JP6777231B2 - Control device and control device design method - Google Patents

Description

The present invention relates to a control device and a method for designing the control device.

As a control device, for example, in addition to an output feedback controller that guarantees improved followability to a target value, a robust disturbance feedback controller that guarantees that the closed loop system of the output feedback controller becomes stable due to disturbance or the like is provided. There is. See, for example, Patent Document 1, Non-Patent Document 1, or Non-Patent Document 2.

However, in the above-mentioned control device, there is a trade-off relationship between the improvement of the control performance and the improvement of the stability of the closed loop system. ..

In addition, redesigning an existing control to improve control performance and stability requires design man-hours, and there is a risk that the characteristics of the system will fluctuate significantly. Therefore, a technique for improving control performance and stability while utilizing the characteristics of existing control is desired.

As another control device, there is also one provided with an anti-windup controller for suppressing the occurrence of a windup phenomenon in which the control performance deteriorates due to the saturation of the output value of the output feedback controller. See, for example, Patent Document 2.

Patent Document 1 provides a control device and a control method for making a system follow a target trajectory under conditions in which the physical parameters of the system that characterize the dynamic characteristics are unknown and random disturbances are applied. .. However, the above control does not include an anti-windup controller that guarantees the stability of the closed loop system even when the control output is saturated. Therefore, even if robustness can be guaranteed on the desk, there is a problem that stability and control performance cannot be guaranteed on mounting.

For mounting problems, Patent Document 2 provides a function of switching to an anti-windup control mode when the control input is saturated, in addition to a control method in which a disturbance observer is introduced for robust control. However, since the function of switching to this anti-windup control mode is rule-based logic control, there is a problem that the stability and control performance of the entire control system cannot be guaranteed by control theory by switching the control method. ..

Japanese Unexamined Patent Publication No. 10-133703 Japanese Unexamined Patent Publication No. 2004-240516

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) Carsten Scherer, Pascal Gahinet and Mahmoud Chilali, Multiobjective Output-Feedback Control via LMI Optimization, Vol. 42, No. 7, pp. 896-91, Journal of IEEE Transactions on Automatic Control, (1997) Nobutaka Wada and Masami Saeki, Synthesis of a Static Anti-Windup Compensator via Linear Matrix Inequalities, the 3rd IFAC Symposium on Robust Control Design, in Prague, June, (2000) H.H. Rosenbrock, D.J. Bell, Ed., Multivariable circle criterion in recent Mathematical Development in Control, (1973) Stephen Boyd, Laurent El Ghaoui, E. Feron and V. Balakrishnan, Society for Industrial and Applied Mathematics (SIAM), Linear Matrix Inequalities in System and Control Theory, (1994) Izadi-Zamanabadi, Roozbeh and Vinther, Kasper and Mojallali, Hamed and Rasmussen, Henrik and Stoustrup, Jakob, Evaporator unit as a benchmark for plug and play and fault tolerant control, Proc. 8th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes, Mexico City, Mexico, August, 2012, pp. 701-706 A. Syaichu-Rohman and R.H. Middleton, Anti-windup schemes for discrete time systems: an LMI-based design, Proc. 5th Asian Control Conference, Melbourne, July, 2004, pp. 554-561 Alan V. Oppenheim and Ronald W. Schafer, Englewood Cliffs, N.J .: Prentice Hall, Discrete-time signal processingl, (1989) Izadi-Zamanabadi, Roozbeh and Vinther, Kasper and Mojallali, Hamed and Rasmussen, Henrik and Stoustrup, Jakob, Evaporator unit as a benchmark for plug and play and fault tolerant control, Proc. 8th IFAC Symposium on Fault Detection, Supervision and Safety of Technical Processes, Mexico City, Mexico, August, 2012, pp. 701-706

An object of one aspect of the present invention is to improve the stability of a closed loop system in a control device while maintaining control performance.

In the control parameter calculation device of the control device according to one embodiment of the present invention, the output value of the controlled object to which the added value of the first manipulated variable and the second manipulated variable is input follows the target value. It includes an output feedback controller that outputs a first manipulated variable, and a robust disturbance feedback controller that outputs a second manipulated variable so as to improve the control performance and stability of the closed loop system.

Further, in the control parameter calculation device, a first state equation representing a first closed-loop system including a first expansion system plant and a robust disturbance feedback controller is set based on a first predetermined parameter. Using the coefficient matrix of the first state equation, we formulate the constraints that guarantee control performance and stability into an optimization problem expressed by the first linear matrix inequality, and robustly satisfy the first linear matrix inequality. Find the coefficient matrix of the state equation that represents the disturbance feedback controller.

According to the present invention, in the control device, the stability of the closed loop system can be improved while maintaining the control performance.

It is a figure which shows an example of the control device of 1st Embodiment. It is a block diagram of an output feedback controller, a controlled object, a nominal plant model, a weighting function, and a robust disturbance feedback controller. FIG. 5 is a block diagram of a first closed-loop system consisting of a first expansion plant and a robust disturbance feedback controller. It is a flowchart which shows the design method of the control device of 1st Embodiment. It is a figure which shows an example of the control device of 2nd Embodiment. FIG. 3 is a block diagram of an output feedback controller, a controlled object, a nominal plant model, a weighting function, a robust disturbance feedback controller, and first and second anti-windup controllers. It is a block diagram of a second closed loop system consisting of a dead zone function and a second expansion plant. It is a flowchart which shows the design method of the control device of 2nd Embodiment. It is a figure which shows the saturation function. It is a figure which shows the dead zone function. It is a more detailed block diagram of an output feedback controller, a controlled object, a nominal plant model, a weighting function, a robust disturbance feedback controller, and first and second anti-windup controllers. It is a flowchart which shows the design method of the control device of 3rd Embodiment. It is a Bode diagram of the second robust disturbance feedback controller before and after the low-dimensional processing. It is a figure which shows the simulation result by PI control + robust disturbance feedback control. It is a figure which shows the simulation result only by PI control. It is a conceptual diagram of the absolute value error of the output value of a controlled object. It is a figure which shows an example of the control device of 4th Embodiment. It is a block diagram of an output feedback controller, a controlled object, a nominal plant model, a robust disturbance feedback controller, and the first and second discrete anti-windup controllers. It is a flowchart which shows the design method of the control device of 4th Embodiment. FIG. 6 is a block diagram of a third closed-loop system consisting of a dead zone function and a third expansion plant. It is a flowchart which shows the design method of the control device of 5th Embodiment. It is a Bode diagram of the robust disturbance feedback controller before and after the low-dimensional processing. It is a figure which shows the simulation result by PI control + robust disturbance feedback control. It is a figure which shows the simulation result only by PI control. It is a figure which shows the hardware configuration of a control device or a design device.

Hereinafter, embodiments will be described in detail based on the drawings.
<First Embodiment>
FIG. 1 is a diagram showing an example of the control device of the first embodiment.

The control device 1 shown in FIG. 1 is a refrigerating system composed of a compressor 2, a condenser 3, an expansion valve 4, and an evaporator 5, and the degree of superheat of the refrigerant T _sh (controlled target) detected by the temperature sensor 6. the output value) to control the opening of the expansion valve 4 (controlled object) so as to follow the target value T _sht, suction pressure P _{e (output} value) the target of the controlled object of the refrigerant detected by the pressure sensor 7 controlling the rotational speed of the compressor 2 motor (controlled object) so as to follow the value P _et.

The control device 1 includes an output feedback controller 11 and a robust disturbance feedback controller 12.

Output feedback controller 11, for example, PI (Proportional Integral) control or PID (Proportional Integral Differential) a controller, superheat degree _{T sh} first manipulated variable so as to follow the target value _{T sht u ka} outputs, and outputs the first operation amount u _kb as suction pressure P _e follows the target value P _et.

Robust disturbance feedback controller 12 outputs the second manipulated variable u _la to control performance and stability of the closed loop system consisting of the expansion valve 4 output feedback controller 11 Metropolitan improved, the compressor 2 and the output The second operation amount _ulb is output so as to improve the control performance and stability of the closed loop system including the feedback controller 11.

Expansion valve 4 is driven based on the sum of the first manipulated variable u _ka and second manipulated variable u _la.

