISHI and Kunio MIYACHI, TORQUE-SPEED REGULATION OF DC MOTOR BASED ON LOAD TORQUE ESTIMATION METHOD, Proc. INTERNATIONAL POWER ELECTRONICS CONFERENCE (IPEC), TOKYO, Mar., pp. 1209-1218, (1983) Kawai, Fukiko and Nakazawa, Chikashi and Vinther, Kasper and Rasmussen, Henrik, and Andersen, Palle and Stoustrup, Jakob, An Industrial Model Based Disturbance Feedback Control Scheme, Proc.The 19th World Congress of the International Federation of Automatic Control (IFAC 2014 ), Cape Town, August., Pp. 804-809, (2014) Unggul Wasiwitono and Masami Saeki, Fixed-Order Output Feedback Control and Anti-Windup Compensation for Active Suspension Systems, Vol. 5, No. 2, pp. 264-278, Journal of System Design and Dynamics, (2011) Fukiko Kawai and Kasper Vinther and Palle Andersen and Jan Dimon Bendtsen, MIMO Robust Disturbance Feedback Control for Refrigeration Systems via an LMI Approach, The 20th World Congress of the International Federation of Automatic Control (IFAC), Toulouse, Jul., (2017)

  An object according to one aspect of the present invention is to improve control performance and stability of a control device.

  A design apparatus according to one aspect of the present invention is configured such that a difference between an output value of a control target including a parametric uncertainty and a target value is input, one or more existing controllers, and a robust disturbance feedback controller. And a state equation expressing a closed loop system including the robust disturbance feedback controller and the expansion plant is set, and an optimization problem based on a linear matrix inequality is formulated based on the state equation to calculate an optimal solution.

  According to the present invention, control performance and stability of the control device can be improved.

It is a figure showing an example of the control device of an embodiment. FIG. 6 is a diagram illustrating an example of data constituting a target value r. FIG. 2 is a block diagram of a closed loop system corresponding to the control device shown in FIG. 1. FIG. 2 is a block diagram of a closed loop system including an expansion system plant P and a robust disturbance feedback controller L. 5 is a flowchart illustrating an example of an operation of the design apparatus according to the first exemplary embodiment. FIG. 4 is a block diagram in which a weighting function W _u is introduced into the closed loop system shown in FIG. 3. FIG. 4 is a Bode diagram showing frequency responses of a sensitivity function T _uu and a weight function W _u . Is a Bode diagram showing the frequency response of the multiplication value of the weight function W _u and sensitivity function T _uu. FIG. 4 is a block diagram of a closed loop system in which a disturbance estimation function H is introduced into the closed loop system shown in FIG. 9 is a flowchart illustrating an example of an operation of the design device according to the second exemplary embodiment. FIG. 5 is a block diagram of a closed-loop system including an expanded system plant P ′ obtained by adding a disturbance estimation function H to the expanded system plant P of FIG. 4 and a robust disturbance feedback controller L. FIG. 2 is a diagram illustrating a hardware configuration of a design device.

Hereinafter, embodiments will be described in detail with reference to the drawings.
<Example 1>
FIG. 1 is a diagram illustrating an example of a control device according to the embodiment.

  The control device 1 shown in FIG. 1 controls, for example, the operation of a moving device 3 that moves a trolley 2 of a gantry crane on a rail, and includes a feedforward controller 11, a state feedback controller 12, a robust And a disturbance feedback controller 13. Although a gantry crane is used as a control target in the present embodiment, the control target is not particularly limited.

The feedforward controller 11 outputs an output value based on the target value r.
State feedback controller 12, the measurement value x _p which is output from the measurement device 4 so as to follow the target value r, and outputs the manipulated variable.

Robust disturbance feedback controller 13, the difference between the nominal value x _pn and the measured value x _p and outputs the manipulated variable u _l so as to follow zero.

