A closed-loop pole-adjustable minimum-beat digital controller design method

Abstract

The application relates to a minimum-beat non-ripple digital controller design method with closed-loop pole adjustment, which adjusts the pole of a desired closed-loop system pole to ensure that the closed-loop system can avoid the inherent frequency of a control object, thereby avoiding system resonance; the dynamic response performance of the system is improved by reasonably designing a desired closed-loop system pulse transfer function model and a digital controller pulse transfer function, so that the system can quickly and non-oscillatingly reach a steady state; the processing of the minimum-beat non-ripple digital controller design method with closed-loop pole adjustment ensures the stability and causality of the system, and avoids instability in implementation. Therefore, the problem that the minimum-beat non-ripple digital controller design method commonly used in the automatic control field cannot avoid system resonance by adjusting the closed-loop pole of the control system to avoid the inherent frequency of the system structure is solved.

Description

Technical Field

[0001] This application relates to the field of automatic control system design, and in particular to a design method for a minimum-cycle ripple-free digital controller with adjustable closed-loop poles. Background Technology

[0002] In automatic control system design, digital controllers are designed using either indirect or direct design methods. The former ignores the impact of the sampling period on system performance, directly using the pulse transfer function of a continuous domain controller as the basis for digital controller algorithm programming. The direct design method considers the impact of the sampling period on system performance, treating the entire system as a completely discrete system. A representative direct design method for digital controllers is the least-cycle ripple-free design method.

[0003] In digital control systems, one sampling period is called a time step. A minimum-time system is a digital control system that, under typical input conditions, can theoretically complete the transient process within a finite number of time steps and has no steady-state error at the sampling time.

[0004] Systems designed using the least-time method often exhibit ripple in their actual output. This is because the least-time method only considers the transition process of the system output within a finite number of time steps, while the controller output signal remains an infinite sequence of decaying oscillations, leading to ripple. In contrast, the ripple-free least-time method for designing digital controllers ensures that the closed-loop pulse transfer function includes all zeros of the pulse transfer function of the subsystem comprised of the hold and the controlled object. This allows the digital controller's output signal to reach a steady-state value within the fewest time steps, ceasing oscillation and theoretically eliminating system ripple.

[0005] The closed-loop pulse transfer function of the system designed using the minimum-step ripple-free design method is obtained through a lookup table based on the input signal type, and all closed-loop poles of the system are located at the origin of the z-plane. This results in the closed-loop poles being unadjustable, meaning the number of steps in the transient response is also unadjustable, and the signal oscillation during the transient response cannot be reduced by extending the transient response time. This implies that it is impossible to avoid the system's inherent structural frequency by adjusting the closed-loop poles of the control system, i.e., it is impossible to avoid system resonance by adjusting the controller.

[0006] Existing minimum-step ripple-free design methods suffer from problems such as the inability to adjust the closed-loop system poles, the inability to adjust the number of steps during system transients, and the inability to avoid system resonance by adjusting the controller. Summary of the Invention

[0007] Therefore, it is necessary to provide a design method for a minimum-cycle ripple-free digital controller with adjustable closed-loop poles to address the aforementioned technical problems.

[0008] To achieve the above objectives, the embodiments of the present invention adopt the following technical solutions:

[0009] On the one hand, a method for designing a minimum-cycle ripple-free digital controller with adjustable closed-loop poles is provided, including:

[0010] Establish and solve the pulse transfer function model of the controlled object to obtain the pulse transfer function of the controlled object;

[0011] Establish the pulse transfer function model of the desired closed-loop system, and obtain the pulse transfer function of the desired closed-loop system based on the selected poles of the desired closed-loop system;

[0012] Calculate the pulse transfer function of the digital controller based on the pulse transfer function of the controlled object and the desired closed-loop system.