The motor of the compressor 2 is driven based on the added value of the first manipulated variable u _kb and the second manipulated variable u _lb.

In general, the model set in the refrigeration system has the characteristics of a relatively slow time constant and wasted time (several tens of seconds), so that a model error is likely to occur in the refrigeration system. In particular, it is difficult to design the control device 1 that expresses the control of the degree of superheat T _sh . The reason is that the refrigerant has non-linearity derived from the gas-liquid two-phase in the evaporator 5. This non-linearity can be expressed as model uncertainty. In addition, experimental results have revealed that the dominant uncertainty is the plant gain of the superheat model (see Non-Patent Document 4).

FIG. 2 is a block diagram of a two-input, two-output closed-loop system of the control device 1 shown in FIG.

The output feedback controller K (s) is a transfer function representing the output feedback controller 11, and is an addition of the output value y _{0 of the} controlled object G (s) and the output value y _w of the weighting function W (s). output value y (the degree of superheat _{T sh,} suction pressure _{P e)} is a value between the target value r (a target value _{T sht,} the target value _{P et)} difference between e is input, the first manipulated variable _{u k} (first The operation amount u _ka and the first operation amount u _kb ) are output.

In the weighting function W (s), the disturbance w is input and the output value y _w is output.
The controlled object G (s) is a transfer function expressing the expansion valve 4 and the compressor 2, and has a first manipulated variable _uk and a second manipulated variable _ul (second manipulated variable _ula , second The addition value u with the operation amount u _lb ) of is input, and the output value y ₀ is output.

The nominal plant model G _n (s) is a transfer function that outputs a nominal value (output value of the controlled object G (s) having no uncertainty) of the output value y ₀ of the controlled object G, and is the first transfer function. manipulated variable u _k is inputted to output an output value y _n.

The robust disturbance feedback controller L (s) is a transfer function expressing the robust disturbance feedback controller 12, and the difference ε between the output value y and the output value y _n is input and the second operation amount u _l is output. To do. In addition, "ε" shall be the same as the following symbol 1.

FIG. 3 is a block diagram of a first closed-loop system including a first expansion plant P (s) and a robust disturbance feedback controller L (s).

The first expansion plant P (s) includes an output feedback controller K (s), a weighting function W (s), a controlled object G (s), and a nominal plant model _Gn (s). The output feedback controller K (s), the weighting function W (s), the controlled object G (s), and the nominal plant model _Gn (s) are linear elements, respectively.

The robust disturbance feedback controller L (s) in the first closed-loop system is input with the difference ε between the output value y and the output value y _n , and outputs the second operation amount u _l .

It is assumed that the difference ε between the output value y and the output value y _n is a signal generated when the disturbance w or the uncertainty of the control target G (s) exists.

FIG. 4 is a flowchart showing an example of the design method of the control device 1 of the first embodiment.
First, the design device that designs the control device 1 sets a coefficient matrix of the equation of state that represents the controlled object G (s) (S11).

Let the equation of state of the controlled object G (s) be the following equation 1.

Further, the equation of state of the nominal plant model _Gn (s) is set to the following equation 2.

Further, A, B, and C are referred to as the following formula 3 and the following formula 4.

In the above equation 4, δ _a = (δ _{a, i} , ···, δ _{a, p} ), δ _b = (δ _{b, i} , ···, δ _{b, q} ), δ _c = (δ). _{c, i} , ···, δ _{c, r} ) are unknown vectors that represent the combination of all uncertainty quantities in a given dynamics. _{Also, A i, B i, C} i is the uncertainty of the controlled object G (s). Further, p, q, and r are arbitrary values. d is a disturbance signal.

That is, the design apparatus sets A, B, C, _An , B _n , and C _n as the coefficient matrix of the equation of state expressing the controlled object G (s). The coefficient matrix of the equation of state representing the controlled object G (s) may be set by the user.

Next, the design apparatus sets a coefficient matrix of the equation of state representing the output feedback controller K (s) (S12).

The equation of state expressing the output feedback controller K (s) is set to the following equation 5.

In addition, A _k , B _k , C _k , and D _k are given by the following equation 6.

That is, the design apparatus sets _Ak , B _k , C _k , and D _k as the coefficient matrix of the equation of state expressing the output feedback controller K (s). The coefficient matrix of the equation of state representing the output feedback controller K (s) may be set by the user.

Next, the design apparatus sets a coefficient matrix of the equation of state expressing the weighting function W (s) (S13).

Let the equation of state of the weighting function W (s) be the following equation 7.

In addition, A _w , B _w , C _w , and D _w are given by the following equation 8.

That is, the design apparatus sets A _w , B _w , C _w , and D _w as the coefficient matrix of the equation of state expressing the weighting function W (s). The coefficient matrix of the equation of state expressing the weighting function W (s) may be set by the user.

Next, the design device optimizes the design of the robust disturbance feedback controller L (s) in the first closed-loop system consisting of the first expansion plant P (s) and the robust disturbance feedback controller L (s). Performs arithmetic processing for this (S14).

For example, two constraints are introduced into the control design by Linear Matrix Inequality (LMI). Here, two constraints, a bounded lemma (Bounded Real Lemma) and a regional Pole Placement, are introduced (see Non-Patent Document 5). When the H _∞ norm of the controlled object G (s) is less than 1, the controlled object G (s) is bounded. That is, the bounded lemma guarantees robust performance. In addition, regional pole arrangement is introduced to specify the control performance (pole region). The robust disturbance feedback controller L (s) belongs to the output feedback control. Therefore, a linearizing change of variable is performed to formulate the optimal problem by the linear matrix inequality.

Let the equation of state of the first disturbance feedback controller L (s) be the following equation 9.

In addition, A _l , B _l , C _l , and D _l are given by the following equation 10.

Further, the equation of state of the first closed loop system including the first expansion system plant P (s) and the robust disturbance feedback controller L (s) is given by the following equation 11.

In addition, x _p , _Ap , B _PW , B _p , C _z , C _p , D _z , and D _PW are given by the following equation 12.

Here, ρ _z and ρ _w are minute values, and I is an identity matrix. ρ _z and ρ _w are introduced to maintain the full rank and avoid numerical problems if D _z and D _pw are zero matrices. That is, since it is necessary to make D _z and D _pw full rank, minute values (ρ _z , ρ _w ) are introduced.

At this time, z defines ε _z and D _z u _l as control performance, and defines each as an independent vector as shown in the following equation 13. Note that "ε _z " is the same as the symbol 2 below.

Here, the following equation 14 is used. ε _z is a vector excluding the disturbance D _w w (direct through).

Under such conditions, the first equation of state expressing the transfer function T (s) of the first closed-loop system in which the disturbance w- is input and the performance evaluation output z- is output is shown in Equation 15 below. Set.

It is defined as shown in the following equation 16.

Further, using the coefficient matrix of the first equation of state shown in the above equation 14, the constraint conditions for guaranteeing control performance and stability are formulated into an optimization problem expressed by the first linear matrix inequality (Equation 17). ..

It is defined as the following equation 18.

Here, N _c and R _c shown in the following equation 19 are used as input / output channels of the transfer function T (s) representing the first closed loop system.

Next, the design apparatus determines whether or not there is a solution that satisfies the first linear matrix inequality shown in the above equation 17 (S15).

When the design device determines that there is no solution satisfying the first linear matrix inequality shown in the above equation 17 (S15: No), after setting the coefficient matrix of the state equation expressing the weighting function W (s) again ( S13), the calculation process of the optimization problem for designing the robust disturbance feedback controller L (s) is performed (S14), and it is determined whether or not there is a solution satisfying the first linear matrix inequality shown in the above equation 17. (S15).

On the other hand, when the design device determines that there is a solution satisfying the first linear matrix inequality shown in the above equation 17 (S15: Yes), the coefficient matrix of the state equation expressing the robust disturbance feedback controller L (s) is lowered. Dimension (S16) and design the control device 1. When the design device determines that there is a solution satisfying the first linear matrix inequality shown in the above equation 17 (S15: Yes), the coefficient matrix of the state equation expressing the robust disturbance feedback controller L (s) is lowered. The control device 1 may be designed without being dimensioned.