The addend u _k between the operation amount and the operation amount of the state feedback controller 12 of the feedforward controller 11, is output from the robust disturbance feedback controller 13 manipulated variable u _l and the mobile device 3 by added value It is assumed that the trolley 2 moves in the x-axis direction by controlling the operation. The trolley 2 and the suspended load 6 are connected to each other via the rope 5, and the suspended load 6 moves on the x-axis as the trolley 2 moves in the x-axis direction. Further, the moving distance of the trolley 2 relative to the point p1 on the x-axis to the position x _T of the trolley 2. The product of the angle θ1 between the vertical line 7 extending vertically downward from the connection point p2 between the trolley 2 and the rope 5 and the rope 5 and the length l of the rope 5 (also referred to as the rope length) is represented by the vertical line 7. Is set as the position x of the suspended load 6 with reference to. Further, the moving speed of the trolley 2 is x ^· _T, and the time derivative of the position x of the suspended load 6 is x ^· . Further, “x ^· _T ” is the same as the following symbol 1, and “x ^· ” is the same as the following symbol 2.

FIG. 2 is a diagram illustrating an example of data constituting the target value r.
Target value r shown in FIG. 2, the moving speed x ^· _T of the trolley _2, the time derivative x ^· position x of the suspended load 6, and a position x of the position x _T, and suspended load 6 of the trolley 2, The moving speed x ^· _T of the trolley 2 is used as an operation amount of the feedforward control.

  FIG. 3 is a block diagram of a closed loop system corresponding to the control device 1 shown in FIG. Note that w is a disturbance, and the causes of the disturbance include a wind and an impact on the suspended load 6, an inclination of a lane on which the trolley runs, and a movement of an occupant.

The feedforward controller _KFF is a transfer function expressing the feedforward controller 11.

State feedback controller K _FB is a transfer function representing the state feedback controller 12, the difference between the target value r and the output values x _p of the control target G is input.

Here, the feedforward controller _KFF and the state feedback controller _KFB are examples of existing controllers. Existing control is not limited to feedforward control and state feedback control, and may be, for example, P control, PI control, PID control, or the like.

Control object G is a transfer function representing the gantry cranes, the addend u _k of the output values of the state feedback controller 12 of the feedforward controller 11, is output from the robust disturbance feedback controller L that the operation amount u _l and is summed value is input, and outputs the measured values x _p.

Nominal plant model G _n is a transfer function that outputs a nominal value x _pn of the measurement values x _p which is output from the control target G _(the output value of the control object G without uncertainty), the operation amount u _k Is entered.

The robust disturbance feedback controller L is a transfer function expressing the robust disturbance feedback controller 13, and receives the difference ε between the nominal value x _pn and the measured value x _p and outputs the manipulated variable u _l .

FIG. 4 is a block diagram of a closed-loop system including an expanded plant P including a state feedback controller K _FB , a control target G, and a nominal plant model _Gn , and a robust disturbance feedback controller L.

The disturbance plant w and the manipulated variable _u1 are input to the expansion system plant P, and the expansion system plant P outputs an evaluation value z.
The robust disturbance feedback controller L receives the difference ε between the nominal value x _pn and the measured value x _p and outputs a manipulated variable u _l .

  FIG. 5 is a flowchart illustrating an example of an operation of the design apparatus according to the first embodiment. In steps S1 to S5 shown in FIG. 5, the robust disturbance feedback controller L is designed. In steps S6 to S9, the robustness of the closed loop system in which the uncertainty of the frequency domain of the control target G is added is added. An evaluation is performed. If the design does not consider the uncertainty in the frequency domain, the processing of steps S6 to S9 may be omitted.

First, in step S1, the design apparatus sets a control target G.
For example, the state equation of the control target G is represented by the following equation 1.

Here, the _{x p} as the following equation 2, the A and the following equation 3, the _{B 2} and formula 4.

G _ASR is an ASR (Automatic Speed Regulator) gain, m _T is the mass of the trolley 2, m _L is the mass of the suspended load 6, and g is the gravitational acceleration.

  When it is assumed that the model variation and the parametric uncertainty of the controlled object G are present in the A matrix, A is represented by the following Expression 5.

Here, the [delta] _a and the following formula 6. Further, the A matrix corresponding to _{A n} in the nominal plant _{G n,} representing the parametric uncertainty by _{A i} and [delta] _a. The parametric uncertainty refers to a parameter variation of an element constituting a control target, and in this embodiment, a parameter variation of a weight of a suspended load, a rope length, and an ASR gain can be considered.

