JP5125875B2 - PID controller tuning apparatus, PID controller tuning program, and PID controller tuning method - Google Patents

Description

  The present invention relates to tuning of a PID (proportional-integral-derivative) controller, and in particular, by providing an appropriate PID parameter to a system in which operation data is periodically oscillating due to a poor tuning of the PID controller, the tuning failure is provided. The present invention relates to a tuning apparatus for a PID controller, a tuning program for a PID controller, and a tuning method for a PID controller.

Conventionally, a number of techniques have been disclosed regarding tuning methods for PID control in a process controller. For example, in Patent Document 1, a process is identified without giving an identification signal to the plant, a simulation is performed using the identified process model and a PID controller model, the result is evaluated, and an optimum PID parameter is determined. The technology to acquire is disclosed.
JP 2002-202801 A

  In the process control, it is considered that the control characteristics vary depending on the process characteristics and the magnitude of the disturbance. And the improvement of the precision about the control of the process in a plant is always calculated | required.

  The present invention has been devised in view of such circumstances, and its purpose is to provide a PID controller tuning apparatus, a PID controller tuning program, and a PID controller that can accurately control a process in a system in which the process is controlled by a controller. It is to provide a tuning method.

  A tuning device for a PID controller according to the present invention is a device for tuning a controller that controls a process for PID (proportional-integral-derivative), and includes a storage means for acquiring and storing operation data of the process, and an operation of the process. Based on the data, the evaluation means for evaluating the controllability of the controller, and on the condition that the controllability is evaluated to be low by the evaluation means, using the acquired operation data, control parameters for the controller model, An identification means for identifying a process parameter for a model of the process based on a certain limit, the control parameter identified by the identification means, the controller model based on the process parameter, and the process model. Control response simulation Characterized in that it comprises a simulation means for executing Deployment.

  In the PID controller tuning device according to the present invention, the identification unit may use the process model as a dynamic model of a second-order lag system including a dead time and an integration system as the fixed restriction, and the operation data as the operation data. It is preferable to identify the parameter using data that is periodically oscillated.

  In the PID controller tuning device of the present invention, it is preferable that the identification unit identifies the control parameter and the process parameter based on a genetic algorithm.

  In addition, the PID controller tuning apparatus of the present invention uses the process model obtained by the identification unit, and based on generalized minimum variance control, distributes the control amount in the process model and the operation amount in the controller model. A calculation unit that evaluates the variance and calculates an optimal control parameter that minimizes the evaluation value, and the simulation unit includes a model of the controller based on the optimal control parameter calculated by the calculation unit; It is preferable to execute the simulation using a model of the process based on the process parameter identified by the identification unit.

  The tuning apparatus for a PID controller according to the present invention performs the simulation using an input unit that changes the optimal control parameter calculated by the calculation unit, a model of the controller based on the changed parameter, and a model of the process. It is preferable to further comprise means for executing.

  A tuning program for a PID controller according to the present invention is a program for tuning a controller that controls a process for PID (proportional-integral-derivative), the step of acquiring and storing operation data of the process in a computer, A step of evaluating the controllability of the controller based on operation data of the process, and on the condition that the controllability is evaluated to be low, using the acquired operation data, the control parameters for the controller model; Identifying a process parameter for a model of the process based on a certain limit; and using the model of the process obtained in the identifying step and distributing the control amount in the model of the process based on generalized minimum variance control And controller model And calculating the optimal control parameter that minimizes the evaluation value, and simulating the control response of the process based on the identified process parameter and the identified control parameter. And executing a simulation of a control response of the process based on the identified process parameter and the calculated optimum control parameter.

  A tuning method for a PID controller according to the present invention is a method for tuning a controller for controlling a process by PID (proportional-integral-derivative), the step of acquiring and storing operation data of the process, and the operation data of the process. On the basis of the control parameters of the controller model using the acquired operation data on the condition that the controllability of the controller is evaluated and the controllability is evaluated to be low. Identifying a process parameter for a process model based on, and using a model of the process obtained in the identifying step, and based on generalized minimum variance control, the variance of the controlled variable in the process model and the controller model The variance of the operation amount in Calculating an optimal control parameter that minimizes an evaluation value; executing a simulation of a control response of the process based on the identified process parameter and the identified control parameter; and the identified process parameter And executing a simulation of a control response of the process based on the calculated optimal control parameter.

  According to the present invention, based on the actual operational data of the process, both the controller model and the process model are identified and a simulation is performed.

  As a result, it is considered possible to identify the closed-loop system controlled by the controller with higher accuracy, and from this, the control characteristics can be grasped more accurately, tuning defects are eliminated, and controllability is improved. It is possible to calculate an optimal PID parameter that improves

  Further, according to the present invention, control parameters and process parameters are identified and simulated on the condition that the controllability of the controller is evaluated and the controllability is evaluated based on the process operation data. .

  As a result, processes such as identification of control parameters and process parameters are performed only when necessary, and therefore, the tuning process is efficiently performed.

[1. Configuration of PID controller tuning device]
The tuning device of the present embodiment is a device for sequentially tuning one or more controllers in a plant. FIG. 1 schematically shows a hardware configuration of the tuning apparatus.