That is, the design device uses a coefficient matrix (A _k , B _k , C _k , D _k ) of the state equation expressing the output feedback controller K (s) and a coefficient matrix of the state equation expressing the controlled object G (s). (A, B, C), the coefficient matrix of the state equation representing the nominal plant model G _n (s) ( _An , B _n , C _n ), and the coefficient matrix of the state equation representing the disturbance w (A _w , Based on B _w , C _w , D _w ), a first state equation representing a first closed-loop system consisting of a first expansion plant P (s) and a robust disturbance feedback controller L (s). Set, convert the first state equation to the first linear matrix inequality, and the coefficient matrix (A _w , B _w , C) of the state equation representing the disturbance w until there is a solution that satisfies the first linear matrix inequality. _w , D _w ) is adjusted.

Then, the design apparatus has a coefficient matrix of the state equation expressing the output feedback controller K (s) set in S12 and a coefficient matrix of the state equation expressing the disturbance feedback controller L (s) set in S16. Therefore, the control device 1 is designed.

In other words, the control parameter calculation device of the control device 1 obtains a first equation of state representing a first closed-loop system including the first expansion system plant P (s) and the robust disturbance feedback controller L (s). It is set based on the first predetermined parameter. Then, the control parameter calculation device of the control device uses the coefficient matrix of the first state equation to formulate the constraint conditions that guarantee the control performance and stability into the optimization problem expressed by the first linear matrix inequality. Then, the coefficient matrix of the state equation representing the robust disturbance feedback controller L (s) satisfying the first linear matrix inequality is obtained.

The first predetermined parameter is the coefficient matrix (A _k , B _k , C _k , D _k ) of the state equation expressing the output feedback controller K (s), and the state equation expressing the controlled object G (s). The coefficient matrix (A, B, C) and the coefficient matrix ( _An , B _n , C _n ) of the state equation representing the nominal plant model G _n (s) that outputs the nominal value of the output value of the controlled object G (s). ), The coefficient matrix of the state equation expressing the weighting function to the disturbance w (A _w , B _w , C _w , D _w ), and the coefficient matrix of the state equation expressing the robust disturbance feedback controller L (s). ..

The first expansion plant P (s) includes an output feedback controller K (s), a controlled object G (s), a nominal plant model _Gn (s), and a weighting function.

In the robust disturbance feedback controller L (s), the difference between the output value and the nominal value of the control target G (s) is input.

According to the control device 1 designed in this way, robustness can be improved against the uncertainty of the disturbance w and the control target G (s) (compressor 2, expansion valve 4), so that the closed loop system can be used. Stability can be improved.

Further, since the output feedback controller K (s) is treated as a part of the first expansion plant P (s), the structure of the output feedback controller 11 and the plant parameters of the transfer function expressing the output feedback controller 11 are set. Can be maintained. Therefore, the output feedback control device 11 is conservatively designed to improve maintainability, which is a weak point of conventional robust control, that is, stability of a closed loop system including uncertainty, and as a result, control performance is deteriorated. You can solve the problem of getting rid of it.

That is, according to the control device 1 of the first embodiment, since the existing control structure can be utilized, the control performance and stability of the closed loop system can be improved while reducing the design burden.

<Second Embodiment>
FIG. 5 is a diagram showing an example of the control device of the second embodiment. In FIG. 5, the same components as those shown in FIG. 1 are designated by the same reference numerals, and the description thereof will be omitted.

The control device 1 shown in FIG. 5 differs from the control device 1 shown in FIG. 1 in that the first anti-windup controller 13 prevents deterioration of control performance due to output saturation of the integrator included in the output feedback controller 11. A second anti-windup controller 14 is provided to prevent deterioration of control performance due to output saturation of the integrator included in the robust disturbance feedback controller 12.

For example, when the upper and lower limit values of the PID controller are reached (saturation) and there is an error between the manipulated variable and the target value, the I item (integrator) of the PID control adds the error (integration). vessel). Therefore, even if the control output of the PID controller is saturated, the output of the integrator in calculation increases. Deterioration of control due to saturation (overshoot, etc.) is called a windup phenomenon.

FIG. 6 is a block diagram when the two-input, two-output closed-loop system of the control device 1 shown in FIG. 5 is represented by a transfer function. Note that, in FIG. 6, the description of the same configuration as that shown in FIG. 2 will be omitted.

Saturation function Φ _{k (u)} is the output value of the output feedback controller K (s), a sum value as the manipulated variable u _k ^~ between the output value of the anti-windup controller lambda _k2 is input, the first manipulated variable _{u k} (first manipulated variable _{u ka,} first manipulated variable _{u kb)} outputs a. It should be noted that the _"u ^{k ~"} is the same as the following symbol 3.

For the saturation function Φ _l (u), the manipulated variable _ul ^~, which is the sum of the output value of the robust disturbance feedback controller L (s) and the output value of the anti-windup controller Λ _l2 , is input, and the second and it outputs the manipulated variable _{u l} (second operation amount u _la, the second manipulated variable u _lb). It should be noted that the _"u ^{l ~"} is the same as the following symbol 4.

Anti-windup controller lambda _k1, lambda _k2 is the difference between the manipulated variable _u ^{k ~} and first manipulated variable _{u k} is inputted.

Anti-windup controller lambda _l1, lambda _l2 the difference between the manipulated variable u _l ^~ and second manipulated variable u _l is entered.

FIG. 7 is a block diagram of a second closed-loop system (continuous system) including a dead zone function Ψ (u ^to ) and a second expansion plant _Tu to _d . In addition, "Ψ (u ^~ )" shall be the same as the following symbol 5, and " _{Tu ~ d} " shall be the same as the following symbol 6.

The second expansion plants _{Tu to d} include an output feedback controller K (s), a control target G (s), a nominal plant model G _n (s), and a first expansion plant P (s). For the robust disturbance feedback controller L (s) designed in, the anti-windup controllers Λ _k1, Λ _k2 for the output feedback controller K (s), and the robust disturbance feedback controller L (s). Includes anti-windup controllers Λ _{l1 and} Λ _l2 .

Further, the output feedback controller K (s) corresponds to the output feedback controller 11 of FIG. 1, and the robust disturbance feedback controller L (s) corresponds to the robust disturbance feedback controller 12 of FIG. 1, and is anti-wine. The do-up controllers Λ _{k1 and} Λ _k2 correspond to the first anti-windup controller 13 in FIG. 1, and the anti-windup controllers Λ _{l1 and} Λ _l2 correspond to the second anti-windup controller 14 in FIG. To express.

FIG. 8 is a flowchart showing an example of the design method of the control device 1 of the second embodiment. Since S11 to S16 shown in FIG. 8 are the same as S11 to S16 shown in FIG. 4, the description thereof will be omitted. Further, in the second embodiment, the anti-windup controllers Λ _k1, Λ _k2 , Λ _{l1, and} Λ _l2 are designed by using the dead zone function Ψ (u ^to ) indicating the dead zone characteristics (Non-Patent Document 3). reference).

The design device sets the upper and lower limit constraint conditions and the sector parameter κ￣ of the controlled object G (s) (compressor 2, expansion valve 4) (S17). In addition, "κ￣" shall be the same as the following symbol 7. Further, the upper and lower limit constraint conditions of the control target G (s) and the sector parameter κ￣ may be set by the user.

The non-linearity of the second closed-loop system shown in FIG. 7 is introduced by the upper and lower limit constraint conditions (maximum value and minimum value) of the controlled object G (s).

FIG. 9 is a diagram showing a saturation function Φ (u ^to ) indicating the input saturation of the controlled object G (s). In addition, "Φ (u ^~ )" shall be the same as the following symbol 8.

As shown in the saturation function Φ (u ^to ) (solid line) shown in FIG. 9, the manipulated variable u ^to _i calculated by the design apparatus peaks at the maximum and minimum values of the actual manipulated variable u _i .

FIG. 10 is a diagram showing a dead band function Ψ (u ^~ ).
As shown in the dead zone function Ψ (u ^~ ) (solid line) shown in FIG. 10, the actual manipulated variable Ψ _i (u ^~ _i ) is −u _i ^~ <manipulated quantity u _i ~ <u _i calculated by the design device. ^At , it becomes zero. Incidentally, "Ψ _{ⁱ (u i} ^~)" is the same as the following symbols 9, "- _u ^{i ~"} is the same as the following symbol 10, _"u ^{i ~"} is the same as the following symbols 11 And.

