TWI533097B - Parameter tuning method and computer program product - Google Patents

Description

Parameter tuning method and computer program product

The present invention relates to a parameter tuning method, and more particularly to a parameter tuning method and computer program product for a cascade control system.

The Proportional Integral Derivative (PID) controller is a closed loop controller with the advantages of simple structure, good reliability and convenient adjustment. Therefore, in the general industrial process, the PID controller is often used to control the process, and the design method of the PID controller is very important for the industrial process. In the conventional PID controller design method, it is usually necessary to establish a model to obtain parameters of the PID controller to control the process. For example, first identify the low-order empirical model of the process, and then apply a specific tuning algorithm to design the PID controller. A good PID design can be obtained when the low-order model is sufficient to reasonably represent process dynamics. However, when applied to high-order process dynamics, the performance of the PID controller is degraded because of inevitable model errors. In addition, although the PID tuning algorithm contains tunable parameters, this tunable parameter can be traded appropriately between control performance and system stability resilience (to cope with model errors), so that better control performance is usually achieved. However, the best of this tunable Values often lack clear criteria for setting, and are usually determined by trial and error by additional process testing or closed-loop simulations under known process dynamics.

For a working control system, the conventional PID Controller design methods are often less feasible to use closed-loop test to collect process data for model identification. Furthermore, for any PID design method based on the process model, whether the process model is sufficiently representative of the process dynamics is a key factor affecting the performance of the controller. In order to obtain a more accurate process model, it is necessary to use more complicated process testing and calculation process to identify the model, which makes the process process identification time-consuming and laborious, and greatly reduces the practicability of the design method.

In addition, PID controllers are also commonly used in the architecture of cascade control. in. The cascade control system has an outer loop and an inner loop, the outer loop has a main controller and a main program, and the inner loop has a secondary controller and a secondary program. When there is interference in the inner loop, the secondary controller can immediately perform control compensation, so that the response to the interference will be faster than the architecture of the single loop. In general, when designing cascade control, the secondary controller is designed first and then the primary controller is designed, so usually two program tests are required. In the case of the open loop of the outer loop, the first test is first performed to design the secondary controller, and then the inner loop is closed and then the second open loop test is performed to design the main controller. However, in some applications the above two open loop tests are not allowed. Therefore, how to propose an effective parameter tuning method to design parameters in cascade control is a topic of interest to those skilled in the art.

The invention provides a parameter tuning method and a computer program product, which can quickly design a controller in a cascade control system.

Embodiments of the present invention provide a parameter tuning method suitable for use in a cascade control system. The cascade control system includes an outer loop including an main controller and a main loop, and an inner loop including a secondary controller and a secondary program. The main controller outputs the second set point according to the difference between the first set point and the first output, and the secondary controller outputs the process data according to the difference between the second set point and the second output, and the secondary program is based on the process data and the second The interference outputs a second output, and the main program outputs the first output according to the second output and the first interference. The parameter tuning method comprises: performing a test on the control system to obtain the process data, the first output and the second output; determining the delay parameter of the secondary program, and according to the delay parameter of the secondary program, the process data, the second output and the second a secondary transfer function of the controller to perform an optimization algorithm to obtain an optimal internal delay parameter; at least one of a proportional parameter and an integral parameter of the secondary transfer function is obtained according to the optimal internal delay parameter, and the first calculation is performed according to the Second set point; given the delay parameter of the main program, and performing the optimization algorithm according to the delay parameter of the main program, the calculated second set point, the first output, and the main transfer function of the main controller Obtaining an optimal outer delay parameter; and obtaining at least one of a proportional parameter, an integral parameter, and a differential parameter of the primary transfer function according to the optimal outer delay parameter.