[0013] In one embodiment, the design method for the minimum-cycle ripple-free digital controller with adjustable closed-loop poles described above includes the following process for selecting the desired closed-loop system poles:

[0014] For systems with an order less than or equal to 2, the poles are chosen as follows:

[0015] s 1,2 = -x ± y·j;

[0016] Where j represents the imaginary unit, x represents the decay rate of the system, y represents the oscillation frequency of the system, and both x and y are positive real numbers.

[0017] In one embodiment, the design method for the minimum-cycle ripple-free digital controller with adjustable closed-loop poles described above includes the following process for selecting the desired closed-loop system poles:

[0018] For a system of order n, where n is greater than 2, the first and second poles are chosen as follows:

[0019] s 1,2 = -x ± y·j;

[0020] Where j represents the imaginary unit, x represents the decay rate of the system, and y represents the oscillation frequency of the system, and both x and y are positive real numbers;

[0021] The 3rd to nth poles are selected according to the non-dominant pole rule.

[0022] In one embodiment, the design method for the minimum-cycle ripple-free digital controller with adjustable closed-loop poles described above uses the following pulse transfer function model for the controlled object:

[0023]

[0024] Where N(z) is the numerator polynomial of the control object's impulse transfer function model with respect to z, and D(z) is the denominator polynomial of the control object's impulse transfer function model with respect to z.

[0025] In one embodiment, the above-described design method for a minimum-cycle ripple-free digital controller with adjustable closed-loop poles aims to have the following pulse transfer function model for the closed-loop system:

[0026]

[0027] Where, N B (z) is the numerator polynomial of the desired closed-loop system impulse transfer function model with respect to z; D B (z) is the denominator polynomial of the desired closed-loop system impulse transfer function model with respect to z, D B (z) contains the pole information of the desired closed-loop system.

[0028] In one embodiment, the above-described design method for a minimum-cycle ripple-free digital controller with adjustable closed-loop poles includes the following steps for calculating the pulse transfer function of the digital controller based on the pulse transfer function of the controlled object and the desired closed-loop system:

[0029] like If the denominator order is greater than or equal to the numerator order, then the pulse transfer function of the digital controller is:

[0030]

[0031] In one embodiment, the above-described design method for a minimum-cycle ripple-free digital controller with adjustable closed-loop poles includes the following steps for calculating the pulse transfer function based on the pulse transfer function model of the controlled object and the pulse transfer function model of the desired closed-loop system:

[0032] like If the order of the denominator is less than that of the numerator, and the order difference is m, then the pulse transfer function of the digital controller is:

[0033]

[0034] Where c is a positive real number that is approximately zero.

[0035] One or more technical solutions provided in the embodiments of this application have at least the following technical effects or advantages:

[0036] The aforementioned design method for a minimum-cycle ripple-free digital controller with adjustable closed-loop poles adjusts the poles of the desired closed-loop system to ensure that the closed-loop system avoids the natural frequency of the controlled object, thereby preventing system resonance. By rationally designing the pulse transfer function model of the desired closed-loop system and the pulse transfer function of the digital controller, the dynamic response performance of the system is improved, ensuring rapid and oscillatory steady-state attainment. Ensuring that the denominator order is not lower than the numerator order ensures the stability and causality of the system, avoiding implementation instability. Therefore, this method solves the problem that commonly used minimum-cycle ripple-free digital controller design methods in the field of automatic control cannot avoid the natural frequency of the system structure by adjusting the closed-loop poles of the control system, thus preventing system resonance. Attached Figure Description

[0037] To more clearly illustrate the technical solutions in the embodiments of this application or the conventional technology, the drawings used in the description of the embodiments or the conventional technology will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0038] Figure 1 This is a flowchart illustrating a design method for a minimum-cycle ripple-free digital controller with adjustable closed-loop poles in one embodiment.

[0039] Figure 2 This is a schematic diagram of a minimum-cycle ripple-free digital controller with adjustable closed-loop poles in one embodiment. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0041] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to be limiting of the application.

[0042] It should be noted that, in this document, the reference to "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The presentation of this phrase in various locations throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments.