Further, the sector parameter κ￣∈ [0,1] shown in FIG. 10 is a linear for setting a sector region (sector nonlinear element) (diagonal portion) in which the nonlinear element of the dead zone function Ψ (u ^~ ) is regarded as a linear element. The slope of the function (broken line) (see Non-Patent Document 6). That is, the dead zone function Ψ (u ^~ ) includes a sector nonlinear element.

Deadband function Ψ ^{_(u k} ~), Ψ a _(u ^{l ~)} and the following equation 20. _{Incidentally, u} ^{k ~} is the operation amount of the front through the saturation function ^{_{Φ (u k ~), u}} l ~ is an operation amount before passing the saturation function Φ _{(u l).}

Next, the design device designs an anti-windup controller that guarantees the stability and control performance of the second closed-loop system consisting of the dead zone function Ψ (u ^~ ) and the second expansion plant _Tu ^~ _d. The calculation process of the optimization problem for the purpose is performed (S18).

_Let the equation of state of the anti-windup controllers Λ _{k1 and} Λ _{k2 be} the following equation 21. _Ak , B _k , C _k , and D _k shown in FIG. 11 indicate the coefficient matrix (A _k , B _k , C _k , D _k ) of the equation of state of the output feedback controller K (s).

_Let the equation of state of the anti-windup controllers Λ _{l1 and} Λ _{l2 be} the following equation 22. In the block diagram shown in FIG. 11, A _l , B _l , C _l , and D _l refer to the coefficient matrix (A _l , B _l , C _l , D _l ) of the equation of state of the robust disturbance feedback controller L (s). Shown.

Here, the last term _(u ^k _-u k ^~) in the formula 20 and the formulas 21 and assuming _{(u l} -u l ^~) a disturbance d (deadband function Ψ ^(u ~)), the internal stability Consider sex.

The second equation of state representing the second closed-loop system consisting of the dead zone function Ψ (u ^~ ) shown in FIG. 7 and the second expansion system plants _Tu ^~ _d is set as shown in Equation 23 below. The subscript δ means the linear matrix inequality of the number of each end point in the uncertainty (δ _a , δ _b , δ _c ) ∈ [-1,1] ^{p + q + r} , and the linear matrix inequality of all the end points. This is an optimization problem for finding only one common matrix P ^ that satisfies (Equation 17).

It is defined as the following equation 24.

Here, consider the positive-real lemma (see Non-Patent Document 8). This lemma derives the conditions converted into the frequency domain for the conversion from the second equation of state to the second linear matrix inequality.
(Lemma) Transfer function G (s): = C (sIA) ^-1 B + D is true. That is, the following equation 25 is obtained.

If there is a solution P that satisfies the linear matrix inequality shown in Equation 26 below, the linear system G (jω) is true.

This positive real is equivalent to the passivity. And this linear matrix inequality is passive only if the linear system G (jω) is divergent.

Next, when the disc theorem (see Non-Patent Document 7) is applied to the above equation 25, the following equation 27 is obtained.

Here, the dead zone function Ψ (u ^~ ) and the second expansion plant _Tu ^~ _d in the above equation 27 will be considered. The stable conditions of the second expansion plants _{Tu to d} shown in the following formula 28 are obtained by the following formula 29.

If there is a solution P ^~ that satisfies the second linear matrix inequality shown in the following equation 30, the second expansion system plant _Tu ^~ _d is stable ( _true ). In addition, "P ^~ " shall be the same as the following symbol 12.

Next, the design apparatus determines whether or not there is a solution P ^~ that satisfies the second linear matrix inequality shown in the above equation 30 (S19).

When the design device determines that there is no solution P ^~ that satisfies the second linear matrix inequality shown in the above equation 30 (S19: No), the upper and lower limit constraint conditions of the controlled object G (s) and the sector parameter κ￣ are again set. Set (S17).

The design device is then optimized for designing an anti-windup controller that guarantees the stability and control performance of the second closed-loop system consisting of the dead zone function Ψ (u ^~ ) and the second expansion plant Tu ^~ d. The problem is calculated (S18), and it is determined whether or not there is a solution P ^~ that satisfies the second linear matrix inequality shown in the above equation 30 (S19).

On the other hand, when the design device determines that there is a solution P ^~ satisfying the second linear matrix inequality shown in the above equation 30 (S19: Yes), the design apparatus expresses the output feedback controller K (s) set in S12. The coefficient matrix of the equation, the coefficient matrix of the state equation representing the disturbance feedback controller L (s) set in S16, and the anti-windup controllers Λ _k1, Λ _k2 , Λ _l1, Λ _l2 set in S18. The control device 1 is designed accordingly.

That is, the design device has a coefficient matrix (A _k , B _k , C _k , D _k ) of the state equation expressing the dead band function Ψ (u ^~ ) and the output feedback controller K (s) obtained by the sector parameter κ ￣. , The coefficient matrix of the state equation representing the controlled object G (s) (A, B, C), the coefficient matrix of the state equation expressing the nominal plant model G _n (s) ( _An , B _n , C _n ), and robustness disturbance feedback controller L (s) coefficient matrix of state equations representing the second _{to (a l, B l, C} l, D l) based on, representing a second expanding system plant _{T U～d} Set the state equation of, convert the second state equation to the second linear matrix inequality, and adjust the sector parameter κ￣ until there is a solution P ^~ that satisfies the second linear matrix inequality.

In other words, the control parameter arithmetic unit of the control device 1 has a second equation of state representing a second closed-loop system consisting of the second expansion system plant _Tu to _d and the dead zone function Ψ (u ^to ). Set based on the predetermined parameters of. Then, the control parameter calculation device of the control device 1 uses the coefficient matrix of the second state equation to express the constraint conditions that guarantee the control performance and stability by the second linear matrix inequality to the optimization problem. Formulate and find the control parameters of the anti-windup controllers Λ _k1, Λ _k2 , Λ _l1, and Λ _{l 2} that satisfy the second linear matrix inequality.

The second predetermined parameter is the coefficient matrix (A _l ) of the equation of state expressing the dead band function Ψ (u ^~ ) obtained by the first predetermined parameter and the sector parameter κ￣ and the robust disturbance feedback controller L (s). , B _l , C _l , D _l ).

The second expansion plants _{Tu to d} include an output feedback controller K (s), a controlled object G (s), a nominal plant model G _n (s), and a robust disturbance feedback controller L (s). , Anti-windup controllers Λ _k1, Λ _k2 , Λ _l1, Λ _l2 and the like.

According to the control device 1 designed in this way, robustness can be improved against the uncertainty of the disturbance w and the control target G (s) (compressor 2, expansion valve 4), so that the closed loop system can be used. Stability can be improved.

Further, since the output feedback controller K (s) is treated as a part of the first expansion plant P (s), the structure of the output feedback controller 11 and the plant parameters of the transfer function expressing the output feedback controller 11 are set. Can be maintained. Therefore, the output feedback control device 11 is conservatively designed in order to improve maintainability, which is a weak point of conventional robust control, that is, stability of a closed loop system including uncertainty, and as a result, control performance is deteriorated. It is possible to solve the problem of doing.

Further, since the control device 1 is provided with the anti-windup controllers Λ _k1, Λ _k2 , Λ _{l1, and} Λ _l2 , the integration included in the output feedback controller K (s) and the robust disturbance feedback controller L (s). It is possible to prevent deterioration of control performance due to output saturation of the integrator.

That is, according to the control device 1 of the present embodiment, while utilizing the features of the existing control which is the effect of the first embodiment, the windup phenomenon of the controller including the integrating element is prevented even if the control output is saturated. , The stability of the closed loop system can be improved.

<Third Embodiment>
FIG. 12 is a flowchart showing an example of the design method of the control device 1 according to the third embodiment. Since S11 to S19 shown in FIG. 12 are the same as S11 to S19 shown in FIG. 8, the description thereof will be omitted. Further, the control device 1 in the third embodiment is the same as the control device 1 shown in FIG.

