Method and device for tuning pi controller parameters

Abstract

The application provides a PI controller parameter setting method and device, relates to the technical field of automation control, is applied to a PI control system, the PI control system comprises a PI controller and a controlled object, and the method comprises the following steps: acquiring a characteristic response curve corresponding to the controlled object; acquiring a first-order inertia delay model by using a square difference integral minimum processing method according to the characteristic response curve; and determining target parameters corresponding to the PI controller according to a first formula acquired in advance through the first-order inertia delay model, so that the dynamic performance of a closed-loop response curve reaches an optimal state. The application finds optimal parameters by using the distribution of root loci on the real axis, realizes the optimal dynamic performance of the closed-loop response curve, and endows controller parameter setting and design with clear physical meanings.

Description

Technical Field

[0001] This invention relates to the field of automation control technology, and more specifically to a PI controller parameter tuning method and a PI controller parameter tuning device. Background Technology

[0002] PID control has a long history and remains the most commonly used control method in process control. In process control, 95% of control loops are PID type. PID control is an error feedback system that determines the adjustment of control force based on the error information between the desired behavior and the actual behavior. This control strategy, which eliminates the error based on the error information between the desired and actual behavior, is called an error feedback control law or error feedback strategy. With a simple error feedback structure, the controller design does not require building complex mathematical models, while simultaneously combating various uncertainties within the system and eliminating steady-state errors. The design structure of a PID controller is not complex; the most challenging task is the selection and tuning of the controller parameters.

[0003] In past engineering practices, engineers often determined the selection of parameters by formulas summarized by predecessors and experience accumulated in their work. For example, the Ziegler-Nichols method and the lambda method are commonly used methods for tuning parameters using empirical formulas.

[0004] However, the parameters and tuning process to be tuned cannot precisely achieve the optimal dynamic performance of the closed-loop response curve, and they have no clear physical meaning. Summary of the Invention

[0005] The purpose of this invention is to provide a method and apparatus for tuning PI controller parameters. This invention can find the optimal parameters by utilizing the distribution of the root locus on the real axis, thereby achieving the best dynamic performance of the closed-loop response curve and giving clear physical meaning to the tuning and design of controller parameters.

[0006] To achieve the above objectives, embodiments of the present invention provide a PI controller parameter tuning method, applied to a PI control system, wherein the PI control system includes a PI controller and a controlled object, and the method includes:

[0007] Obtain the characteristic response curve corresponding to the controlled object;

[0008] Based on the characteristic response curve, the first-order inertial delay model is obtained using the method of minimizing the squared difference integral.

[0009] Using the first-order inertial delay model and based on the pre-obtained first formula, the target parameters corresponding to the PI controller are determined, so that the dynamic performance of the closed-loop response curve reaches the optimal state.

[0010] Specifically, before obtaining the characteristic response curve corresponding to the controlled object, the method further includes:

[0011] Based on the PI control system, obtain the first transfer function corresponding to the PI controller and the second transfer function corresponding to the controlled object;

[0012] The first formula is derived based on the first transfer function and the second transfer function.

[0013] Specifically, deriving the first formula based on the first transfer function and the second transfer function includes:

[0014] Based on the first transfer function and the second transfer function, the system closed-loop transfer function corresponding to the PI control system is derived.

[0015] Based on the closed-loop transfer function of the system, the closed-loop characteristic equation is derived.

[0016] Based on the closed-loop characteristic equation, the first formula is obtained through root locus analysis.

[0017] Specifically, obtaining the first formula based on the closed-loop characteristic equation using root locus analysis includes:

[0018] The integral time constant of the PI controller is set to be equal to the system inertia time constant of the PI control system. The closed-loop characteristic equation is then simplified to obtain the simplified closed-loop characteristic equation.

[0019] Based on the simplified closed-loop characteristic equation, the first formula is obtained through the root locus analysis method.