In an embodiment, the secondary controller is a proportional-integral controller, and the step of performing the optimization algorithm is performed according to the delay parameter of the secondary program, the process data, the secondary output function of the second output and the secondary controller. Includes the following steps. Setting the second set point is expressed as the following equation (1), the second turn The shift function is expressed as the following equation (2), and the second closed loop transfer function of the inner loop for the second disturbance is expressed as the following equation (3).

Where Y ₂ (s) is the second output, KP ₂ is the proportional parameter, I ₂ is the integral parameter, λ ₂ is the adjustable parameter, and θ ₂ is the delay parameter of the secondary program. Next, the expected process data is calculated according to the second closed loop transfer function, the second output, and the secondary transfer function. And, the difference between the expected process data and the process data is set as the first objective function to perform the optimization algorithm. The delay parameter θ ₂ corresponding to the minimum of the first objective function is the optimal internal delay parameter described above.

In one embodiment, the expected process data described above is expressed as equation (4) below:

In an embodiment, the first objective function described above is expressed by the following equations (5) and (6). Where ω _M2 is the frequency at which the sensitivity function of the inner loop produces the maximum value.

In an embodiment, the above-described frequency ω _{M2 is} expressed by the following equation (7), wherein the complementary sensitivity function of the inner loop is expressed as the following equation (8).

In an embodiment, the step of calculating the second set point is performed according to the following equation (9).

In an embodiment, the step of performing the optimization algorithm according to the delay parameter of the main program, the calculated second set point, the first output, and the main transfer function of the main controller includes the following steps. First, the first set point is set to be expressed as the following equation (10), the first closed loop transfer function of the outer loop for the first set point is the following equation (11), and the main transfer function is expressed as the following equation (12).

R ₁ ( s )= T ₁ ( s ) ^-1 Y ₁ ( s )...(10)

Where Y ₁ (s) is the first output, λ ₁ is the adjustable parameter, θ ₁ is the delay parameter of the main program, I ₁ is the integral parameter, KP ₁ is the proportional parameter, and D ₁ is the differential parameter. Next, an expected second set point is calculated according to the first closed loop transfer function, the primary transfer function, and the first output. And, the difference between the second set point calculated by the above equation (9) and the expected second set point is set as the second objective function to perform the optimization algorithm. The delay parameter θ ₁ corresponding to the second objective function is the best outer delay parameter.

In one embodiment, the second objective function described above is expressed as equations (13) and (14) below, where ω _M1 is the frequency at which the sensitivity function of the outer loop produces a maximum value.

In an embodiment, the above-mentioned frequency ω _M1 is calculated according to the following equation (15).

Embodiments of the present invention also propose a computer program product, The parameter tuning method described above is performed by loading a computer system and being executed by a processor.

The above described features and advantages of the invention will be apparent from the following description.

100‧‧‧ Cascade Control System

110‧‧‧Outer loop

120‧‧‧ Inner Ring Road

101‧‧‧Master Controller

102‧‧‧ controllers

103‧‧‧ procedures

104‧‧‧ main program

R ₁ (s)‧‧‧ first set point

R ₂ (s)‧‧‧second set point

U(s)‧‧‧ process data

D ₂ (s)‧‧‧second interference

Y ₂ (s)‧‧‧ second output

D ₁ (s)‧‧‧First interference

Y ₁ (s)‧‧‧ first output

G _c1 (s)‧‧‧ primary transfer function

G _c2 (s)‧‧‧ transfer function

G ₂ (s), G ₁ (s), G _1a (s)‧‧‧ function

T _d2 (s)‧‧‧second closed loop transfer function

T ₁ (s)‧‧‧First closed loop transfer function

S501~S510‧‧‧Steps

1 is a schematic diagram showing a cascade control system in accordance with an embodiment.

2 is a schematic diagram showing an inner loop reference mode according to an embodiment; FIG. 3 is an equivalent block diagram showing a cascade control system according to an embodiment; 4 is a schematic diagram showing a reference mode of an outer loop according to an embodiment; and FIG. 5 is a flowchart illustrating a parameter tuning method according to an embodiment.