The flow chart shown in FIG. 12 differs from the flowchart shown in FIG. 8 after the design apparatus lowers the coefficient matrix of the equation of state representing the robust disturbance feedback controller L (s) (S16), and then anti-wine. This is a point (S17α) for determining whether or not to design the do-up controllers Λ _k1, Λ _k2 , Λ _{l1, and} Λ _l2 .

When the design device determines to design the anti-windup controllers Λ _k1, Λ _k2 , Λ _{l1, and} Λ _l2 (S17α: Yes), the design of the anti-windup controllers Λ _k1, Λ _k2 , Λ _{l1, and} Λ _l2 . When it is determined that the control device 1 is designed and the anti-windup controllers Λ _k1, Λ _k2 , Λ _{l1, and} Λ _l2 are not designed after the processing (S17 to S19) (S17α: No), the anti-windup is performed. The control device 1 is designed without _performing the design processing of the controllers Λ _k1, Λ _k2 , Λ _{l1, and} Λ _l2 .

According to the third embodiment, the degree of freedom in the design method of the control device 1 can be improved as compared with the second embodiment. Further, when it is desired to change the control system of the mounting destination from the first embodiment to the second embodiment or vice versa, the third embodiment can realize both embodiments, so that the cost required for the change is high. There is also a merit that it does not cost.

<Examples corresponding to the first to third embodiments>
The transfer function (model) corresponding to the expansion valve 4 and the transfer function (model) corresponding to the compressor 2 shown in FIG. 1 or 5 can be described with a first-order delay + dead time (see Non-Patent Document 9). .. These transfer functions are then obtained by step response tests under different operating conditions.

For example, the manipulated variable input to the expansion valve 4 is u ₁ , the superheat degree T _sh is y ₁ , the manipulated variable input to the compressor 2 is u ₂ , the suction pressure _Pe is y ₂ , and the subsystem is g ₁₁ . The control target g including the uncertainty when g ₁₂ , g ₂₁ and g ₂₂ are set to the following equations 31 and 32. Let k be the gain, τ be the time constant, and θ be the wasted time. Further, "g" is the same as the symbol 13 below.

Next, the nominal model G _n (t) shown in the following equations 33 and 34 is obtained by the average value of the subsystem _gij .

Here, for a simpler control design, the dead time is approximated to the first-order lag system. For a simpler design, some gain parameters of the controlled object G are set to the gain parameter k ₁₁ including uncertainty, and the remaining gain parameters of the model are the gain parameters k ₁₂ and k _{21 of} the nominal plant model. Set to k ₂₂ . It is assumed that the gain parameter k ₁₁ corresponds to the degree of superheat T _sh and indicates the most dominant uncertainty).

Therefore, the subsystem g ₁₁ is approximated by the following equation 35. In addition, "g ₁₁ " shall be the same as the following symbol 14.

Further, the remaining subsystem _gij is _expressed by the following equation 36. In addition, " _gij " shall be the same as the following symbol 15.

Then, the output feedback controller K (s) and the weighting function W (s) are designed based on, for example, Table 1 and Table 2 below.

Next, the robust disturbance feedback controller L (s) is designed.

As a result of the optimum calculation, γ = 0.8255 is obtained as the value of the H _∞ performance of the robust disturbance feedback L (s) having a dimension of full order (dim (A _l ) = 2 (n + m), n = 8, m = 2). It shall be. The dimensions of the expansion plant P (s) including the output feedback controller K (s), the controlled object G (s), the nominal plant model _Gn (s), and the weighting function W (s) are in full order. .. In order to apply it to the system of the industrial world, it is necessary to lower the dimension of the equation of state expressing the robust disturbance feedback controller L (s). Therefore, the dimension of the equation of state expressing the robust disturbance feedback controller L (s) is reduced. For example, the dimension is reduced to the equation of state expressing the robust disturbance feedback controller L (s) of the second-order lag system.

The matrix coefficients (A _l , B _l , C _l , D _l ) of the equation of state expressing the robust disturbance feedback controller L (s) after the reduction in dimension are set to the following equation 37.

The second-order lag system robust disturbance feedback controller L (s) shall retain the main features of the original (full-order) robust disturbance feedback controller L (s) (see FIG. 13).

Next, the anti-windup controllers Λ _k1, Λ _k2 , Λ _{l1, and} Λ _l2 are designed. The sector parameter κ￣ is 0.9I. I is an identity matrix.

As a result of the calculation, Λ _k1, Λ _k2 , Λ _{l1, and} Λ _l2 are given by the following equation 38.

Under the conditions shown in Table 3 below, the simulation of the step response and the disturbance response is performed under the conditions of the presence / absence of the output feedback controller + robust disturbance feedback controller and the presence / absence of the first and second anti-windup controllers. (See FIGS. 14 and 15). Three cases subsystems _{g 11 (case1: k min =} -10.0, case2: k max = -9.0, case3: k n = -9.5) was simulated.

Table 4 below shows the evaluation results of each design method. Five design methods were evaluated, and six items were evaluated. The evaluation items 1 and 2 are values for evaluating the robustness of the control devices 1a and 1b with respect to the uncertainty of the control target G (s). For example, the absolute value error of the output value y of the control target G (s). | The maximum value of y _casei (t) -y _casei (t) | (see FIG. 16). It should be noted that i = 1,2,3, t = [0, T]. Further, the smaller the values of the evaluation items 1 and 2, the higher the robustness. In addition, evaluation items 3 and 4 calculate the average value of Integral Absolute Error (IAE) in each case. Further, the evaluation item 5 confirms whether or not the upper / lower limit constraint of u ₂ deviates. Further, the evaluation item 6 confirms whether or not the target value r is being followed. Design number 1: PI + robust DFC with anti-windup controller obtained the best value (minimum value) for all evaluation items. On the other hand, in design number 2: PI + robust DFC without anti-windup, the control performance of the evaluation item deteriorated due to the decrease in the windup of the integral term (see FIG. 14). Design numbers 3, 4, and 5 have not cleared evaluation items 5 and 6. Although the output values y ₂ can follow the target value r in the design numbers 3 and 5, they deviate from the constraint of the control output u ₂ . On the other hand, in design number 4, the output value y ₂ could not follow the target value r because the control output u ₂ was saturated (see FIG. 15). Therefore, it can be confirmed that design numbers 3, 4, and 5 do not work in the actual system.

That is, when the control device 1 is designed by the design method of the first embodiment, the evaluation item 1 becomes 0.1677, the evaluation item 2 becomes 0.0201, and the output value y becomes the target value r, as shown in Table 4 below. I followed.

When the control device 1 was designed by the design method of the second embodiment, the evaluation item 1 was 0.1677, the evaluation item 2 was 0.0193, and the output value y followed the target value r.

When the control device 1 having only the output feedback controller 11 was designed, the evaluation item 1 was 0.5455 and the evaluation item 2 was 0.0172, but the operation amount u was saturated and the output value y followed the target value r. I didn't.

As described above, when the control device 1 is designed by the design method of the first embodiment or when the control device 1 is designed by the design method of the second embodiment, the control device 1 including only the output feedback controller 11 It is possible to improve the stability of the closed loop system while maintaining the control performance as compared with the case of designing.

Further, when the control device 1 is designed by the design method of the first embodiment, the stability of the closed loop system can be improved as compared with the case where the control device 1 is designed by the design method of the second embodiment. it can.

<Fourth Embodiment>
FIG. 17 is a diagram showing an example of the control device of the fourth embodiment. In FIG. 17, the same components as those shown in FIG. 5 are designated by the same reference numerals, and the description thereof will be omitted.

The control device 1 shown in FIG. 17 differs from the control device 1 shown in FIG. 5 in that the first discrete anti-windup controller 15 is provided instead of the first anti-windup controller 13. The point is that the second discrete anti-windup controller 16 is provided instead of the second anti-windup controller 14.

Further, the control device 1 shown in FIG. 17 is different from the control device 1 shown in FIG. 5 in that the discrete output feedback controller 11'is provided instead of the output feedback controller 11 and the robust disturbance feedback controller is provided. Instead of 12, a discrete robust disturbance feedback controller 12'is provided.

FIG. 18 is a block diagram when the two-input, two-output closed-loop system of the control device 1 shown in FIG. 17 is represented by a transfer function. In FIG. 18, the description of the same configuration as that shown in FIG. 11 will be omitted.

The output feedback controller K (s) corresponds to the discrete output feedback controller 11'in FIG.