Next, in step S2 of the flowchart in FIG. 5, the design apparatus sets the state feedback controller _KFB .

The state feedback controller K _{FB is represented} by the following equation (7).

  Further, the robust disturbance feedback controller L is represented by the following equation (8).

  The state equation of the expanded system plant P is represented by the following equation 9.

_Here, the _{x pp} as the following equation _10, the _{A pp} form the following equation _11, the _{B pp1} the following equation _12, the _{B pp2} the following equation 13, the _{C z} to form the following equation 14, the following equation 15 to _{D z} I do.

Next, in step S3 of the flowchart of FIG. 5, the design apparatus sets the B ₁ matrix.

B ₁ matrix is set based on the kind of disturbance envisaged.
Further, by replacing the B ₁ matrix weighting function may be designed to specify a frequency region to improve the control performance. To replace the B ₁ matrix weighting function, after defining the weighting function, to redesign the above formula 9 formula 15.

  Next, in step S4, the design device performs an arithmetic process of an optimization problem for obtaining the robust disturbance feedback controller L.

  The disturbance equation w is input to the expansion system plant P, and the state equation of the closed loop system in which the evaluation value z is output from the expansion system plant P is represented by the following Expression 16.

  Formulating the optimization problem by the linear matrix inequality (LMI) based on the state equation of the above formula 16, the following formulas 17 and 18 are obtained.

γ is an objective function to be minimized.
Here, X is a Lyapunov matrix, and X ₁ and X ₂ are matrices that are elements of the Lyapunov matrix X. Further, it is assumed that Y: = LX ₁ and W: = LX ₂ . μ is the upper limit of the control signal (the speed command value of the trolley 2).

The decision variables of the optimization problem are X ₁ , X ₂ , Y, and W. If an optimal solution for these four decision variables can be obtained, an optimal robust disturbance feedback controller L can be obtained.

  That is, in step S5, when there is a solution of the above four decision variables that satisfy the linear matrix inequalities shown in the above equations 17 and 18 (step S5: Yes), the optimal robust disturbance feedback controller L determines It is determined that it has been performed, and the process proceeds to step S6.

  On the other hand, when there is no solution of the above four decision variables that satisfies the linear matrix inequalities shown in Equations 17 and 18 (Step S5: No), the design apparatus returns to Step S1, and performs the expansion system plant P and the robust disturbance feedback control. Redesign of the closed loop system consisting of the container L is performed.

In step S6, the design device adds the weight function W _u as the uncertainty in the frequency domain of the control target G. That is, when adding the weight function W _u to the closed loop system designed in steps S1 to S5, the weight function W _u is set in order to evaluate whether robust stability can be ensured.

As an example of the weighting function W _u , a first-order lag system is represented by the following Expression 19.

  Here, α, β, and κ are adjustment parameters, and α, β, and κ are set according to the control target G. For example, the above three adjustment parameter values are determined on the assumption that the influence of noise is large in a high frequency region. For example, α = 1000, β = 0.0001, and κ = 2.2721.

Next, in step S7, the design device calculates the sensitivity function T _uu in order to consider the robustness to the weight function W _u .

FIG. 6 is a block diagram in which a weighting function W _u is introduced into the closed loop system shown in FIG. Note that the feedforward controller _KFF is omitted.

deriving a transfer function up to u is inputted outputs a u ^~ as a sensitivity function _T u~u, obtain the following equation 20. It should be noted that the "u ^~" is the same as the following symbol 3.

Usually, when examining the uncertainty in the frequency domain of the control target G, the uncertainty is examined based on the nominal model _Gn . In the present embodiment, however, the nominal model _Gn also has the parametric model variation element set in step S1. Suppose there is. That is, G _n = G is defined in the above equation 20, and the robustness of the proposed control device with respect to the parametric uncertainty and the uncertainty in the frequency domain is examined.

FIG. 7 is a diagram illustrating frequency responses of the sensitivity functions _Tu to _u and the weight function W _u . Note that α = 1000, β = 0.0001, and κ = 2.2721.