1 is a schematic diagram showing a cascade control system in accordance with an embodiment. Referring to FIG. 1, the cascade control system 100 includes an outer loop 110 and an inner loop 120. The outer loop includes a main controller 101 and a main routine 104, and the inner loop 120 includes a secondary controller 102 and a secondary program 103. The main controller 101 has a main transfer function G _c1 (s) that outputs a second set point R ₂ (s) according to the difference between the first set point R ₁ (s) and the first output Y ₁ (s). The secondary controller 102 has a secondary transfer function G _c2 (s) that outputs process data U(s) based on the difference between the second set point R ₂ (s) and the second output Y ₂ (s). Subroutine 103 can be represented as a function G ₂ (s), will come second output Y ₂ (s) according to process data U (s) and a second interference D ₂ (s). The main program 104 may be represented as a function G ₁ (s), will be the first output Y ₁ (s) according to the second output Y ₂ (s) and the first interference D ₁ (s).

In one embodiment, the cascade control system 100 is used to control the oxygen concentration, wherein the primary controller 101 is used to control the concentration and the secondary controller 102 is used to control the flow. However, the cascade control system 100 can be applied to any process plant, and the present invention is not limited thereto. In addition, in this embodiment, the main controller 101 is a PID controller, and the secondary controller 102 is a PI controller. However, in other embodiments, the main controller 101 may also be a PI controller, and the secondary controller 102 may also For the P controller. How to design the parameters in the primary transfer function G _c1 (s) and the secondary transfer function G _c2 (s) will be explained below.

First, a test (which may be a closed loop test or an open loop test) is performed on the control system 100 to obtain process data U(s), a first output Y ₁ (s), and a second output Y ₂ (s). Next, the delay parameter of the secondary program 103 is given, and the most performed according to the delay parameter of the secondary program 103, the process data U(s), the second output Y ₂ (s), and the secondary transfer function G _c2 (s) The algorithm is optimized to achieve the best internal delay parameters. The above optimization algorithm is to minimize the difference between the process data U(s) and a calculated expected process data, thereby determining the proportional parameter and integral in the secondary transfer function G _c2 (s). At least one of the parameters.

Specifically, the inner loop 120 itself is a single loop system for the purpose of quickly eliminating the second disturbance D ₂ (s), so the design method of the secondary controller 102 should be designed for interference rejection performance. In this embodiment, the reference mode architecture of inner loop 120 is as shown in FIG. 2, where T _d2 (s) is the second closed loop transfer function that is expected for inner loop 120 for second interference D ₂ (s). . According to Fig. 2, the second set point can be expressed as the following equation (1).

In this embodiment, the secondary controller 102 is a PI controller. The subtransfer function can be written as the following equation (2).

Where I ₂ is the integral parameter and KP ₂ is the proportional parameter. In order to be able to track the second set point without generating an offset, the second closed loop transfer function T _d2 (s) described above may be set to the following equation (3).

Where λ ₂ is an adjustable parameter, the designer can make an appropriate trade-off between the control efficiency and the stability and toughness of the inner loop 120. θ ₂ is the delay parameter of the secondary program.

Next, an expected process data is calculated based on the second closed loop transfer function T _d2 (s), the second output Y ₂ (s), and the secondary transfer function G _c2 (s). Specifically, the expected process data output by the secondary controller 102 at this time It can be expressed as the following equation (4).

Since the process data U(s) can be obtained through testing, it is expected that the process data The difference from the process data U(s) can be set as an objective function (also known as a first objective function) to perform an optimization algorithm. This first objective function can be expressed as the following equations (5) and (6).

Where ω _M2 is the frequency at which the sensitivity function of the inner loop produces a maximum value, which can be expressed as the following equation (7), and at this time, the complementary sensitivity function of the inner loop can be expressed as the following equation ( 8).