The robust disturbance feedback controller L (s) corresponds to the discrete robust disturbance feedback controller 12'in FIG.

The discrete anti-windup controllers Λ _k1 , Λ _k2 and the first sampling delayer z ^-1 correspond to the first discrete anti-windup controller 15 in FIG. The first sampling delayer z- ¹ delays the output value of the discrete anti-windup controller Λ _k2 by one sampling in order to avoid the problem of algebraic loop due to discretization.

The discrete anti-windup controllers Λ _l1 , Λ _l2 and the second 1 sampling delayer z ^-1 correspond to the second discrete anti-windup controller 16 in FIG. The second sampling delayer z ^-1 delays the output value of the discrete anti-windup controller Λ _l2 by one sampling in order to avoid the problem of algebraic loop due to discretization.

Saturation function .phi.k (u) is the output value of the output feedback controller K (s), a sum value as the manipulated variable u _k ^~ between the output value of the first first sampling delay unit z ^-1 is input, the Outputs the operation amount uk of 1 (first operation amount u _ka , first operation amount u _kb ).

For the saturation function Φl (u), the operation amount _ul ^~ which is the sum of the output value of the robust disturbance feedback controller L (s) and the output value of the second sampling delayer z ^-1 is input. The second operation amount u _l (second operation amount u _la , second operation amount u _lb ) is output.

Discrete anti-windup controller lambda _k1, lambda _k2 is the manipulated variable _u ^{k ~} and difference _{v k} of the first manipulated variable _{u k} is inputted.

Discrete anti-windup controller lambda _l1, lambda _l2 the operation amount u _l ^~ and difference v _l of the second manipulated variable u _l is entered.

FIG. 19 is a flowchart showing an example of the design method of the control device 1 of the fourth embodiment. Since S11 to S16 shown in FIG. 19 are the same as S11 to S16 shown in FIG. 8, the description thereof will be omitted.

The design device discretizes the entire system (S21).
The discretized anti-windup control design has been proposed by A. Syaichu-Rohman and RH Middleton et al., And the design method has been prepared for one degree of freedom control (see Non-Patent Document 10). The system in the fourth embodiment is classified into two degrees of freedom control. Therefore, the discretized anti-windup control design proposed by A. Syaichu-Rohman and RH Middleton et al. Is redesigned into a two-degree-of-freedom type.

First, the discretization of the continuous system (controlled object G (s), nominal plant model _Gn (s), weighting function W (s), disturbance feedback controller L (s)) shown in FIG. 11 is based on the bilinear method. It is carried out (see Non-Patent Document 11).

For example, when a general continuous system is defined as Hc (s) and a discretized system is defined as H (z), the conversion from s to z by the bilinear method is described by the following equation 39.

That is, the following equation 40 is obtained.

In addition, T _d is a sampling period. Further, t is the sampling discrete time.

Using the s to z conversion method by the bilinear method, the above equations 1, 2, 2, 4, 5, 5, 7 and 9 representing the continuous system shown in FIG. 11 are discrete shown in FIG. It can be converted into the following equations 45, 46, 47, and 48 that represent the system.

In the discrete system shown in FIG. 18, the vector v (t), the dead band function Ψ (u ^~ (t)), and the saturation function Φ (u ^~ (t)) are described by the following equations 41 to 44.

Here, u ^~ is the input (control output) of the saturation function, Φ: R ^m → R ^m is the saturation function, Ψ: R ^m → R ^m is the dead zone function, and I is the identity matrix. The saturation function Φ is shown in FIG. 9, and the dead zone function Ψ is shown in FIG. Further, "R ^m " is the same as the symbol 16 below.

Further, in the discrete system shown in FIG. 18, the difference equation of the output feedback controller K (s) including the discrete anti-windup controllers Λ _k1 and Λ _k2 is described by the following equation 45.

Further, in the discrete system shown in FIG. 18, the difference equations of the discrete anti-windup controllers Λ _l1 and Λ _l2 are described by the following equation 46.

Then, the above expression ^{_{45 (u k ~ (t)}} -u k (t)) and of the formula ^{_{46 (u l ~ (t)}} -u l (t)) of the disturbance v (t) (the vector v (t )), And by summarizing the above equations 41 to 46, the following equation 47 is obtained. That is, the difference equation expressing the third closed loop system (discrete system) including the dead band function Ψ (u ^to (t)) shown in FIG. 20 and the third expansion system plants _Tu to _d is given by the following equation 47.

FIG. 20 is a block diagram of a third closed-loop system consisting of a dead zone function Ψ (u ^to (t)) and a third expansion plant _Tu to _d .

The system shown in FIG. 20 is a simplification of the system shown in FIG.
That is, in the third expansion plant _{Tu to d} , the discretized output feedback controller K, the discretized controlled object G, the discretized nominal plant model G _n, and the discretized robust Disturbance feedback controller L, first 1-sampling delayer z ^-1 , second 1-sampling delayer z ^-1 , discrete anti-windup controllers Λ _k1 , Λ _k2 , and discrete anti-windup Includes controllers Λ _l1 and Λ _l2 .

It is defined as the following equation 48.

Next, the design device is for designing an anti-windup controller that guarantees the stability and control performance of the third closed-loop system consisting of the dead zone function Ψ (u ~) and the third expansion plant Tu ~ d. Performs arithmetic processing of the optimization problem of (S22).

A. The discrete anti-windup controller proposed by Syaichu-Rohman and RH Middleton et al. Is formulated using the above equations 47 and 48 to solve the optimization problem including the third linear matrix inequality. Is obtained.

Here, M> 0 ∈ R ^{2m × 2m} is a diagonal matrix, V: = ΛM ∈ R ^{2m × 2m} is an arbitrary matrix, and γ ₂ and η are scalars. The subscript δ means the linear matrix inequality of the number of each end point in the uncertainty (δ _a , δ _b , δ _c ) ∈ [-1,1] ^{p + q + r} , and the linear matrix inequality of all the end points. It is an optimization problem to find only one common matrix Q ^~ that satisfies. “R ^{2m × 2m} ” shall be the same as the symbol 17 below, and “Q ^~ ” shall be the same as the symbol 18 below.

Next, the design apparatus determines whether or not there is a solution Q ^~ that satisfies the third linear matrix inequality shown in the above equation 47 (S23).

When the design device determines that there is no solution Q ^~ that satisfies the third linear matrix inequality shown in the above equation 47 (S23: No), the entire system is discretized again (S21) to obtain an anti-windup controller. The calculation process of the optimization problem is performed (S22), and it is determined whether or not there is a solution Q ^~ that satisfies the third linear matrix inequality (S23).

On the other hand, when the design device determines that there is a solution Q ^~ that satisfies the third linear matrix inequality (S23: Yes), the coefficient matrix of the state equation expressing the output feedback controller K (s) set in S12 , The coefficient matrix of the state equation representing the disturbance feedback controller L (s) set in S16, and the discrete anti-windup controllers Λ _k1 , Λ _k2 and the discrete anti-windup controller Λ set in S21. _The control device 1 is designed according to _{l1 and} Λ _l2 .

That is, the design device has a dead band function Ψ (u ^~ ), a coefficient matrix (A _k , B _k , C _k , D _k ) of the state equation expressing the output feedback controller K (s), and a controlled object G (s). The coefficient matrix (A, B, C) of the state equation representing the state equation, the coefficient matrix ( _An , B _n , C _n ) of the state equation expressing the nominal plant model G _n (s), and the robust disturbance feedback controller L. A third deadband function Ψ (u ^~ (t)) and a third robust disturbance feedback controller based on the coefficient matrix (A _l , B _l , C _l , D _l ) of the state equation representing (s). A difference equation representing a third closed-loop system consisting of _Tu to _d is set, and the difference equation is converted into a third linear matrix inequality to obtain a solution Q ^~ that satisfies the third linear matrix inequality.