The model variation of the controlled object G depends on the length 1 of the rope 5, and FIG. 7 shows the frequency responses of the sensitivity functions _{Tu to u} in three patterns. That is, the solid line shown in FIG. 7 shows the frequency response of the sensitivity function _Tu to _u when the length 1 of the rope 5 is 45 m, and the broken line shows the sensitivity function _Tu when the length 1 of the rope 5 is 30 m. shows the frequency response of _~u, dashed line shows the frequency response of the sensitivity function T _U～u when the length l of the rope 5 and 15 m, the two-dot chain line shows the frequency response of the weighting function W _u .

Next, in step S8 of the flowchart in FIG. 5, the design apparatus multiplies the weighting function W _u and the sensitivity functions _Tu to _u in order to evaluate the robust stability of the closed loop system including the uncertainty in the frequency domain. The absolute value (| _{WuTu- u} |) of the calculated value is calculated.

Next, in step 9, the design device determines whether or not the absolute value of the value obtained by multiplying the weighting function W _u and the sensitivity functions _Tu to _u is smaller than one.

When the design apparatus determines that the absolute value of the value obtained by multiplying the weight function W _u and the sensitivity functions _Tu to _u is 1 or more (step S9: No), the closed loop system including the uncertainty in the frequency domain is robust. Assess that it does not have stability and return to step S1 to redesign the closed loop system.

On the other hand, when the design apparatus determines that the absolute value of the value obtained by multiplying the weighting function W _u and the sensitivity functions _Tu to _u is smaller than 1 (step S9: Yes), the closed loop system including the uncertainty in the frequency domain is determined. Is evaluated as having robust stability, and the design of the control device 1 ends.

FIG. 8 is a diagram illustrating a frequency response of a multiplication value of the weighting function W _u and the sensitivity functions _Tu to _u . Incidentally, the solid line shown in FIG. 8 shows the frequency response of _W u _{· T u~u} when the length l of the rope 5 and 45 m, _{W u} · when the dashed line to 30m length l of the rope 5 The frequency response of _{Tu to u} is shown, and the dashed line indicates the frequency response of _Wu · _{Tu to u} when the length 1 of the rope 5 is 15 m. Further, it is assumed that α = 1000, β = 0.0001, and κ = 2.2721.

Since the amplitudes (Magnitude (dB)) of W _u · _{Tu to u} shown in FIG. 8 are 0 dB in all frequency domains, the uncertainties in the frequency domain (α = 1000, β = 0.0001, κ = 2) .2721) can be evaluated as having robust stability.

  In steps S6 to S9, uncertainty is introduced into the closed loop system designed in steps S1 to S5, and the robustness of the closed loop system in which the uncertainty is introduced is evaluated. May be configured to obtain the uncertainty (α, β, κ) when the evaluation value indicating the robust stability of the closed loop system designed in the above becomes a predetermined evaluation value.

As described above, the design apparatus of the present embodiment includes the state feedback controller K _FB , the control target G including the parametric uncertainty, the enlarged plant P including the nominal plant model G _n , the robust disturbance feedback controller A state equation expressing a closed loop system composed of L is set, and based on the state equation, an optimization problem based on a linear matrix inequality is formulated, and an optimal solution is calculated.

Further, the design device of the present embodiment further adds a weight function W _u indicating the uncertainty of the frequency domain of the control target G, and a sensitivity function _Tu from the operation amount output to the input of the system including the weight function. _{To u} , and a robust disturbance feedback controller that satisfies the robust stability against the uncertainty in the frequency domain is calculated.

  As a result, the control device 1 designed by the design device of the present embodiment can improve the robustness against the disturbance w and the uncertainty of the control target G, thereby improving the stability of the control device 1. Can be.