[0043] In one embodiment, such as Figure 1As shown, this application provides a design method for a minimum-cycle ripple-free digital controller with adjustable closed-loop poles, including the following processing steps S12-16:

[0044] S12, Establish and solve the pulse transfer function model of the controlled object to obtain the pulse transfer function of the controlled object.

[0045] It is understandable that the pulse transfer function of the controlled object can be obtained by discretizing the continuous part consisting of the holder, the controlled object, the power amplifier, the actuator, and the sensor as a whole using a discretization method. The pulse transfer function of the controlled object can be denoted as G(z).

[0046] Specifically, discretization methods may include, but are not limited to, zero-order preserved discretization, bilinear transformation, forward difference method, or backward difference method.

[0047] S14. Establish the desired closed-loop system pulse transfer function model and obtain the desired closed-loop system pulse transfer function based on the selected desired closed-loop system poles.

[0048] It is understandable that we can first select the poles of the desired closed-loop system. After selecting the poles, the denominator of the desired closed-loop system pulse transfer function can be determined by these poles. Then, we can determine the numerator of the desired closed-loop system pulse transfer function and then use the discretization rule to obtain the desired closed-loop system pulse transfer function. The desired closed-loop system pulse transfer function can be denoted as B(z).

[0049] Specifically, discretization methods may include, but are not limited to, zero-pole matching discretization, bilinear transformation, forward difference method or backward difference method, and after algebraic operations, the discretized pulse transfer function B(z) is obtained.

[0050] S16. Calculate the pulse transfer function based on the pulse transfer function of the controlled object and the pulse transfer function of the desired closed-loop system.

[0051] It is understandable that, based on the pulse transfer function of the controlled object and the pulse transfer function of the desired closed-loop system, the preliminary pulse transfer function of the digital controller can be obtained through derivation and calculation.

[0052] The initial digital controller pulse transfer function can be further improved. If the order of the denominator is greater than or equal to the order of the numerator, the final digital controller pulse transfer function is equal to this initial digital controller pulse transfer function. If the order of the denominator is less than the order of the numerator, and the order difference is m, the final digital controller pulse transfer function needs to add a factor to the denominator. The degree of this factor can be set to m, making the order of the denominator equal to the order of the numerator; alternatively, the degree of the added factor can be set to be greater than m, making the order of the denominator greater than the order of the numerator.

[0053] In the aforementioned design method for a minimum-cycle ripple-free digital controller with adjustable closed-loop poles, adjusting the poles of the desired closed-loop system ensures that the closed-loop system can avoid the natural frequency of the controlled object, thereby preventing system resonance. By rationally designing the pulse transfer function model of the desired closed-loop system and the pulse transfer function of the digital controller, the dynamic response performance of the system is improved, ensuring rapid and oscillatory steady-state attainment. Ensuring that the denominator order is not lower than the numerator order ensures the stability and causality of the system, avoiding implementation instability. Therefore, this method solves the problem that commonly used minimum-cycle ripple-free digital controller design methods in the field of automatic control cannot avoid system resonance by adjusting the closed-loop poles of the control system to avoid the natural frequency of the system structure.

[0054] In one embodiment, the process of selecting the desired closed-loop system poles in the above-described design method for a minimum-cycle ripple-free digital controller with adjustable closed-loop poles includes:

[0055] For systems with an order less than or equal to 2, the poles are chosen as follows:

[0056] s 1,2 = -x ± y·j;

[0057] Where j represents the imaginary unit, x represents the decay rate of the system, y represents the oscillation frequency of the system, and both x and y are positive real numbers.