In the optimization algorithm, the parameters of the given delay in advance a range of ₂ [theta] (by custom designer), may generate a corresponding ₂ I ₂ ratio of the integral parameter KP ₂ The parameters given delay parameters [theta] . Next, the golden parameter search method can be used to update the delay parameter θ ₂ , and the new delay parameter θ ₂ can be used to generate a new integral parameter I ₂ and a proportional parameter KP ₂ . When the objective function J _{2, PI} (θ ₂ ) is the smallest, the corresponding delay parameter θ _{2 is} called the optimal internal delay parameter, and the integral parameter I ₂ and the proportional parameter KP ₂ corresponding to the optimal internal delay parameter are Is the parameter that is tuned. However, in other embodiments, the Newton method or other search methods may be used instead of the above-described gold search method, and the present invention is not limited thereto.

Referring back to FIG. 1, after the design of the secondary controller 102 is completed, the main controller 101 must be designed to take into account the inner loop dynamics generated by the secondary controller 102. Therefore, the second set point R ₂ (s) can be recalculated according to the parameters of the designed secondary transfer function G _c2 (s). Next, similar to the design method of the inner loop 120, the delay parameter of the main program 104 is given, and according to the delay parameter of the main program 120, the calculated second set point R ₂ (s), the first output Y ₁ (s), and the main transfer function G _c1 (s) to perform an optimization algorithm to obtain the optimal outer delay parameter. In the design of the outer loop 110, the optimization algorithm is to minimize the difference between the calculated second set point R ₂ (s) and an expected second set point, thereby determining the primary transfer function G. At least one of a proportional parameter, an integral parameter, and a differential parameter of _c1 (s).

Specifically, the equivalent block of the cascade control system 100 at this time is as shown in FIG. 3, wherein the function G _1a (s) represents an equivalent program faced by the main controller 101, expressed as the following equation (9). The process data output by the secondary controller 102 can be expressed as the following equation (10).

Therefore, the integral parameter I ₂ and the proportional parameter KP ₂ designed according to the above can determine the secondary transfer function G _c2 (s), and then the second setting can be calculated according to the second output Y ₂ (s) and the process data U(s). Point R ₂ (s) is expressed as the following equation (11).

When the second set point R ₂ (s) and the second output Y ₂ (s) are known, the design of the main controller takes into account that the outer loop must cope with the set point change of the system, so the main controller 101 here It is designed for servo control. The reference mode architecture of the outer loop is shown in Figure 4, where T ₁ (s) represents the first closed loop transfer function expected by the outer loop for the first set point. The first set point can be expressed as the following equation (12).

R ₁ ( s )= T ₁ ( s ) ^-1 Y ₁ ( s )...(12)

When the control target is set point tracking, the first closed loop transfer function T ₁ (s) can be selected as the following equation (13).

The delay parameter θ ₁ , λ ₁ where θ _{1 is the} main transfer function G _c1 (s) is an adjustable parameter. On the other hand, in this embodiment, the main controller 101 is a PID controller, and thus the main transfer function can be written as the following equation (14).

Where KP ₁ is the proportional parameter, I ₁ is the integral parameter, and D ₁ is the differential parameter. Next, according to the first closed loop transfer function T ₁ (s), the main transfer function G _c1 (s) and the first output Y ₁ (s), the expected second set point output by the main controller 101 can be calculated, expressed as The following equation (15).

Since the second set point R ₂ (s) is known, the problem of the main controller design is to minimize the difference between equations (15) and (11) above, which can be set as the second objective function to perform Optimize the algorithm. The second objective function can be expressed as the following equations (16) and (17).

Where ω _M1 is the frequency at which the sensitivity function of the outer loop produces a maximum value, which can be expressed as the following equation (18).