The control device 1 which is designed by the design apparatus of the present embodiment, to handle the state feedback controller K _FB as part of the expansion system plant P, and the plant parameters of the structure and transfer function of the state feedback controller K _FB Can be maintained. For this reason, the state feedback controller 12 is conservatively designed to improve maintainability, which is a weak point of the conventional robust control, that is, stability of a closed loop system including uncertainty, and as a result, control performance is reduced. Can solve the problem. That is, according to the design apparatus of the present embodiment, since the existing control structure can be utilized, the control performance of the control apparatus 1 can be improved while reducing the design load.
<Example 2>
In the first embodiment, the robust disturbance feedback controller L is designed so that robustness against various disturbances w is improved. As the disturbance w, for example, a disturbance having a relatively small time constant, such as a measurement error of a deflection angle sensor (a sensor for measuring the angle θ shown in FIG. 1) due to a wind hitting the suspended load 6 or an impact on the suspended load 6, or a disturbance of the trolley 2 Disturbance having a relatively large time constant, such as displacement of the deflection angle sensor due to lane bending due to movement, may be considered.

  In the second embodiment, a disturbance such as a sensor displacement is estimated (estimated disturbance w ^), and this estimation amount is subtracted from ε as an offset, thereby removing the sensor error disturbance to obtain an estimation error (ε ＾ = ε−w). ^). As described above, by introducing the disturbance estimation function H for removing a sensor error or the like, highly accurate control can be realized. In the second embodiment, a closed loop system including a disturbance estimation function H (disturbance observer) for obtaining the disturbance w ＾ is designed. Note that “w ＾” is the same as the symbol 4 below.

FIG. 9 is a block diagram of a closed loop system in which a disturbance estimation function H is introduced into the closed loop system shown in FIG. Note that the feedforward controller K _FF , state feedback controller K _FB , control target G, and nominal plant model G _n shown in FIG. 9 are the feed forward controller K _FF , state feedback controller K _FB , Since it is the same as the control object G and the nominal plant model _Gn , the description is omitted. The control device according to the second embodiment is the same as the control device 1 illustrated in FIG.

Disturbance estimation function H is the difference between the nominal value x _pn and the measured value x _p epsilon, and outputs the disturbance w ^ ^·. Disturbance w ^ is determined by the disturbance w ^ ^· output from the disturbance estimating function H is integrated, the difference epsilon ^ is determined by the disturbance w ^ is subtracted from the difference epsilon. Then, the difference ε ＾ is input to the robust disturbance feedback controller L, and the manipulated variable _ul is output from the robust disturbance feedback controller L. Note that “w ＾ ^· ” is the same as the symbol 5 below.

  FIG. 10 is a flowchart illustrating an example of the operation of the design apparatus according to the second embodiment. Steps S1 to S5 shown in FIG. 10 are the same as steps S1 to S5 shown in FIG. 5, and a description thereof will be omitted.

  FIG. 11 is a block diagram of a closed-loop system including an enlarged plant P ′ obtained by adding a disturbance estimation function H to the enlarged plant P of FIG. 4 and a robust disturbance feedback controller L.

  After obtaining the robust disturbance feedback controller L (Step S5: Yes), the design apparatus performs an arithmetic process for obtaining the disturbance estimation function H (Step S10).

For example, the dynamic characteristic of the control target G is represented by the following Expression 21.
Next, in Step S11, when there is a solution that satisfies the linear matrix inequality shown in Equation 25 (Step S11: Yes), the design apparatus determines that the disturbance estimation function H has been obtained, and ends the processing.

  On the other hand, when there is no solution that satisfies the linear matrix inequality shown in Equation 25 (Step S11: No), the design apparatus returns to Step S1, and the closed loop system including the enlarged plant P and the robust disturbance feedback controller L shown in FIG. Redesign.

Here, it is assumed that the dynamic characteristic of the disturbance w is sufficiently slower than the control cycle of the control target G. For example, the control cycle of the control target G is set to about 2 ms to 10 ms, and the time constant of the displacement of the deflection angle sensor as the disturbance w is set to several seconds to several tens seconds. As described above, when there is a difference in dynamic characteristics of 100 times or more between the controlled object G and the disturbance w, the approximation of w ^· = 0 is sufficiently established.

  Further, the dynamic characteristics of the nominal model Gn and the disturbance estimation function H are represented by the following Expression 22.

Further, the disturbance w is regarded as a state variable, and as shown in FIG. 11, an enlarged system plant P ′ including a state feedback controller K _FB , a control target G, a nominal plant model G _n , and a disturbance estimation function H is constructed.