  Referring to FIG. 1, tuning device 100 includes a central processing unit (CPU) 101 that controls the operation of tuning device 100 as a whole. In the tuning device 100, the CPU 101 transmits and receives information to and from other elements via the input / output device (I / O) 102.

  The CPU 101 is connected to the communication control unit 109 via the I / O 102, and is connected to other devices and networks via the communication control unit 109. Then, the CPU 101 acquires the operation data of the plant as described above from an external device or a server on the network.

  The hard disk (HD) 103 includes a program storage unit 103A that stores programs executed by the CPU 101, and an operation data storage unit 103B that stores operation data acquired as described above. The HD 103 stores various data such as constants and variable values required when the CPU 101 executes the program stored in the program storage unit 103A. The CPU 101 accesses the HD 103 via the I / O 102.

  The tuning device 100 includes a random access memory (RAM) 105 that functions as a work area of the CPU 101, an input unit 106 that accepts input of information from the outside such as a keyboard, and information on a recording medium 104A that is detachable from the tuning device 100. Includes a media drive 104 for writing and reading, and a display unit 108 for displaying processing contents of the CPU 101 and the like.

  The CPU 101 can execute a program recorded in the program storage unit 103A of the HD 103, or can execute a program recorded in the recording medium 104A. The tuning apparatus 100 can also install a program recorded in the recording medium 104A and a program stored in an external storage device via the communication control unit 109 in the program storage unit 103A, and can perform communication control. It is also possible to read and execute a program recorded in another device via the unit 109.

[2. System identification concept]
The tuning apparatus 100 evaluates the controllability of the closed loop system as shown in the block diagram of FIG. 11 and identifies both the controller and the process for those evaluated as having low controllability. Then, using the process model obtained as the identification result, an optimal control parameter is calculated as a parameter when the controller controls the process.

  In FIG. 11, r indicates a target value for the system shown in FIG. 11, u indicates an operation amount of the controller C with respect to the process P, y indicates a control amount that is an output of the process P, and w indicates disturbance. Is shown.

  For the system (closed loop system) as shown in FIG. 11, the relationship expressed by the following expression (1) is established.

  In Expression (1), C and P represent transfer functions representing a controller and a process, respectively. U (s) and Y (s) are Laplace transforms of the manipulated variable u (t) and the controlled variable y (t), respectively.

  When trying to identify the controller and process in the actual system from equation (1), both the controller and process transfer functions (C, P) are unknown and the controller and process transfer functions (C, P) are separated. Because of this, closed-loop system identification has been considered difficult.

  Here, FIG. 2 schematically shows a virtual system configuration for system identification set in the present embodiment.

  In FIG. 2, the controller and process in the actual plant are shown as a controller 10 and a process 20, respectively. In this embodiment, a virtual controller 51 and a virtual process 52 are defined in parallel with these systems. Here, u ′ and y ′ are an operation amount and a control amount in the virtual system, respectively.

  In the present embodiment, the virtual controller 51 and the virtual process 52 are modeled using the actual system operation data composed of the controller 10 and the process 20.

  Then, using the model of the process 52 thus obtained, the optimum control parameter of the controller 51 is calculated, and the actual controller 10 is tuned with reference to the value.

FIG. 3 is a diagram schematically illustrating a functional configuration of the tuning device 100.
Referring to FIG. 3, in tuning device 100, parameter processing unit 54 performs processing such as generation of initial values of parameters used in the respective models (described later) for virtual controller 51 and virtual process 52. The generation of an initial generation of solids in system identification using a genetic algorithm. The fitness calculation unit 53 calculates u ′ and y ′ using the parameters at that time, and calculates a value indicating how close these values are to u and y in the actual operation data. To do.

  When the fitness calculation unit 53 calculates the degree, the parameter processing unit 54 newly generates parameters for the models of the controller 51 and the process 52. When a new parameter is provided by the parameter processing unit 54, the fitness calculation unit 53 calculates the fitness as described above based on the new parameter.

  In the tuning device 100, the parameters are corrected so that each of the controller 51 and the process 52 matches the actual controller and process by repeating the above processing by the parameter processing unit 54 and the fitness calculation unit 53. Thus, the controller 10 and the process 20 are identified.

  In the present embodiment, the parameter processing unit 54 is realized by the CPU 101 that executes initial setting processing (generation of individuals of the initial generation), crossover processing, and mutation processing in the system identification processing (see FIG. 5) described later. The In addition, the fitness calculation unit 53 is realized by the CPU 101 that executes selection processing in the system identification processing.

[3. Processing for tuning the PID controller]
FIG. 4 is a flowchart of processing executed by the tuning device 100 for tuning the controller 10.

  Referring to FIG. 4, in tuning device 100, as processing for controller tuning, CPU 101 first acquires operation data of the system including controller 10 and process 20 via communication control unit 109 in step S <b> 1. The process stored in the operation data storage unit 103B is executed, and the process proceeds to step S1A.

  An example of the structure of the operation data acquired in step S1 is shown in Table 1.

  The operation data acquired by the tuning device 100 in the present embodiment includes values of the target value r, the control amount y, and the operation amount u for the controller 10 at a predetermined time interval (1 minute interval in Table 1). .

  In step S1A, the controllability is evaluated for the control amount of the control loop to be processed. In the present embodiment, the controllability is evaluated based on, for example, the presence or absence of periodicity of the control amount or the value of the controllability evaluation index based on the minimum variance control.