[0058] It's understandable that a larger x indicates a shorter system transition process, meaning a faster response speed; conversely, a larger y indicates a higher oscillation frequency during the system transition. Specific values ​​are selected based on the system's application, functional requirements, and hardware performance limitations, following performance trade-off rules. Specifically, performance trade-off rules are a set of principles widely used in control system design. They aim to achieve optimal system performance by finding the best balance among multiple conflicting performance indicators. Key principles include trade-offs between response speed and stability, overshoot and response time, steady-state error and robustness, fast response and noise sensitivity, and control energy and system performance. In practical design, these trade-off parameters can be adjusted through simulation and actual debugging to achieve optimal system performance.

[0059] In one embodiment, the process of selecting the desired closed-loop system poles in the above-described design method for a minimum-cycle ripple-free digital controller with adjustable closed-loop poles includes:

[0060] For a system of order n, where n is greater than 2, the first and second poles are chosen as follows:

[0061] s 1,2 = -x ± y·j;

[0062] Where j represents the imaginary unit, x represents the decay rate of the system, and y represents the oscillation frequency of the system, and both x and y are positive real numbers;

[0063] The 3rd to nth poles are selected according to the non-dominant pole rule.

[0064] It is understandable that for a system with an order greater than 2, assuming its order is n, its first and second poles are selected according to the above rules, and the third to nth poles are selected according to the non-dominant pole rule.

[0065] Specifically, the non-dominant pole rule is a principle used in the design of high-order control systems. It aims to minimize the impact of non-dominant poles on the system's main dynamic characteristics by appropriately selecting their locations, thereby achieving stability and good transient response. These principles include: keeping away from dominant poles: avoiding the influence of non-dominant poles on the main dynamic characteristics determined by dominant poles; ensuring system stability: non-dominant poles should be placed in locations that ensure system stability; location selection: for discrete systems, non-dominant poles should be as close as possible to the center of the unit circle; for continuous systems, non-dominant poles should be located as far as possible on the negative real axis and away from the imaginary axis. By following these rules, high-performance and reliable high-order control systems can be designed.

[0066] After selecting the poles, we expect the denominator D of the transfer function of the closed-loop system to be... B (z) can be determined by these poles.

[0067] In one embodiment, the process of obtaining the desired closed-loop system pulse transfer function in the above-described design method for a minimum-cycle ripple-free digital controller with adjustable closed-loop poles further includes:

[0068] A constant is selected as the numerator of the pulse transfer function model of the desired closed-loop system based on the gain requirements of the desired closed-loop system.

[0069] It is understandable that after selecting the poles, the numerator of the closed-loop system transfer function is chosen to be a constant based on the system's gain requirements. Then, according to the discretization rules, the desired pulse transfer function B(z) of the closed-loop system can be obtained. Specifically, discretization methods can include, but are not limited to, zero-pole matching discretization, bilinear transform, forward difference method, or backward difference method. After algebraic operations, the discretized pulse transfer function B(z) is obtained.

[0070] In one embodiment, the pulse transfer function model of the controlled object in the above-described design method for a minimum-cycle ripple-free digital controller with adjustable closed-loop poles is as follows:

[0071]

[0072] Where N(z) is the numerator polynomial of the control object's impulse transfer function model with respect to z, and D(z) is the denominator polynomial of the control object's impulse transfer function model with respect to z.

[0073] In one embodiment, the above-described design method for a minimum-cycle ripple-free digital controller with adjustable closed-loop poles aims to produce the following closed-loop system pulse transfer function model:

[0074]

[0075] Where, N B (z) is the numerator polynomial of the desired closed-loop system impulse transfer function model with respect to z; D B (z) is the denominator polynomial of the desired closed-loop system impulse transfer function model with respect to z, D B (z) contains the pole information of the desired closed-loop system.

[0076] In one embodiment, the above-described design method for a minimum-cycle ripple-free digital controller with adjustable closed-loop poles includes the following steps for calculating the pulse transfer function of the digital controller based on the pulse transfer function of the controlled object and the desired closed-loop system:

[0077] like If the denominator order is greater than or equal to the numerator order, then the pulse transfer function of the digital controller is:

[0078]

[0079] In one embodiment, the design method for the minimum-cycle ripple-free digital controller with adjustable closed-loop poles described above includes the following steps for calculating the pulse transfer function based on the pulse transfer function model of the controlled object and the pulse transfer function model of the desired closed-loop system:

[0080] like If the order of the denominator is less than that of the numerator, and the order difference is m, then the pulse transfer function of the digital controller is:

[0081]

[0082] Where c is a positive real number that is approximately zero.