In one embodiment, the above-described optimization algorithm used is a golden section search method, the parameters given delay range θ ₁ after a split search method will be continuously updated delay parameter θ ₁ through gold, and the target The delay parameter θ ₁ corresponding to the function J ₁ and the minimum _PID (θ ₁ ) is called the optimal outer delay parameter. The proportional parameter KP ₁ , the integral parameter I ₁ and the differential parameter D ₁ corresponding to the optimal outer delay parameter θ ₁ are the tuned PID parameters.

FIG. 5 is a flow chart illustrating a method of parameter tuning in accordance with an embodiment. Referring to FIG 5, in step S501, a test of the control system to obtain process data U (s), a first output Y ₁ (s) and the second output Y ₂ (s). In step S502, the delay parameter θ _{2 of the} secondary program is given. In step S503, the optimization algorithm is executed based on the delay parameter θ ₂ , the process data U(s), the second output Y ₂ (s), and the secondary transfer function G _c2 (s). If the optimization algorithm has not stopped, step S504 is performed to update the delay parameter θ ₂ and calculate a new PI parameter. If the optimization algorithm has stopped, step S505 is performed to obtain the optimal internal delay parameter, and the corresponding integration parameter I ₂ and the proportional parameter KP ₂ are calculated.

In step S506, the second set point R ₂ (s) is calculated. In step S507, a given delay parameter θ _1. In step S508, the optimization algorithm is executed based on the delay parameter θ ₁ , the calculated second set point, the first output Y ₁ (s), and the main transfer function G _c1 (s). If the optimization algorithm has not stopped, step S509 is performed to update the delay parameter θ ₁ and calculate a new PID parameter. If the optimization algorithm has stopped, proceeding to step S510, the optimal outer delay parameter is obtained, and the corresponding proportional parameter KP ₁ , integral parameter I ₁ and differential parameter D ₁ are calculated.

However, the steps in Figure 5 have been described in detail above, here No longer. It should be noted that the steps in FIG. 5 can be implemented as multiple code codes or circuits, and the present invention is not limited thereto. In addition, the method of FIG. 7 can be used in conjunction with the above embodiments, or can be used alone. In another aspect, some embodiments of the present invention also provide a computer program product that can be stored in any form of memory or transmitted over a network. lose. The computer program product can be downloaded to a computer system that is executed by a processor in the computer system to implement the parameter tuning method described above.

In summary, in the parameter tuning method and the computer program product proposed by the embodiment of the present invention, two controllers in the cascade control system can be designed only once with one test.

Although the present invention has been disclosed in the above embodiments, it is not intended to limit the present invention, and any one of ordinary skill in the art can make some changes and refinements without departing from the spirit and scope of the present invention. The scope of the invention is defined by the scope of the appended claims.

S501~S510‧‧‧Steps

Claims (10)