  As the determination of the presence or absence of periodicity, for example, the power spectrum of the control amount data is calculated, and if there is a peak exceeding a certain value (for example, 15 dB) in the power spectrum, there is periodicity. to decide. Here, calculation of the power spectrum will be described.

  First, the time series data “x (t)” of the control amount is normalized by the following equation (A1) so that the average becomes 0 and the variance becomes 1.

  Then, the normalized data is Fourier transformed, and the power spectrum is calculated using the following equation (A2).

  The determination mode of the presence or absence of periodicity in the power spectrum of control amount data is based on well-known techniques (for example, literature (Hidekazu Kushitamoto, valve sticking detection and control performance improvement utilizing plant operation data, instrumentation control technology conference, Japan, Japan Management Association, 2006)). When it is determined that there is periodicity, it is determined that the controllability is low.

Next, evaluation of controllability by the controllability evaluation method based on minimum variance control will be described.
Here, the controllability evaluation index is a controllability evaluation index η calculated according to the following equation (A3). In equation (A3), σ _MV ² is the minimum variance of the control amount, σ _y ² is the variance of the actual control amount, and d−1 represents the dead time in the control loop. Note that η takes a value from 0 to 1.

  In the present embodiment, when the value of the controllability evaluation index η is equal to or greater than a predetermined threshold value, it is determined that the controllability is high, and when the value is smaller than the threshold value, it is determined that the controllability is low. The

  Then, after evaluating the controllability in step S1A, the CPU 101 determines in step S1B whether the controllability is good as a result of the evaluation, that is, whether the controllability is high. If the CPU 101 determines that the controllability is high, the CPU 101 terminates the process shown in FIG. 4. If the CPU 101 determines that the controllability is low, the CPU 101 advances the process to step S2.

  In step S2, the CPU 101 models a system composed of the virtual controller 51 and the virtual process 52, and the process proceeds to step S3. Details of the system identification process in step S2 will be described later.

  After executing the system identification process in step S2, the CPU 101 calculates the optimum control parameter of the controller 51 (optimum parameter calculation process) using the model of the process 52 obtained by the system identification process in step S3. ) And the process proceeds to step S4. Details of the optimum parameter calculation process will be described later.

  In step S4, the CPU 101 executes a simulation for the system including the controller 51 and the process 52 based on the information obtained by the system identification process and the optimum parameter calculation process, and advances the process to step S5.

  In step S <b> 5, the CPU 101 executes a process (result presentation process) for presenting the results of the system identification process and the optimum parameter calculation process and the simulation result on the display unit 108. Therefore, if a satisfactory result is not obtained, the user manually corrects the control parameter of the controller 51 and performs simulation again. If a satisfactory result is obtained, the user actually refers to the control parameter. The control parameter of the controller 10 is changed, and the tuning process ends.

  As described above, in the process described with reference to FIG. 4, only when the controllability evaluated in step S1A is low (when NO is determined in step S1B), the process after step S2 is executed, and the controllability evaluated in step S1A. Is high (when YES is determined in step S1B), the processing after step S2 is not executed. Note that the processing after step S2 may be executed even when it is evaluated that the controllability is high, and after the operation data is acquired in step S1, the judgment regarding the evaluation of controllability in steps S1A and 1B. The process after step S2 may be directly executed without being performed.

[4. System identification]
4.1 Process Model As a premise of the system identification process in step S <b> 2 described above, a CARIMA (Controlled Auto-Regressive and Integrated Moving-Average) model is adopted as a model of the process 52 in the present embodiment. The CARIMA model is shown in Equation (2).

  In equation (2), y is a controlled variable, u is a manipulated variable, d is a dead time, wy is a disturbance related to the controlled variable y, and a and b are used in the CARIMA model. And Δ represents a difference operator.

  In the present embodiment, as the model of the process 52, the CARIMA model expressed by the equation (2) is considered up to the second order lag system including the dead time. Thereby, the model of the process 52 used for system identification in the present embodiment is expressed as Expression (3).

  In equation (3), y represents control amount operation data, y ′ represents a control amount calculation value calculated from the process model, u represents operation amount operation data, and u ′ will be described later. The calculation value of the operation amount calculated from the controller model is shown.

4.2 Controller Model The controller (the controller shown in the block diagram of FIG. 11) to be tuned by the tuning device 100 of the present embodiment is a PID controller. In this embodiment, an I-PD controller (proportional advance type PID) is used as a controller model as an example of a PID controller. Such a controller model is represented by the following equation (4).

Here, y is a control amount that is an output of the process 20 of FIG. 2, u is an operation amount of the controller 10 with respect to the process 20, K _c is a proportional gain generally used in the PID control equation, and T _i Is an integration time, _Td is a differentiation time, Ts is a sampling period (a period for collecting data for control calculation), and W _u is an error related to the manipulated variable u.

  As described above, when modeling the system in the present embodiment, the process model of the process 20 employs a second-order lag system including integration, and takes the dead time into consideration. Based on this, the model of the controller 51 in the present embodiment is expressed by the following equation (5). In equation (5), d represents the dead time, and u ′ represents the calculated value of the operation amount calculated from the controller model.