In the enlarged system plant P ′ shown in FIG. 11, the disturbance w and the manipulated variable _ul are input, and the evaluation value z is output.

The robust disturbance feedback controller L shown in FIG. 11 receives the difference ε ＾ and outputs the manipulated variable _ul .

  That is, by combining the above Expression 21 and the above Expression 22, the following Expression 23 as the enlarged system plant P 'shown in FIG. 11 is obtained. At this time, A￣ and X￣ are represented by the following Expression 24. Note that “A￣” is the following symbol 6 and “X￣” is the following symbol 7.

  In addition, when the constraint condition for stabilizing the expansion system plant P ′ shown in FIG. 11 is expressed by a linear matrix inequality, the following equation 25 is obtained. Note that “P” is the symbol 8 below. P is a Lyapunov matrix, and Equation 25 below is called a Lyapunov inequality.

  Then, the disturbance estimating function H that satisfies Expression 25 is obtained by the design device. If the above equation 25 is satisfied, the expansion system plant P 'becomes stable.

  In the closed-loop system designed in steps S1 to S5, S10, and S11 as described above, a disturbance such as a sensor displacement is estimated (estimated disturbance w ^), and the estimated amount is subtracted from ε as an offset to obtain a sensor error. An estimation error (ε ＾ = ε−w ^) from which disturbance has been removed can be obtained. For this reason, highly accurate control can be realized. Note that the design device may execute steps S6 to S9 shown in FIG. 5 after performing the arithmetic processing for obtaining the disturbance estimation function H.

FIG. 12 is a diagram illustrating a hardware configuration of the design apparatus according to the present embodiment.
As shown in FIG. 12, the design device includes a processor 1501, a main storage device 1502, an auxiliary storage device 1503, an input device 1504, an output device 1505, an input / output interface 1506, a communication control device 1507, and a medium. A driving device 1508. The elements 1501 to 1508 are interconnected by a bus 1510 so that data can be transferred between the elements.

  The processor 1501 is a Central Processing Unit (CPU), a Micro Processing Unit (MPU), or the like. The processor 1501 controls the overall operation of the design apparatus by executing various programs including an operating system. In addition, the processor 1501 performs, for example, each processing illustrated in FIG. 5 or FIG.

  The main storage device 1502 includes a read only memory (ROM) and a random access memory (RAM) (not shown). In the ROM of the main storage device 1502, for example, a predetermined basic control program read by the processor 1501 when the design device is started is recorded in advance. The RAM of the main storage device 1502 is used as a work storage area as needed when the processor 1501 executes various programs.

  The auxiliary storage device 1503 is a storage device having a larger capacity than the RAM of the main storage device 1502, such as a hard disk drive (HDD) or a nonvolatile memory (including a solid state drive (SSD)) such as a flash memory. is there. The auxiliary storage device 1503 can be used for storing various programs executed by the processor 1501, various data, and the like.

  The input device 1504 is, for example, a keyboard device, a touch panel device, or the like. When the user of the design device performs a predetermined operation on the input device 1504, the input device 1504 transmits input information associated with the operation content to the processor 1501. The input device 1504 can be used, for example, for inputting various setting values such as a coefficient matrix of a state equation expressing a closed loop system.

  The output device 1505 includes, for example, a device such as a liquid crystal display device and a sound reproducing device such as a speaker.

  The input / output interface 1506 connects the design device to another electronic device. The input / output interface 1506 includes, for example, a Universal Serial Bus (USB) standard connector or the like.

  The communication control device 1507 is a device that connects the design device to a network such as the Internet and controls various communications between the design device and other electronic devices via the network.