[0083] It's understandable that when the denominator's order is smaller than the numerator's, this can be addressed by increasing (z+c). m This term ensures the feasibility and stability of the system, where c is a positive real number that is approximately zero, such as 0.01.

[0084] In one embodiment, the above-mentioned design method for a minimum-cycle ripple-free digital controller with adjustable closed-loop poles obtains the pulse transfer function of the controlled object through a zero-order hold discretization method.

[0085] The aforementioned design method for a minimum-cycle ripple-free digital controller with adjustable closed-loop poles utilizes a zero-order hold discretization method. During the discretization process, the dynamic characteristics of the original system are preserved, especially the transient and steady-state characteristics. By holding the input of the continuous-time system to a constant value until the next sampling time, the transfer function of the system can be accurately transformed. This accurate transformation ensures that the discrete system model accurately reflects the characteristics of the continuous system, avoiding controller design deviations caused by inaccurate model transformation.

[0086] In one embodiment, the above-mentioned design method for a minimum-cycle ripple-free digital controller with adjustable closed-loop poles involves selecting the desired closed-loop system poles and the numerator of the desired closed-loop system pulse transfer function model, and then obtaining the desired closed-loop system pulse transfer function through a zero-pole matching discretization method.

[0087] The aforementioned design method for a minimum-cycle ripple-free digital controller with adjustable closed-loop poles utilizes a pole-zero matching discretization method. This method accurately preserves the poles and zeros of the original system, resulting in a discretized system with the same dynamic characteristics and frequency response as the continuous-time system. This ensures consistent behavior between the discrete and continuous systems during controller design. Furthermore, the pole-zero matching method precisely places the desired closed-loop poles into the discrete-time system, ensuring the system reaches steady-state without ripple in the shortest possible time.

[0088] In some embodiments, to more intuitively and comprehensively illustrate the above-described design method for a minimum-cycle ripple-free digital controller with adjustable closed-loop poles, the following are application examples of this design method. It should be noted that the implementation examples given in this specification are merely illustrative and not the only limitation on specific implementation examples of the present invention. Those skilled in the art can use the above-described design method for a minimum-cycle ripple-free digital controller with adjustable closed-loop poles, based on the illustrative examples provided by the present invention, to solve the problem that commonly used minimum-cycle ripple-free digital controller design methods in the field of automatic control cannot avoid the system's inherent frequency by adjusting the closed-loop poles of the control system, thereby preventing system resonance.

[0089] The controlled object in this embodiment of the invention is a second-order pure integral element connected in series with a zero-order hold, and the digital controller for its design unit negative feedback control system is a digital controller.

[0090] In this embodiment, the pulse transfer function model of the controlled object can be obtained by discretizing the continuous part consisting of the hold and the controlled object as a whole using the zero-order hold discretization method. The pulse transfer function of the digitally controlled object is denoted as a rational fraction in z:

[0091]

[0092] By selecting the two desired closed-loop poles as 0.707 ± 0.707j, and then selecting the desired steady-state gain of the closed-loop system as 1, the desired closed-loop system transfer function can be calculated as follows:

[0093]

[0094] With a sampling period of 1 second selected, the pulse transfer function of the desired ideal closed-loop system model can be derived using the well-known zero-pole matching discretization method in the field:

[0095]

[0096] The digital controller is calculated below using the method of this invention based on the above expressions for G(z) and B(z).