A parameter tuning method is applicable to a cascade control system, wherein the cascade control system includes an outer loop and an inner loop, the outer loop includes a main controller and a main program, and the inner loop includes one time a controller and a program, the main controller outputs a second set point according to a difference between a first set point and a first output, wherein the controller is based on the second set point and a second output The difference output is a process data, the program outputs the second output according to the process data and a second interference, and the main program outputs the first output according to the second output and a first interference, the parameter tuning method includes: Performing a test on the cascade control system to obtain the process data, the first output and the second output; giving a delay parameter of the program, and according to the delay parameter of the program, the process data, The second output and the primary transfer function of the secondary controller perform an optimization algorithm to obtain an optimal internal delay parameter; and obtain a proportional parameter and an integral parameter of the secondary transfer function according to the optimal internal delay parameter At least one of the second set point is calculated accordingly; a delay parameter of the main program is given, and the second set point is calculated according to the delay parameter of the main program, the first Outputting, a primary transfer function with the primary controller to perform the optimization algorithm to obtain an optimal outer delay parameter; and obtaining a proportional parameter and an integral parameter of the primary transfer function according to the optimal outer delay parameter And at least one of the differential parameters. The parameter tuning method of claim 1, wherein the secondary controller is a proportional-integral controller, and according to the delay parameter of the secondary program, the process data, the second output, and the secondary controller The step of performing the optimization algorithm to perform the optimization algorithm includes: setting the second set point to be expressed as the following equation (1), the secondary transfer function being expressed as the following equation (2), and the inner loop is for the The second closed loop transfer function of the second disturbance is expressed as the following equation (3): Where Y ₂ (s) is the second output, KP ₂ is the proportional parameter, I ₂ is the integral parameter, λ ₂ is the adjustable parameter, and θ ₂ is the delay parameter of the subroutine; according to the second closed loop transfer a function, the second output and the secondary transfer function calculate an expected process data; and set a difference between the expected process data and the process data as a first objective function to perform the optimization algorithm, wherein the The delay parameter θ ₂ corresponding to the minimum of the first objective function is the optimal internal delay parameter. The parameter tuning method as described in claim 2, wherein the expected process data is expressed as the following equation (4): The parameter tuning method of claim 3, wherein the first objective function is expressed as the following equations (5) and (6): Where ω _{M2 is} the frequency at which the sensitivity function of the inner loop produces a maximum value. The parameter tuning method of claim 4, wherein the frequency ω _{M2 is} expressed by the following equation (7): The complementary sensitivity function of the inner loop is expressed as the following equation (8): The parameter tuning method of claim 5, wherein the calculating the second set point comprises: calculating the second set point according to the following equation (9): The parameter tuning method of claim 6, wherein the delay parameter according to the main program, the calculated second set point, the first output, and the main transfer function of the main controller are The step of performing the optimization algorithm includes: setting the first set point to be expressed as the following equation (10), and the first closed loop transfer function of the outer loop for the first set point is the following equation (11), And the main transfer function is expressed as the following equation (12): R ₁ ( s ) = T ₁ ( s ) ^-1 Y ₁ ( s ) (10) Where Y ₁ (s) is the first output, λ ₁ is an adjustable parameter, θ ₁ is the delay parameter of the main program, I ₁ is an integral parameter, KP ₁ is a proportional parameter, and D ₁ is a differential parameter; The first closed loop transfer function, the primary transfer function and the first output calculate an expected second set point; and the second set point calculated by the above equation (9) and the expected second set point The difference between the two is set to a second objective function to perform the optimization algorithm, wherein the delay parameter θ ₁ corresponding to the second objective function is the optimal outer delay parameter. The parameter tuning method of claim 7, wherein the second objective function is expressed by the following equations (13) and (14): Where ω _{M1 is} the frequency at which the sensitivity function of the outer loop produces a maximum value. The parameter tuning method of claim 8, wherein the frequency ω _M1 is calculated according to the following equation (15): A computer program product for performing a parameter tuning method by loading a computer system and executing by a processor, wherein the parameter tuning method is used for a cascade control system including an outer loop and an inner loop a loop, the outer loop includes a main controller and a main program, the inner loop includes a primary controller and a program, and the main controller outputs a difference according to a difference between a first set point and a first output. a second set point, the controller outputs a process data according to a difference between the second set point and a second output, the program outputs the second output according to the made data and a second interference, the main The program outputs the first output according to the second output and a first interference, the parameter tuning method includes: performing a test on the cascade control system to obtain the process data, the first output and the second output; Given a delay parameter of the program, and performing an optimization algorithm according to the delay parameter of the program, the process data, the second output, and the transfer function of the secondary controller to obtain one of the most a good internal delay parameter; obtaining at least one of a proportional parameter and an integral parameter of the transfer function according to the optimal internal delay parameter, and calculating the second set point according to the second set point; given a delay parameter of the main program And performing the optimization algorithm according to the delay parameter of the main program, the calculated second set point, the first output, and a main transfer function of the main controller to obtain an optimal An outer delay parameter; and obtaining at least one of a proportional parameter, an integral parameter, and a differential parameter of the primary transfer function according to the optimal outer delay parameter.