[0020] Specifically, the target parameters include the target gain parameter and the target integration time parameter;

[0021] The step of determining the target parameters of the PI controller based on the first formula obtained in advance using the first-order inertial delay model includes:

[0022] The system gain parameters, time constant, and delay time are obtained using the first-order inertial delay model.

[0023] The target gain parameter and the target integration time parameter are determined using the first formula, based on the system gain parameter, time constant, and delay time.

[0024] Specifically, determining the target gain parameter and the target integration time parameter using the first formula, based on the system gain parameter, time constant, and delay time, includes:

[0025] If the ratio between the delay time and the time constant is less than or equal to 1, then the target gain parameter and the target integration time parameter are determined by the first formula.

[0026] Specifically, determining the target gain parameter and the target integration time parameter using the first formula, based on the system gain parameter, time constant, and delay time, includes:

[0027] If the ratio between the delay time and the time constant is greater than 1, then the target gain parameter and the target integral time parameter are determined by using the minimum value corresponding to the first formula as the initial value of the target parameter.

[0028] On the other hand, embodiments of the present invention provide a PI controller parameter tuning device, the device comprising:

[0029] The characteristic response curve acquisition unit is used to acquire the characteristic response curve corresponding to the controlled object;

[0030] A first-order inertial delay model acquisition unit is used to acquire a first-order inertial delay model based on the characteristic response curve using the method of minimizing the squared difference integral.

[0031] The target parameter acquisition unit is used to determine the target parameters of the PI controller based on the first formula obtained in advance through the first-order inertial delay model, so that the dynamic performance of the closed-loop response curve reaches the optimal state.

[0032] Specifically, the target parameters include the target gain parameter and the target integration time parameter;

[0033] The target parameter acquisition unit is specifically used for:

[0034] The system gain parameters, time constant, and delay time are obtained using the first-order inertial delay model.

[0035] The target gain parameter and the target integration time parameter are determined using the first formula, based on the system gain parameter, time constant, and delay time.

[0036] Specifically, determining the target gain parameter and the target integration time parameter using the first formula, based on the system gain parameter, time constant, and delay time, includes:

[0037] If the ratio between the delay time and the time constant is less than or equal to 1, then the target gain parameter and the target integration time parameter are determined by the first formula.

[0038] This invention can find the optimal parameters by utilizing the distribution of the root locus on the real axis, thereby achieving the best dynamic performance of the closed-loop response curve and giving clear physical meaning to the controller parameter tuning and design.

[0039] Other features and advantages of the embodiments of the present invention will be described in detail in the following detailed description section. Attached Figure Description

[0040] The accompanying drawings are provided to further illustrate embodiments of the present invention and form part of the specification. They are used together with the following detailed description to explain the embodiments of the present invention, but do not constitute a limitation thereof. In the drawings:

[0041] Figure 1 This is a flowchart illustrating a PI controller parameter tuning method according to an embodiment of this application;

[0042] Figure 2 This is a schematic diagram of a PI controller parameter tuning device provided in an embodiment of the present invention. Detailed Implementation

[0043] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the scope of the present invention.

[0044] The term "comprising" and any variations thereof in this application are intended to cover non-exclusive inclusion.

[0045] Specifically, this device can be integrated into a computer device, which can be a terminal, server, or other similar device. The terminal can be a mobile phone, tablet computer, smart Bluetooth device, laptop computer, or personal computer (PC), etc.; the server can be a single server or a server cluster composed of multiple servers.

[0046] In some embodiments, the device may also be integrated into multiple electronic devices, such as multiple servers, with the multiple servers implementing the method of this application.

[0047] In some embodiments, the server may also be implemented as a terminal.

[0048] The following sections provide detailed descriptions of each example. It should be noted that the sequence numbers of the following embodiments are not intended to limit the preferred order of the embodiments.

[0049] Example 1

[0050] This invention provides a method for tuning PI controller parameters, applied to a PI control system, which includes a PI controller and a controlled object.