4.3 Genetic Algorithm In the system identification process described in step S2 of FIG. 4, the eight parameters (a ₁ , a ₂ ) used in the controller model of equation (5) and the process model of equation (3) are used. , B ₀ , b ₁ , d, K _c , T _i , T _d ) are identified. Here, the contents of the system identification process in step S2 will be described with reference to FIG. 5 which is a flowchart of the subroutine of the process.

  Referring to FIG. 5, in the system identification process, CPU 101 first performs initialization in step S21, and advances the process to step S22.

  In the present embodiment, the eight parameters necessary for the system identification described above are determined using a genetic algorithm (GA). In the initial setting in step S21, initial conditions necessary for determining parameters by the GA are set. Here, an outline of how the determination of the eight parameters by the GA is performed will be described. FIG. 6 schematically shows the flow of parameter determination by the GA.

  With reference to FIG. B. Determination of initial population. Selection, C.I. Intersection, D. Four steps of mutation are included. Hereinafter, the content of each process is demonstrated.

A. Generation of initial population In the GA, the CPU 101 generates N sets of initial individuals, with the eight parameters described above as one set. Here, for each of the eight parameters, an upper limit value and a lower limit value as shown in Expression (6) to Expression (13) are set. For each parameter, the CPU 101 adds an upper limit value (subscript of max for each parameter) from a lower limit value (subscript of min for each parameter) as shown in the equations (6) to (13). Within the range of the ones).

In the following description, each individual (a set of eight parameters) is represented as P _{1 to} P _N. N initial individuals are referred to as an initial population.

B. Selection The CPU 101 calculates the fitness for each of the _N individuals P _{1 to} P _N. The fitness is calculated using the parameters included in each individual for the objective function f (P _n ). The objective function f (P _n ) is expressed by the following equation (14).

The objective function f (P _n ) is controlled every predetermined time interval (1 minute interval in the present embodiment) from time (d + 1) to time X in the operation data for each set of parameters constituting each individual. The square of the difference between the operation data of the quantity and the calculated value (predicted value) of the control quantity calculated using the process model, and the operation calculated using the operation data and the controller model of the operation quantity of the previous (d + 1) time It is a value obtained by integrating the sum of the squares of the difference between the calculated values (predicted values) of the quantities. In the present embodiment, it is attempted to obtain a set of parameters that causes the controller 51 and the process 52 to behave as close as possible to the controller 10 and the process 20 by the GA. Therefore, the smaller the value of the objective function f (P _n ), the more the individual (parameter set) used for the calculation is adapted by the controller 10 and the process 20. That is, in this embodiment, it is considered that the smaller the value of the objective function f (P _n ), the higher the fitness of the individual (parameter set) used for the calculation. In the GA according to the present embodiment, M individuals (M <N) are selected from the initial population including N individuals (or the next generation population described later) in ascending order of the objective function value. Is done.

C. Crossing In the crossing, the CPU 101 arbitrarily selects two individuals P _i and P _j from the M individuals obtained by the selection, and then sets all eight parameters to the following equations (15) and ( 16) to generate new individuals P _k and solids P _l ). At such an intersection, for example, E individuals are newly generated.

In Expressions (15) and (16), P _sup represents the solid P _i and P _J having a small objective function value (high fitness).

D. Mutation A certain percentage of individuals are selected from the M individuals selected by the above selection, and the values of a certain number of parameters among the parameters included in each individual are expressed by the above formulas (6) to (13). ), The CPU 101 newly generates F individuals.

  By the process from the generation of the initial population described above to the mutation, a population composed of N individuals is selected from among the M individuals, E individuals are generated by crossing, and Mutations generate F individuals. These individuals, that is, (M + E + F) individuals are taken as the next generation population.

  Then, the next generation population is further generated by applying the above-described processing from selection to mutation again to the next generation population.

  In the present embodiment, a group is generated up to a predetermined generation, and a set of parameters included in an individual having the smallest objective function value in the finally generated group is configured as a model of the controller 51 and the process 52. Parameter.

4.4 Contents of System Identification Process FIG. 5 is a flowchart of a system identification process subroutine in step S2 of FIG. Hereinafter, the contents of the system identification process will be described.

  Referring to FIG. 5, in the system identification process, CPU 101 first performs initial setting for system identification (determination of the above eight parameters) by GA in step S21, and advances the process to step S22.

  Here, the initial setting is to accept the input of the lower limit value and the upper limit value of the eight parameters shown in the above formulas (6) to (13), and generate a group for determining the parameters by GA. The input of the generation number G to be accepted is accepted.

  In step S22, the CPU 101 determines whether or not the current group generation is G for which the setting has been accepted in step S21. If so, the process proceeds to step S26, where the number of generations is still G. If it is determined that the value has not been reached, the process proceeds to step S23.

  In step S23, the CPU 101 executes “selection” described with reference to FIG. 6, and advances the process to step S24.

  In step S24, the CPU 101 executes the “intersection” described with reference to FIG. 6 and advances the process to step S25.

  In step S25, the CPU 101 executes the “mutation” described with reference to FIG. 6 and returns the process to step S22.

  As described above, the processing from step S23 to step S25 is continued until the number of generations of the group of individuals handled in GA becomes G. When the number of generations of the group becomes G, the process proceeds to step S26.

  In step S <b> 26, the CPU 101 determines a set of parameters constituting a model having the smallest objective function value (high adaptability) in the G-th generation group as a parameter constituting the model of the controller 51 and the process 52. The set is determined, and the process returns to FIG.