[0097] First, calculate N. D (z), in the embodiment:

[0098]

[0099] Then calculate D. D (z), in the embodiment:

[0100]

[0101] Therefore, digital controller:

[0102]

[0103] Specifically, this embodiment also provides a schematic diagram of a minimum-cycle ripple-free digital controller with adjustable closed-loop poles, as shown below. Figure 2 As shown. Where 1 represents a digital controller, and its pulse transfer function is... 11 represents the numerator of the pulse transfer function of the digital controller, 12 represents the denominator of the pulse transfer function of the digital controller; 2 represents the pulse transfer function model of the controlled object, 21 represents the numerator of the pulse transfer function model of the controlled object, and 22 represents the denominator of the pulse transfer function model of the controlled object.

[0104] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0105] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0106] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these modifications and improvements all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A design method for a minimum-cycle ripple-free digital controller with adjustable closed-loop poles, characterized in that, include: Establish and solve the pulse transfer function model of the controlled object to obtain the pulse transfer function of the controlled object; Establish the pulse transfer function model of the desired closed-loop system, and obtain the pulse transfer function of the desired closed-loop system based on the selected poles of the desired closed-loop system; Calculate the pulse transfer function of the digital controller based on the pulse transfer function of the controlled object and the pulse transfer function of the desired closed-loop system. The process of selecting the desired closed-loop system poles includes: For systems with an order less than or equal to 2, the poles are chosen as follows: ； For a system of order n, where n is greater than 2, the first and second poles are chosen as follows: ； Where j represents the imaginary unit, x Indicates the decay rate of the system. y Indicates the oscillation frequency of the system. x and y All are positive real numbers; The 3rd to nth poles are selected according to the non-dominant pole rule.

2. The design method for a minimum-cycle ripple-free digital controller with adjustable closed-loop poles according to claim 1, characterized in that, The process of obtaining the desired closed-loop system pulse transfer function further includes: A constant is selected as the numerator of the pulse transfer function model of the desired closed-loop system based on the gain requirements of the desired closed-loop system.

3. The design method for a minimum-cycle ripple-free digital controller with adjustable closed-loop poles according to claim 1, characterized in that, The pulse transfer function model of the controlled object is as follows: ； in, Let z be the numerator polynomial of the pulse transfer function model of the controlled object. Let z be the denominator polynomial of the pulse transfer function model of the controlled object.

4. The design method for a minimum-cycle ripple-free digital controller with adjustable closed-loop poles according to claim 3, characterized in that, The desired closed-loop system pulse transfer function model is as follows: ； in, Let z be the numerator polynomial of the pulse transfer function model of the desired closed-loop system. Let z be the denominator polynomial of the desired closed-loop system pulse transfer function model. It contains information about the poles of the desired closed-loop system.

5. The design method for a minimum-cycle ripple-free digital controller with adjustable closed-loop poles according to claim 4, characterized in that, The step of calculating the pulse transfer function of the digital controller based on the pulse transfer function of the controlled object and the pulse transfer function of the desired closed-loop system includes: like If the denominator order is greater than or equal to the numerator order, then the pulse transfer function of the digital controller is: 。 6. The design method for a minimum-cycle ripple-free digital controller with adjustable closed-loop poles according to claim 4, characterized in that, The step of calculating the pulse transfer function based on the pulse transfer function model of the controlled object and the pulse transfer function model of the desired closed-loop system includes: like If the order of the denominator is less than that of the numerator, and the order difference is m, then the pulse transfer function of the digital controller is: ； Where c is a positive real number that is approximately zero.

7. The design method for a minimum-cycle ripple-free digital controller with adjustable closed-loop poles according to claim 2, characterized in that, The pulse transfer function of the controlled object is obtained by the zero-order hold discretization method.

8. The design method for a minimum-cycle ripple-free digital controller with adjustable closed-loop poles according to claim 7, characterized in that, After selecting the poles of the desired closed-loop system and the numerator of the desired closed-loop system impulse transfer function model, the desired closed-loop system impulse transfer function is obtained by the zero-pole matching discretization method.

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