[0051] like Figure 1 The specific process of the method includes steps 110 to 130:

[0052] 110. Obtain the characteristic response curve corresponding to the controlled object.

[0053] In some embodiments of this application, the characteristic response curve of the controlled object is obtained through a step disturbance test.

[0054] Specifically, prior to step 110, the method further includes the following specific steps:

[0055] S1. Based on the PI control system, obtain the first transfer function corresponding to the PI controller and the second transfer function corresponding to the controlled object.

[0056] S2. Based on the first transfer function and the second transfer function, the first formula is derived.

[0057] In some embodiments of this application, step S2 includes the following specific steps:

[0058] S2a. Based on the first transfer function and the second transfer function, the closed-loop transfer function of the PI control system is derived.

[0059] S2b. Based on the closed-loop transfer function of the system, the closed-loop characteristic equation is derived.

[0060] S2c. Based on the closed-loop characteristic equation, the first formula is obtained through root locus analysis.

[0061] In some embodiments of this application, step S2c includes the following specific steps:

[0062] S2c01. Set the integral time constant of the PI controller to be equal to the system inertia time constant of the PI control system, and simplify the closed-loop characteristic equation to obtain the simplified closed-loop characteristic equation.

[0063] S2c02. Based on the simplified closed-loop characteristic equation, the first formula is obtained through the root locus analysis method.

[0064] 120. Based on the characteristic response curve, obtain the first-order inertial delay model using the method of minimizing the integral of the squared difference.

[0065] 130. Using the first-order inertial delay model, the target parameters corresponding to the PI controller are determined according to the pre-obtained first formula, so that the dynamic performance of the closed-loop response curve reaches the optimal state.

[0066] In some embodiments of this application, the target parameters include target gain parameters and target integration time parameters.

[0067] Specifically, step 130 includes the following specific steps:

[0068] 131. Obtain the system gain parameters, time constant, and delay time using the first-order inertial delay model.

[0069] 132. Using the first formula, the target gain parameter and the target integration time parameter are determined based on the system gain parameter, time constant, and delay time.

[0070] Specifically, step 132 includes the following implementation process:

[0071] If the ratio between the delay time and the time constant is less than or equal to 1, then the target gain parameter and the target integration time parameter are determined by the first formula.

[0072] If the ratio between the delay time and the time constant is greater than 1, then the target gain parameter and the target integral time parameter are determined by using the minimum value corresponding to the first formula as the initial value of the target parameter.

[0073] Following the above embodiments of the present invention, the following detailed implementation process will further illustrate the following:

[0074] The control system includes a PI controller and a controlled object. Since most process controls in industrial production are non-integral, and self-balancing processes without overshoot can be simplified to first-order inertia plus delay, the controlled object is chosen as a first-order inertia plus delay object. The PI controller includes a proportional unit P, an integral unit I, and a controller gain coefficient kc. The transfer function of the PI controller is:

[0075]

[0076] Where, k c For the PI controller gain, T i This is the integral time constant of the PI controller.

[0077] The controlled object is a first-order inertial plus delay object, and its transfer function is:

[0078]

[0079] Among them, K is the system gain, T is the system inertia time constant, and τ is the delay time.

[0080] Combining the forms of the controller transfer function and the controlled object transfer function, the closed-loop transfer function of the system can be obtained as:

[0081]

[0082] The closed-loop characteristic equation is:

[0083]

[0084] According to the Lamda method, assume T i = T, and the closed-loop characteristic equation is simplified to the following form:

[0085]

[0086] According to the root locus analysis method, the open-loop transfer of the control system is:

[0087]

[0088]

[0089] The gain at the breakaway point is:

[0090]

[0091] The PI controller gain is inversely proportional to the steady-state gain K, inversely proportional to the delay time, and directly proportional to the inertia time T.

[0092] From this, the PI controller parameter tuning formula can be obtained:

[0093] T i = T

[0094]

[0095] The functional relationship expression between λ and Ω is:

[0096] λ = (Ω - 1)τ.