[5. Calculation of optimal parameters]
In the present embodiment, in the optimum parameter calculation process in step S3 of FIG. 4, the optimum parameter is calculated for the PID control for the process 20 of the controller 10 based on the generalized minimum variance control (GMVC). Here, the contents will be described.

  First, it is assumed that the discrete time model of the process 20 in the present embodiment can be expressed by the following equation (17).

In equation (17), A (z ⁻¹ ) and B (z ⁻¹ ) are assumed to be coefficient polynomials of the discrete time model expressed by the following equations (18) and (19).

In equation (17), y (t) represents a control amount, u (t) represents an operation amount, χ (t) represents a modeling error, and z ⁻¹ represents a time delay operator (z ^{− 1} y (t) = y (t−1)), and Δ means a difference operator (1-z ⁻¹ ).

  At time t + 1, equation (17) becomes the following equation (20).

  Expression (20) can be written as the following expression (21).

  Here, the Diophantine equation is shown in Formula (22).

  From this Diophantine equation, the relationship of the following equation (23) can be obtained.

  The relationship between the control amount y (t + 1) and the predicted value y ′ (t + 1 | t) can be expressed as Expression (24).

  Thereby, the relationship of the following equation (25) is obtained.

  On the other hand, the model of the PID controller (controller 10) is expressed by equation (4) and can be rewritten as the following equation (26).

C (z ⁻¹ ) in Expression (26) is represented by a coefficient polynomial in Expression (27) below.

  Next, it is considered to obtain an optimum PID parameter based on the evaluation standard of generalized minimum dispersion control.

  One form of the evaluation criteria is given as the following equation (28).

Here, P (z ⁻¹ ) is expressed by the following formula (29).

  In equation (28), λ represents a weighting factor. How to give λ will be described later.

P (z ⁻¹ ) is a design polynomial of a discrete time model, and each coefficient is given as in the following Expression (30) to Expression (35) so as to indicate a desired controllability.

  Here, σ is a parameter representing the rise time, and is preferably 0.5 to 1.0 times the sum of the process time constant T and the dead time L. In the present embodiment, as exemplified by the equation (34), it is 0.75 times.

  On the other hand, μ is a parameter representing the attenuation characteristic of the response, and is given by δ as shown in the equation (33). δ is preferably in the range of 0.0 to 2.0. In this embodiment, δ is set to 0.0 as exemplified in Equation (35).

  Next, how to obtain the time constant T, the dead time L, and the process gain K from the discrete time model of the process will be described by taking the “primary delay + dead time” system and the “integration + dead time” system as examples.

  The “first order delay + dead time” system is often used to represent processes such as temperature control, and the “integral + dead time” system is often used to represent processes such as liquid level control.

  In the “first order delay + dead time” system, each parameter is obtained according to the following equations (36) to (38).

  Further, in the “integration + dead time” system, each parameter is obtained according to the following equations (39) to (41).

  Here, d is a pure time delay in a discrete time system, and L means a practical time delay including the initial rise. In the case of an integral system, since gentle control is preferred, the time constant T is specially set to twice the integral time constant.

  Substituting equation (23) into the evaluation criterion of equation (28) above yields the following equation (42).

  And the control law which minimizes this by using the property which is uncorrelated is obtained as following Formula (43).

  Further, when the coefficient polynomial of the second term in the equation (43) is replaced with a stationary term, the equation (44) is obtained.

  Then, the second term of the equation (44) is defined as the following equation (45).

  Thereby, Formula (44) becomes like the following Formula (46).

  Here, when the equation (46) is compared with the equation (26) which is a discrete model of the PID controller, the relationship of the following equation (47) is obtained.

  And thereby, the PID parameter which minimizes an evaluation norm can be calculated | required by following Formula (48)-Formula (50).

That is, given an appropriate λ, the coefficient of F (z ⁻¹ ) can be obtained, and thereby the PID parameter can be calculated using the equations (48) to (50).

In the evaluation criterion of equation (28), the variance of the control error when λ is changed (that is, the variance E [e ² (t)] of the deviation between the target value and the controlled variable) and the variance of the control input (ie, When the state of the variance [(Δu (t)) ² ]) of the operation change amount is plotted, a Trade-off curve (curve L) as shown in FIG. 7 is obtained. In order to obtain the most desirable λ from this curve, an evaluation function shown in the following equation (51) is defined.

Here, K ² corresponds to a weighting factor, and be determined by the process gain of formula (37) or formula (40).

  The control error e (t) and the operation amount Δu (t) have the relationship of the following equations (52) and (53) in a steady state.

However, T (z ^<-1> ) is represented by Formula (54).

At this time, the variance of the control error e (t) and the manipulated variable Δu (t) is calculated using the H ₂ norm, and λ that minimizes the following equation (55) is obtained. Thereby, the optimum PID parameter described above is obtained.

  A specific PID parameter calculation procedure can be shown as the following procedures SA1 to SA6.