In other words, the design device has a dead band function Ψ (u ^~ (t)), a coefficient matrix of the state equation expressing the output feedback controller K (s), a coefficient matrix of the state equation expressing the controlled object G (s), Based on the coefficient matrix of the state equation representing the nominal plant model G _n (s) and the coefficient matrix of the state equation representing the robust disturbance feedback controller L (s), a difference equation representing the third closed-loop system is obtained. Set. In addition, the design device uses the coefficient matrix of the difference equation to formulate the constraint conditions that guarantee control performance and stability into an optimization problem expressed by the third linear matrix inequality, and the third linear matrix. _Find the parameters of the matrices Q ^~ that satisfy the inequality, the discrete anti-windup controllers Λ _k1 , Λ _k2, and the discrete anti-windup controllers Λ _l1 , Λ _l2 .

According to the control device 1 designed in this way, robustness can be improved against the uncertainty of the disturbance w and the control target G (s) (compressor 2, expansion valve 4), so that the closed loop system can be used. Stability can be improved.

Further, since the output feedback controller K (s) is treated as a part of the third expansion plant _{Tu to d} , the structure of the discrete output feedback controller _11'and the discrete output feedback controller _11'are expressed. The plant parameters of the transfer function can be maintained. Therefore, in order to improve maintainability, which is a weak point of conventional robust control, that is, stability of a closed loop system including uncertainty, the discrete output feedback controller 11'is designed conservatively, and as a result, control is performed. It is possible to solve the problem of reduced performance.

Further, since the control device 1 is provided with the discrete anti-windup controllers Λ _{k1 and} Λ _k2 and the discrete anti-windup controls Λ _{l1 and} Λ _l2 , the output feedback controller K (s) and the robust disturbance feedback controller are provided. It is possible to prevent deterioration of control performance due to output saturation of the integrator included in L (s).

In addition, after discretizing the closed-loop system, the coefficient matrix of the difference equation expressing the third expansion system plants _Tu to _d satisfying the third linear matrix inequality, the discrete anti-windup controllers Λ _k1 , Λ _k2. And since the parameters of the discrete anti-windup controllers Λ _l1 and Λ _l2 are obtained, the stability can be improved for the discrete closed-loop system.

That is, according to the control device 1 of the present embodiment, while utilizing the features of the existing control which is the effect of the first embodiment, the windup phenomenon of the controller including the integrating element is prevented even if the control output is saturated. , A discrete closed-loop system, that is, the stability of a real system can be improved.

<Fifth Embodiment>
FIG. 21 is a flowchart showing an example of the design method of the control device 1 according to the fifth embodiment. Since S11 to S16 and S21 to S23 shown in FIG. 21 are the same as S11 to S16 and S21 to S23 shown in FIG. 19, the description thereof will be omitted. Further, the control device 1 in the fifth embodiment is the same as the control device 1 in the fourth embodiment shown in FIG.

The flow chart shown in FIG. 21 differs from the flowchart shown in FIG. 19 after the design apparatus lowers the coefficient matrix of the equation of state representing the robust disturbance feedback controller L (s) (S16), and then the discrete type. This is a point (S17β) for determining whether or not to design the anti-windup controllers Λ _k1, Λ _k2 , Λ _{l1, and} Λ _l2 .

When the design device determines to design the discrete anti-windup controllers Λ _k1, Λ _k2 , Λ _l1, Λ _l2 (S17β: Yes), the discrete anti-windup controllers Λ _k1, Λ _k2 , Λ _l1, After designing Λ _l2 (S21 to S23), when the controller 1 is designed and it is determined that the discrete anti-windup controllers Λ _k1, Λ _k2 , Λ _{l1, and} Λ _l2 are not designed (S17β: No), the control device 1 is designed without designing the discrete anti-windup controllers Λ _k1, Λ _k2 , Λ _{l1, and} Λ _l2 .

According to the fifth embodiment, the degree of freedom in the design method of the control device 1 can be improved as compared with the fourth embodiment. Further, when it is desired to change the control system of the mounting destination from the first embodiment to the fourth embodiment or vice versa, the fifth embodiment can realize both embodiments, so that the cost required for the change is high. There is also a merit that it does not cost.

<Examples corresponding to the 4th and 5th embodiments>
In the examples corresponding to the fourth embodiment and the fifth embodiment, the output feedback controller K (s) and the weighting function W (s) are designed based on Table 1 and Table 2 above. Since it is the same as the embodiment corresponding to the first to third embodiments, the description thereof will be omitted.

The dimension of the equation of state expressing the robust disturbance feedback controller L (s) is reduced.
The gain matrix coefficient D _l of the matrix coefficients (A _l , B _l , C _l , D _l ) of the equation of state expressing the robust disturbance feedback controller L (s) after the reduction in dimension is set to 50 below. ..

The low-dimensional post-robust disturbance feedback controller L (s) shall retain the main features of the original (full-order) robust disturbance feedback controller L (s) (see FIG. 22).

Next, the discrete anti-windup controllers Λ _k1, Λ _k2 , Λ _{l1, and} Λ _l2 are designed using the above equations 48 and 49.

As a result of the calculation, Λ _k1, Λ _k2 , Λ _{l1, and} Λ _l2 are set to the following equation 51.

The simulation conditions for step response and disturbance response are shown in Table 5 below under the conditions with and without the output feedback controller + robust disturbance feedback controller, and with and without the first and second discrete anti-windup controllers. It was carried out under (see FIGS. 23 and 24). Three cases subsystems _{g 11 (case1: k min =} -10.0, case2: k max = -9.0, case3: k n = -9.5) was simulated.

Table 6 below shows the evaluation results of each design method. Five design methods were evaluated, and five items were evaluated. The evaluation items 1 and 2 are values for evaluating the robustness of the control devices 1a and 1b with respect to the uncertainty of the control target G (s). For example, the absolute value error of the output value y of the control target G (s). | The maximum value of y _casei (t) -y _casei (t) | (see FIG. 16). It should be noted that i = 1,2,3, t = [0, T]. Further, the smaller the values of the evaluation items 1 and 2, the higher the robustness. In addition, evaluation items 3 and 4 calculates the maximum value of _{y 1} and _{y 2.} Furthermore, evaluation items 5 to check for deviations to a lower limit restriction on the u _2. Design number 1: PI + robust DFC with anti-windup controller has obtained the best value (minimum value) for all evaluation items. On the other hand, in design number 2: PI + robust DFC without anti-windup, the control performance of the evaluation items deteriorates due to the decrease in the windup of the integral term (see Table 6 and FIG. 23). Design number 3: PI + robust DFC with no saturation has some evaluation items that are smaller than design number 1, but design number 3 cannot be implemented in an actual system because the limiter is not considered.

Both design number 4 and design number 5 are designed only for PI control, and their performance is inferior to that of robust disturbance feedback control (see FIG. 24).

From these results, it was confirmed that the design number 1 corresponding to the fourth embodiment and the fifth embodiment shows the best control performance in consideration of the input constraint.

As described above, when the control device 1 is designed by the design method of the fourth embodiment or when the control device 1 is designed by the design method of the fifth embodiment, the control device 1 including only the output feedback controller 11 is designed. It is possible to improve the stability of the closed loop system while maintaining the control performance.

Further, when the control device 1 is designed by the design method of the fourth embodiment, the stability of the closed loop system can be improved as compared with the case where the control device 1 is designed by the design method of the first embodiment.

<Hardware configuration of control device 1 or design device>
FIG. 25 is a diagram showing a hardware configuration of the control device 1 or the design device.

As shown in FIG. 25, the control device 1 or 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, and a communication control device. It includes 1507 and a medium drive device 1508. These elements 1501 to 1508 in the control device 1 or the design device are connected to each other by a bus 1510, and data can be exchanged 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 control device 1 or the design device by executing various programs including the operating system. Further, the processor 1501 performs each process shown in FIG. 4, FIG. 8, FIG. 12, FIG. 19, or FIG. 21, for example.

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 control device 1 or the design device is started is recorded in advance. Further, the RAM of the main storage device 1502 is used as a work storage area by the processor 1501 as needed when executing 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 non-volatile 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, various data, and the like executed by the processor 1501.

The input device 1504 is, for example, a keyboard device, a touch panel device, or the like. When the user of the control device 1 or the design device performs a predetermined operation on the input device 1504, the input device 1504 transmits the input information associated with the operation content to the processor 1501. The input device 1504 can be used, for example, for inputting various set values such as a coefficient matrix of a state equation expressing the output feedback controller K (s).