[0097] The dominant poles of the system are in the interval -π < jτω < π, and the dynamic performance of the poles outside this interval is slower. Combining the above information, qualitatively draw the root locus diagram between the imaginary axis -π < jτω < π (T = T i ), there are 2 root loci on the real axis, starting from infinity and the origin respectively, and finally separating at D1. That is, the entire real axis is the points on the root locus, and the closed-loop performance depends on the root locus starting from the origin, and it can reach the breakaway point D1 at the farthest on the real axis.

[0098] From the root locus, it can be summarized that:

[0099] (1) The interval where the closed-loop dominant real pole is in

[0100] (2) The dominant conjugate poles are at the separation point Point on the imaginary axis Symmetric about the real axis.

[0101] Therefore, the optimal range of the closed-loop poles can be derived:

[0102] The value of Ω is determined by using the parameter ξ<1 of the closed-loop poles.

[0103] Closed-loop poles are Substitute into the closed-loop characteristic equation

[0104] We can obtain:

[0105]

[0106]

[0107]

[0108] From the above two equations, we can deduce that:

[0109]

[0110]

[0111]

[0112] It can also be calculated

[0113] If it is a real root, let

[0114] Substitute into the closed-loop characteristic equation

[0115]

[0116] That is, we get the first formula.

[0117] Next, select according to the controlled object. At this point, the system delay θ = 0.5. During debugging, a disturbance of 0.2 was added. When θ < 1, based on the above analysis, parameter T is selected. i The system's dynamic characteristics are optimal when T=1 and δ=1. Following the criteria of overshoot not exceeding 5% and undershoot not exceeding 2%, the system's integral time constant and proportional band are gradually adjusted until T... i The dynamic performance reaches its optimal state when δ = 1 and δ = 0.98.

[0118] The embodiments of the present invention utilize the distribution of the root locus on the real axis to find the optimal parameters, thereby achieving the best dynamic performance of the closed-loop response curve and giving clear physical meaning to the controller parameter tuning and design.

[0119] Example 2

[0120] Both embodiments of the present invention and Embodiment 1 belong to the same inventive concept. The present invention provides a PI controller parameter tuning device, such as... Figure 2 As shown, the device includes:

[0121] Characteristic response curve acquisition unit 201 is used to acquire the characteristic response curve corresponding to the controlled object;

[0122] The first-order inertial delay model acquisition unit 202 is used to acquire the first-order inertial delay model based on the characteristic response curve using the method of minimizing the integral of the difference of squares.

[0123] The target parameter acquisition unit 203 is used to determine the target parameters corresponding to the PI controller through the first-order inertial delay model and according to the pre-acquired first formula, so that the dynamic performance of the closed-loop response curve reaches the optimal state.

[0124] Specifically, the target parameters include target gain parameters and target integration time parameters;

[0125] The target parameter acquisition unit 203 is specifically used for:

[0126] The system gain parameters, time constant, and delay time are obtained using the first-order inertial delay model.

[0127] The target gain parameter and the target integration time parameter are determined using the first formula, based on the system gain parameter, time constant, and delay time.

[0128] The step of determining the target gain parameter and the target integration time parameter using the first formula, based on the system gain parameter, time constant, and delay time, includes:

[0129] If the ratio between the delay time and the time constant is less than or equal to 1, then the target gain parameter and the target integration time parameter are determined by the first formula.

[0130] In practice, each of the above units can be implemented as an independent entity or can be arbitrarily combined to be implemented as the same or several entities. For the specific implementation of each of the above units, please refer to the previous method embodiments, which will not be repeated here.

[0131] For details on the implementation of each of the above operations, please refer to the previous examples, which will not be repeated here.

[0132] Those skilled in the art will understand that all or part of the steps in the various methods of the above embodiments can be accomplished by instructions, or by instructions controlling related hardware. These instructions can be stored in a storage medium and loaded and executed by a processor.