SA1: Calculate T, K, and L based on Formula (36) to Formula (38) or Formula (39) to (41) SA2: Calculate P based on Formula (30) to Formula (35) SA3: Formula Calculate F based on (22) (If there is a dead time, find F from a discrete-time model that approximates the process by paddy, or obtain F considering the dead time by sequential calculation)
SA4: An initial value is given to λ, and a PID parameter corresponding to λ is calculated based on equations (48) to (50). SA5: Control error variance E [based on equations (52) and (53) e ² (t)] and the variance [(Δu (t)) ² ] of the control input (control amount) are calculated. SA6: SA4 and SA5 are repeatedly calculated to obtain λ that minimizes the expression (55). The λ that minimizes the expression (55) in such a case corresponds to the point P in the curve L in FIG.

[6. simulation]
Next, the contents of the simulation process in step S4 of FIG. 4 will be described.

As described above, in the tuning device 100 according to the present embodiment, the system identification process is performed, whereby the process parameters (a ₁ , a ₂ , b ₀ , b ₁ ) used in the process model (formula (3)). , D) and estimated values of parameters (K _c , T _i , T _d ) used in the controller model (equation (5)) are obtained (step S2). Then, using the estimated process model, an optimal PID parameter for the controller is calculated (step S3).

  Then, the CPU 101 uses the process model obtained as described above as the simulation process, and calculates the simulation of the time variation of the control amount when the estimated PID parameter (hereinafter, “estimated parameter”) is applied. Then, a simulation of the time variation of the control amount when the optimum PID parameter (hereinafter, “recommended parameter”) is applied is executed. FIG. 8A shows the simulation result. Note that the horizontal axis of the graph in FIG. 8A represents time.

  First, in FIG. 8A, a target value that changes stepwise is indicated by a solid line. In FIG. 8A, the change over time in the control amount when the estimation parameter is applied when the target value changes stepwise as indicated by the solid line is indicated by a broken line, and the recommended parameter is applied. The time change of the control amount in this case is indicated by a one-dot chain line.

  FIG. 8B shows the parameters of the estimated process model described above, and FIG. 8C shows the PID parameters of the controller.

  In FIG. 8C, four types of PID parameters, “Previous”, “Estimated”, “Recommended”, and “Current” are shown. “Previous” is a parameter applied to the controller in the actual plant before the processing shown in FIG. 4 is executed. “Estimation” is a result of estimating a “previous” parameter from operation data by the system identification process shown in FIG. 5 and is a PID parameter calculated as a result of controller model identification. If the “previous” value is close to the “estimated” parameter value, the user can evaluate that the system identification accuracy by the system identification process is high and the result is reliable.

  In FIG. 8C, “recommended” is the PID parameter calculated by the optimum parameter calculation process executed in step S3. “Current” is an actual PID parameter newly set by the user. The user can set this parameter with reference to recommended parameters, for example. These four types of PID parameters are all stored in the HD 103.

[7. Presentation of results]
The CPU 101 can cause the display unit 108 to display the information shown in FIGS. 8A to 8C as a result presentation process (step S5). An example of the screen displayed on the display unit 108 in such a case is shown in FIG.

  Referring to FIG. 9, screen 900 displays a display column 910 for displaying the graph shown in FIG. 8A, a display column 911 for displaying the process parameters shown in FIG. 8B, and FIG. Display fields 912 and 915 for displaying the PID parameters shown in FIG. Note that when the button 913 in the screen 900 is clicked, the CPU 101 executes the process shown in FIG. The display column 912 displays “estimated” PID parameters, and the display column 915 displays “recommended” PID parameters. Note that the user can change the numerical value in the display field 912 by appropriately operating the input unit 106.

  The CPU 101 operates the button 914 to use the process model to which the PID parameter displayed in the display fields 912 and 915 and the process parameter displayed in the display field 911 are applied. Simulate time changes and display the results. In addition, the aspect of patent document 1 is employable as the aspect of simulation.

  In the screen 900, the display field 920 presents the change of the set value SV (Set Variable) with a broken line for one day and the control amount PV (Process Variable) with a solid line as time on the horizontal axis. In addition, the display column 930 presents changes in the operation amount MV (Manipulative Variable) for one day, with the horizontal axis as time.

  In the display column 910, the change in the control amount for 5 hours is shown as the step response characteristic of the process 52 as a result of the simulation. Specifically, in the display column 910, the set value that changes in a step shape is indicated by a solid line, the simulation result of the control amount using the “estimated” parameter indicated in the display column 912 is indicated by a broken line, and The simulation result of the controlled variable using the “recommended” parameter shown in the display field 915 is indicated by a one-dot chain line.

[8. Tuning by the tuning device of the present embodiment]
FIG. 10 shows the behavior before and after tuning of the PID controller by the tuning apparatus of the present embodiment actually applied to the plant.

  FIG. 10A shows the time change of the control amount of the process before tuning, and FIG. 10B shows the time change of the control amount of the process after tuning. Note that “after tuning” means that the PID parameter used in the process controller has been tuned with reference to the above-mentioned “recommended” parameters.

  Comparing FIG. 10 (A) and FIG. 10 (B), the amount of change in the control amount is narrower after tuning than before tuning.

  Thereby, according to this Embodiment, the behavior of a process can be made calm.

[9. Display screen association]
As described with reference to FIG. 4, in the present embodiment, the controllability of the control loop to be processed is evaluated (step S1A), and whether or not the processing after step S2 is executed according to the contents of the control loop. No is determined by the program executed by the CPU 101.