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

The input / output interface 1506 connects the control device 1 or the design device to other electronic devices. 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 control device 1 or the design device to a network such as the Internet and controls various communications between the control device 1 or the design device and other electronic devices via the network.

The medium drive device 1508 reads out the programs and data recorded in the portable storage medium 16 and writes the data stored in the auxiliary storage device 1503 to the portable storage medium 16. As the medium drive device 1508, for example, a memory card reader / writer corresponding to one or a plurality of types of standards can be used. When a memory card reader / writer is used as the medium drive device 1508, the portable storage medium 16 is a memory card (flash memory) of a standard supported by the memory card reader / writer, for example, a Secure Digital (SD) standard. ) Etc. are available. Further, as the portable recording medium 16, for example, a flash memory provided with a USB standard connector can be used. Further, when the control device 1 or the design device 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 discs that can be used 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 to store a program or the like including the processing shown in FIGS. 4, 8, 12, 19, or 21.

The control device 1 or the design device does not need to include all the elements 1501 to 1508 shown in FIG. 25, and some elements may be omitted depending on the application and conditions.

The present invention is not limited to the above embodiments, and various improvements and changes can be made without departing from the gist of the present invention.

1 Control device 2 Compressor 3 Condenser 4 Expansion valve 5 Evaporator 6 Temperature sensor 7 Pressure sensor 11 Output feedback controller 12 Robust disturbance feedback controller 13 First anti-windup controller 14 Second anti-windup controller 15 1st discrete anti-windup controller 16 2nd discrete anti-windup controller

Claims (11)

An output feedback controller that outputs the first manipulated variable so that the output value of the controlled object to which the sum of the first manipulated variable and the second manipulated variable is input follows the target value, and the closed loop system. In a device for calculating control parameters of a control device including a robust disturbance feedback controller that outputs the second manipulated variable so as to improve control performance and stability.
A first equation of state representing a first closed-loop system consisting of a first expansion plant and the robust disturbance feedback controller is set based on a first predetermined parameter.
Using the coefficient matrix of the first equation of state, the constraints that guarantee control performance and stability are formulated into an optimization problem expressed by the first linear matrix inequality.
Find the coefficient matrix of the equation of state representing the robust disturbance feedback controller that satisfies the first linear matrix inequality .
Order of the coefficient matrix of state equation that expresses the robust disturbance feedback controller, the control parameter calculating device of the control device, characterized in that that will be dimension reduction. The first predetermined parameter is a coefficient matrix of a state equation representing the output feedback controller, a coefficient matrix of a state equation representing the controlled object, and a nominal plant model that outputs a nominal value of an output value of the controlled object. It is a coefficient matrix of the state equation expressing the above, a coefficient matrix of the state equation expressing the weighting function to the disturbance, and a coefficient matrix of the state equation expressing the robust disturbance feedback controller.
The first expansion plant includes the output feedback controller, the controlled object, the nominal plant model, and a weighting function.
The control parameter calculation device for a control system according to claim 1, wherein the robust disturbance feedback controller is input with a difference between an output value to be controlled and a nominal value. The control device is
A first anti-windup controller that prevents deterioration of control performance due to output saturation of the integrator included in the output feedback controller, and
A second anti-windup controller that prevents deterioration of control performance due to output saturation of the integrator included in the robust disturbance feedback controller, and
With more
A second equation of state representing a second closed-loop system consisting of a second expansion plant and a dead zone function is set based on a second predetermined parameter.
Using the coefficient matrix of the second equation of state, the constraints that guarantee control performance and stability are formulated into an optimization problem expressed by the second linear matrix inequality.
The control parameter calculation device of the control device according to claim 1 or 2, wherein the control parameters of the first and second anti-windup controllers satisfying the second linear matrix inequality are obtained. The first predetermined parameter is a coefficient matrix of a state equation representing the output feedback controller, a coefficient matrix of a state equation representing the controlled object, and a nominal plant model that outputs a nominal value of an output value of the controlled object. It is a coefficient matrix of the state equation expressing the above, a coefficient matrix of the state equation expressing the weighting function to the disturbance, and a coefficient matrix of the state equation expressing the robust disturbance feedback controller.
The second predetermined parameter is a coefficient matrix of the equation of state expressing the dead zone function obtained by the first predetermined parameter and the sector parameter and the robust disturbance feedback controller.
The second expansion plant includes the output feedback controller, the controlled object, the nominal plant model, the robust disturbance feedback controller, the first anti-windup controller, and the second anti. The control parameter calculation device for a control system according to claim 3 , further comprising a windup controller. The first predetermined parameter is a coefficient matrix of a state equation representing the output feedback controller, a coefficient matrix of a state equation representing the controlled object, and a nominal plant model that outputs a nominal value of an output value of the controlled object. It is a coefficient matrix of the state equation expressing the above, a coefficient matrix of the state equation expressing the weighting function to the disturbance, and a coefficient matrix of the state equation expressing the robust disturbance feedback controller.
Claims 1 to 4 are characterized in that some of the plant parameters to be controlled are set to plant parameters indicating uncertainty, and the remaining plant parameters are set to the plant parameters of the nominal plant model. The control parameter calculation device of the control device according to any one of the above items. An output feedback controller that outputs the first manipulated variable so that the output value of the controlled object to which the sum of the first manipulated variable and the second manipulated variable is input follows the target value, and the closed loop system. It is a method of designing a control device including a robust disturbance feedback controller that outputs the second manipulated variable so as to improve control performance and stability.
The design device for designing the control device is
The first equation of state corresponding to the first closed-loop system including the first expansion plant and the robust disturbance feedback controller is set based on the first predetermined parameter.
Using the coefficient matrix of the first equation of state, the constraints that guarantee control performance and stability are formulated into an optimization problem expressed by the first linear matrix inequality.
Find the coefficient matrix of the equation of state representing the robust disturbance feedback controller that satisfies the first linear matrix inequality .
Order of the coefficient matrix of state equation that expresses the robust disturbance feedback controller, a method of designing a control device, characterized in that that will be dimension reduction. The first predetermined parameter is a coefficient matrix of a state equation representing the output feedback controller, a coefficient matrix of a state equation representing the controlled object, and a nominal plant model that outputs a nominal value of an output value of the controlled object. It is a coefficient matrix of the state equation expressing the above, a coefficient matrix of the state equation expressing the weighting function to the disturbance, and a coefficient matrix of the state equation expressing the robust disturbance feedback controller.
The first expansion plant includes the output feedback controller, the controlled object, the nominal plant model, and a weighting function.
The method for designing a control device according to claim 6 , wherein the robust disturbance feedback controller is input with a difference between an output value to be controlled and a nominal value. The control device is
A first anti-windup controller that prevents deterioration of control performance due to output saturation of the integrator included in the output feedback controller, and
A second anti-windup controller that prevents deterioration of control performance due to output saturation of the integrator included in the robust disturbance feedback controller, and
With more
A second equation of state representing a second expansion plant and a second closed-loop system consisting of dead zone functions is set based on a second predetermined parameter.
Using the coefficient matrix of the second equation of state, the constraints that guarantee control performance and stability are formulated into an optimization problem expressed by the second linear matrix inequality.
The method for designing a control device according to claim 6 or 7 , wherein the control parameters of the first and second anti-windup controllers satisfying the second linear matrix inequality are obtained. The first predetermined parameter is a coefficient matrix of a state equation representing the output feedback controller, a coefficient matrix of a state equation representing the controlled object, and a nominal plant model that outputs a nominal value of an output value of the controlled object. It is a coefficient matrix of the state equation expressing the above, a coefficient matrix of the state equation expressing the weighting function to the disturbance, and a coefficient matrix of the state equation expressing the robust disturbance feedback controller.
The second predetermined parameter is a coefficient matrix of the equation of state expressing the dead zone function obtained by the first predetermined parameter and the sector parameter and the robust disturbance feedback controller.
The second expansion plant includes the output feedback controller, the controlled object, the nominal plant model, the robust disturbance feedback controller, the first anti-windup controller, and the second anti. The method for designing a control device according to claim 8 , further comprising a wind-up controller. A control device, characterized in that it is set by a control parameter calculated by the control parameter calculation device according to any one of claims 1 to 5 . A control device designed by the method for designing a control device according to any one of claims 6 to 9 .