[0133] The above description, in conjunction with the accompanying drawings, details some optional embodiments of the present invention. However, the embodiments are not limited to the specific details described above. Within the scope of the technical concept of the embodiments of the present invention, various simple modifications can be made to the technical solutions of the embodiments of the present invention, and these simple modifications all fall within the protection scope of the embodiments of the present invention.

[0134] It should also be noted that the various specific technical features described in the above embodiments can be combined in any suitable manner without contradiction. To avoid unnecessary repetition, the embodiments of the present invention will not describe the various possible combinations separately.

[0135] Furthermore, various different implementations of the present invention can be combined arbitrarily, as long as they do not violate the spirit of the present invention, they should also be regarded as the content disclosed in the present invention.

Claims

1. A method for tuning PI controller parameters, characterized in that, Applied to a PI control system, the PI control system including a PI controller and a controlled object, the method includes: Based on the PI control system, obtain the first transfer function corresponding to the PI controller and the second transfer function corresponding to the controlled object; Based on the first transfer function and the second transfer function, the system closed-loop transfer function corresponding to the PI control system is derived. Based on the closed-loop transfer function of the system, the closed-loop characteristic equation is derived. Based on the closed-loop characteristic equation, the first formula is obtained through root locus analysis. Obtain the characteristic response curve corresponding to the controlled object; Based on the characteristic response curve, the first-order inertial delay model is obtained using the method of minimizing the squared difference integral. Using the first-order inertial delay model and based on the pre-obtained first formula, the target parameters corresponding to the PI controller are determined to achieve the optimal dynamic performance of the closed-loop response curve, including: The system gain parameters, time constant, and delay time are obtained using the first-order inertial delay model. If the ratio between the delay time and the time constant is less than or equal to 1, then the target gain parameter and the target integration time parameter are determined by the first formula. If the ratio between the delay time and the time constant is greater than 1, then the target gain parameter and the target integration time parameter are determined by using the minimum value corresponding to the first formula as the initial value of the parameter corresponding to the target parameter; The target parameters include the target gain parameter and the target integration time parameter.

2. The method according to claim 1, characterized in that, The step of obtaining the first formula based on the closed-loop characteristic equation using root locus analysis includes: The integral time constant of the PI controller is set to be equal to the system inertia time constant of the PI control system. The closed-loop characteristic equation is then simplified to obtain the simplified closed-loop characteristic equation. Based on the simplified closed-loop characteristic equation, the first formula is obtained through the root locus analysis method.

3. A PI controller parameter tuning device, characterized in that, The device includes: The characteristic response curve acquisition unit is used to acquire the first transfer function corresponding to the PI controller and the second transfer function corresponding to the controlled object based on the PI control system. Based on the first transfer function and the second transfer function, the system closed-loop transfer function corresponding to the PI control system is derived. Based on the closed-loop transfer function of the system, the closed-loop characteristic equation is derived. Based on the closed-loop characteristic equation, the first formula is obtained through root locus analysis. Obtain the characteristic response curve corresponding to the controlled object; A first-order inertial delay model acquisition unit is used to acquire a first-order inertial delay model based on the characteristic response curve using the method of minimizing the squared difference integral. The target parameter acquisition unit is used to determine the target parameters of the PI controller according to the first formula obtained in advance through the first-order inertial delay model, so that the dynamic performance of the closed-loop response curve reaches the optimal state. The target parameter acquisition unit is specifically used for: The system gain parameters, time constant, and delay time are obtained using the first-order inertial delay model. If the ratio between the delay time and the time constant is less than or equal to 1, then the target gain parameter and the target integration time parameter are determined by the first formula. If the ratio between the delay time and the time constant is greater than 1, then the target gain parameter and the target integration time parameter are determined by using the minimum value corresponding to the first formula as the initial value of the parameter corresponding to the target parameter; The target parameters include the target gain parameter and the target integration time parameter.

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