  The process described with reference to FIG. 4 displays such an evaluation result on the display unit 108, and according to the operation content on the screen, that is, according to the selection operation of the control loop to be analyzed, It may be changed so as to determine whether or not to execute the processing after step S2.

  FIG. 12 is an example of a screen on which the evaluation content for controllability for each control loop is displayed, and FIG. 13 is a flowchart of the above-described modification of the flowchart of FIG. In the flowchart of FIG. 13, steps S1C and S1D are provided instead of step S1B of the flowchart of FIG.

  In this modification, the screen shown in FIG. 12 is displayed as a result of step S1A. The screen 800 shows trends 810 and 820 of the control amount for each control loop evaluated as having low controllability. Then, in association with the respective trends 810 and 820, the evaluation contents of the controllability for each control loop are displayed in the display columns 811 and 821.

  In the display columns 811 and 821, the “total index” is a value related to the controllability evaluation index η, and the “period” is a period when it is determined that the control amount has periodicity. is there.

  In the display fields 811 and 821, “comment” is a message displayed based on the presence or absence of periodicity, the value of the controllability evaluation index η, and other diagnostic results. For example, a message “Tuning failure” is displayed in the display column 811, and a message “There is a suspicion of valve or instrument failure” is displayed in the display column 821. Such a message is associated with the evaluation content and stored in the HD 103, for example.

  These messages are linked with the processing contents for executing the processing after step S2.

  Referring to FIG. 13, controllability is evaluated in step S1A, and as a result, the extraction result of the control loop with low controllability is displayed on a screen 800 as shown in FIG. In step S1D, it is determined whether or not a link that advances the processing after step S2 as described above has been operated (a message has been clicked).

  When it is determined that the message has been clicked, the processes after step S2 are executed for the control loop to which the clicked message corresponds. Thereby, the system identification process (step S2) etc. about the said control loop are performed, and the screen 900 (refer FIG. 9) based on the result presentation process about the said control loop is displayed as a result. Note that the screen 900 in FIG. 9 is a screen corresponding to a control parameter calculation result for a controller corresponding to the trend 810. The control amount PV in the display field 920 is the same as the trend 810.

  On the other hand, when an operation for terminating display of the controllability evaluation result is performed without clicking any message (comment) displayed on the screen 800 (when “NO” is determined in step S1D). , It ends as it is.

  In the tuning apparatus 100 of the present embodiment described above, the actual plant operation data composed of the controller 10 and the process 20 is used to model the virtual controller 51 and the virtual process 52, and The optimal control parameters of the controller 51 are calculated using the obtained model of the process 52. When tuning the controller 10, the tuning can be performed with reference to the calculated numerical values of the control parameters. Note that the tuning device 100 evaluates the controllability for each controller 51, and only the controller 51 that is determined to have low controllability executes the above modeling, calculation of optimal control parameters, and the like. Can be reduced. Further, as in the modification shown in FIG. 13, if the controllability of a plurality of control loops is evaluated in advance, tuning can be performed intensively for a controller with low controllability, so that control is efficiently performed. There is an advantage that the performance can be improved.

  The embodiment disclosed this time should be considered as illustrative in all points and not restrictive. The scope of the present invention is defined by the terms of the claims, rather than the description above, and is intended to include any modifications within the scope and meaning equivalent to the terms of the claims.

It is a figure which shows typically the hardware constitutions of the tuning apparatus which is one embodiment of this invention. It is a figure which shows typically the virtual system structure for the system identification set in the tuning apparatus of FIG. It is a figure which shows typically the functional structure of the tuning apparatus of FIG. It is a flowchart of the process which the tuning device of FIG. 1 performs for controller tuning. 5 is a flowchart of a subroutine of system identification processing in FIG. 4. It is a figure which shows roughly the flow of the determination of the parameter by GA in the system identification process of FIG. FIG. 5 is a diagram plotting the relationship between the variance of control error and the variance of manipulated variable, which is used for calculating the PID parameter in the optimum parameter calculation process of FIG. 4. It is a figure which shows the result of the simulation of FIG. It is a figure which shows an example of the screen displayed on a display part in the result presentation process of FIG. It is a figure which shows the behavior of the system before and after the tuning of the PID parameter by the tuning apparatus of this Embodiment. 1 is a block diagram of a system including a controller to be tuned by the tuning device of the present embodiment. It is a figure which shows an example of the screen which displays the content of evaluation of the controllability of the plant in this Embodiment. It is a figure which shows the modification of the flowchart shown by FIG.

Explanation of symbols

  10, 51 controller, 20, 52 process, 53 fitness calculation unit, 54 parameter processing unit, 100 tuning device, 101 CPU, 102 I / O, 103 HD, 103A program storage unit, 103B operation data storage unit, 104 media drive , 104A recording medium, 105 RAM, 106 input unit, 108 display unit, 109 communication control unit, 800, 900 screen.