  The medium driving device 1508 reads out programs and data recorded in the portable storage medium 16 and writes data and the like stored in the auxiliary storage device 1503 to the portable storage medium 16. As the medium driving device 1508, for example, a reader / writer for a memory card compatible with one or more types of standards can be used. When a memory card reader / writer is used as the medium driving device 1508, the portable storage medium 16 may be a memory card (flash memory) conforming to a standard supported by the memory card reader / writer, for example, a Secure Digital (SD) standard. ) Etc. are available. In addition, as the portable recording medium 16, for example, a flash memory having a USB standard connector can be used. Further, when the design apparatus is equipped with an optical disk drive that can be used as the medium drive device 1508, various optical disks that can be recognized by the optical disk drive can be used as the portable recording medium 16. Optical disks usable as the portable recording medium 16 include, for example, Compact Disc (CD), Digital Versatile Disc (DVD), Blu-ray Disc (Blu-ray is a registered trademark), and the like. For example, the portable recording medium 16 can be used for storing a program or the like including the processing shown in FIG. 5 or FIG.

Note that the design device does not need to include all the elements 1501 to 1508 shown in FIG. 12, and some of the elements can be omitted depending on the application and conditions.
In the above embodiment, the control of the gantry crane is described as the control target, but the control is not limited to this. INDUSTRIAL APPLICABILITY The present invention can be widely applied when designing a control system including a disturbance, such as control of a storage battery of a power system and control of rolling of a steel plant.
Further, the present invention is not limited to the above embodiments, and various improvements and modifications can be made without departing from the gist of the present invention.

DESCRIPTION OF SYMBOLS 1 Control device 2 Trolley 3 Moving device 4 Measuring device 5 Rope 6 Suspended load 7 Vertical line 11 Feedforward controller 12 State feedback controller 13 Robust disturbance feedback controller

Claims (10)

A design device for designing a control device including one or more existing controllers and a robust disturbance feedback controller, to which a difference between an output value and a target value of a control target including a parametric uncertainty is input. ,
Set a state equation representing a closed-loop system consisting of the robust disturbance feedback controller and the expansion system plant,
A design apparatus for formulating an optimization problem based on a linear matrix inequality based on the state equation and calculating an optimal solution. The design device according to claim 1,
The expansion system plant corresponds to the existing controller, the control target to which an added value of the operation amount of the existing controller and the operation amount of the robust disturbance feedback controller is input, and the output value of the control target. A nominal plant model that outputs a nominal value to
The design apparatus, wherein the robust disturbance feedback controller receives a difference between an output value of the controlled object and the nominal value and outputs the manipulated variable. The design device according to claim 2,
For the control target, add a weight function that becomes uncertain in the frequency domain,
Calculate the sensitivity function from the manipulated variable output to the input including the weight function,
A design apparatus for evaluating whether robust stability is satisfied even in the uncertainty of the frequency domain. It is a design device according to any one of claims 1 to 3,
The expansion system plant includes a disturbance estimation function for estimating disturbance,
A design apparatus, wherein a constraint condition for stabilizing the extended system plant is expressed by a linear matrix inequality, and the disturbance estimation function that satisfies the linear matrix inequality is obtained. A design method of a design device for designing a control device including one or a plurality of existing controllers and a robust disturbance feedback controller to which a difference between an output value of a control target including a parametric uncertainty and a target value is input. And
Expansion system plant, set a state equation representing a closed loop system consisting of the robust disturbance feedback controller,
A design method characterized by formulating an optimization problem based on a linear matrix inequality based on the state equation and calculating an optimal solution. The design method according to claim 5, wherein
The expansion system plant corresponds to the existing controller, the control target to which an added value of the operation amount of the existing controller and the operation amount of the robust disturbance feedback controller is input, and the output value of the control target. A nominal plant model that outputs a nominal value to
The robust disturbance feedback controller receives a difference between an output value of the controlled object and the nominal value and outputs the manipulated variable. The design method according to claim 6, wherein
For the control target, add a weight function that becomes uncertain in the frequency domain,
Calculate the sensitivity function from the manipulated variable output to the input including the weight function,
A design method characterized by evaluating whether robust stability is satisfied even for uncertainties in the frequency domain. The design method according to any one of claims 5 to 7,
The expansion system plant includes a disturbance estimation function for estimating disturbance,
A design method comprising: expressing a constraint condition for stabilizing the expanded system plant by a linear matrix inequality, and obtaining the disturbance estimation function that satisfies the linear matrix inequality.   A control device characterized by being designed by the design device according to claim 1.   A control device designed by the design method according to claim 4.