Claims (7)

A device that tunes a controller that controls PID (proportional-integral-derivative) processes,
Storage means for acquiring and storing operation data of the process;
Evaluation means for evaluating the controllability of the controller based on the operation data of the process;
Identification that identifies a control parameter for a controller model and a process parameter for a process model based on a certain restriction using the acquired operation data on the condition that the controllability is evaluated by the evaluation means. and means,
The identification means calculates a value of an objective function f (P _n ) represented by the following formula (1) :

The objective function f (P _n )
y is a control amount that is an output of the process,
y ′ is a calculated value of the controlled variable calculated from the model of the process,
u is the operation amount of the controller;
u ′ is a calculated value of the operation amount calculated from the model of the controller,
d is the dead time,
From time (d + 1) to time X, the objective function f (P _n ) is the square of the difference between the operation data of the control amount and the calculated value of the control amount for each predetermined time interval, and (d + 1) time before Is a function that adds the sum of the squares of the difference between the operation data of the manipulated variable and the calculated value of the manipulated variable,
The identification means calculates a value of the objective function f (P _n ) for each of the plurality of sets (n) of the process parameter and the control parameter, and sets a group having the smallest value of the objective function f (P _n ), Identifying process parameters for the process model and control parameters for the controller model;
The device is
A tuning apparatus for a PID controller, further comprising simulation means for simulating a control response of the process using the controller model and the process model based on the control parameter and the process parameter identified by the identification means. The identification means includes
As the certain limitation, the model of the process is a dynamic model of a second order lag system including a dead time and an integration system,
The PID controller tuning device according to claim 1, wherein a parameter is identified by using periodic vibration data as the operation data.   The PID controller tuning device according to claim 1, wherein the identification unit identifies the control parameter and the process parameter based on a genetic algorithm. Using the process model obtained by the identification means, based on generalized minimum variance control, evaluate the variance of the control amount in the process model and the variance of the operation amount in the controller model, and the evaluation value is the minimum A calculation means for calculating the optimal control parameter
The simulation means executes the simulation using a model of the controller based on the optimal control parameter calculated by the calculation means and a model of the process based on the process parameter identified by the identification means. The tuning device for a PID controller according to any one of claims 1 to 3. Input means for changing the optimum control parameter calculated by the calculating means;
5. The PID controller tuning device according to claim 1, further comprising means for executing the simulation using a model of the controller and a model of the process based on the changed parameter. 6. A program for tuning a controller for controlling a process by PID (proportional-integral-derivative),
On the computer,
Obtaining and storing operational data of the process;
Evaluating the controllability of the controller based on operational data of the process;
On the condition that the controllability is evaluated to be low, with the operational data the acquired and a step of identification and control parameters for the model of the controller, and process parameters for the model of the process based on certain restrictions Let
The identifying step includes calculating a value of an objective function f (P _n ) represented by the following equation (1) :

The objective function f (P _n )
y is a control amount that is an output of the process,
y ′ is a calculated value of the controlled variable calculated from the model of the process,
u is the operation amount of the controller;
u ′ is a calculated value of the operation amount calculated from the model of the controller,
d is the dead time,
From time (d + 1) to time X, the objective function f (P _n ) is the square of the difference between the operation data of the control amount and the calculated value of the control amount for each predetermined time interval, and (d + 1) time before Is a function that adds the sum of the squares of the difference between the operation data of the manipulated variable and the calculated value of the manipulated variable,
The identifying step calculates a value of the objective function f (P _n ) for each of a plurality (n) of the process parameters and the control parameters, and sets the smallest value of the objective function f (P _n ). Identifying as process parameters for the model of the process and control parameters for the model of the controller,
In the computer,
Using the process model obtained in the identifying step, based on the generalized minimum variance control, evaluate the variance of the control amount in the process model and the variance of the operation amount in the controller model, and the evaluation value is Calculating an optimal control parameter that minimizes; and
Performing a simulation of a control response of the process based on the identified process parameter and the identified control parameter;
A PID controller tuning program for further executing a step of executing a simulation of a control response of the process based on the identified process parameter and the calculated optimum control parameter. A method for tuning a controller that controls a process with PID (proportional-integral-derivative),
Obtaining and storing operational data of the process;
Evaluating the controllability of the controller based on operational data of the process;
On the condition that the controllability is evaluated to be low, with the operational data the acquired comprises a step of identification and control parameters for the model of the controller, and process parameters for the model of the process based on certain restrictions ,
The identifying step includes calculating a value of an objective function f (P _n ) represented by the following equation (1) :

The objective function f (P _n )
y is a control amount that is an output of the process,
y ′ is a calculated value of the controlled variable calculated from the model of the process,
u is the operation amount of the controller;
u ′ is a calculated value of the operation amount calculated from the model of the controller,
d is the dead time,
From time (d + 1) to time X, the objective function f (P _n ) is the square of the difference between the operation data of the control amount and the calculated value of the control amount for each predetermined time interval, and (d + 1) time before Is a function that adds the sum of the squares of the difference between the operation data of the manipulated variable and the calculated value of the manipulated variable,
The identification means calculates a value of the objective function f (P _n ) for each of the plurality of sets (n) of the process parameter and the control parameter, and sets a group having the smallest value of the objective function f (P _n ), Identifying as a process parameter for the model of the process and a control parameter for the model of the controller,
The tuning method is:
Using the process model obtained in the identifying step, based on the generalized minimum variance control, evaluate the variance of the control amount in the process model and the variance of the operation amount in the controller model, and the evaluation value is Calculating an optimal control parameter that minimizes; and
Performing a simulation of a control response of the process based on the identified process parameter and the identified control parameter;
A method of tuning a PID controller, further comprising the step of simulating a control response of the process based on the identified process parameter and the calculated optimal control parameter.

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