Design method of inner and outer ring zero pole cancellation robust controller
By designing a robust controller with zero-pole cancellation between inner and outer loops, the problem of high complexity in dual-loop feedback control systems is solved. This approach improves robustness and disturbance rejection performance without increasing the system order, while reducing the difficulty of analysis.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NAT UNIV OF DEFENSE TECH
- Filing Date
- 2026-02-25
- Publication Date
- 2026-05-19
AI Technical Summary
While dual-loop feedback control systems offer both robustness and disturbance rejection capabilities, their high system complexity and analytical difficulty limit their application in certain scenarios.
Design a robust controller for canceling zeros and poles in the inner and outer loops. By defining the system structure and establishing a transfer function model, an inner and outer loop controller is formed through unity negative feedback to cancel unwanted zeros and poles and introduce the desired dominant poles of the closed-loop system, thus constructing a two-layer controller with inner and outer loops.
Without increasing the system order, it improves the robustness to parameter perturbations and external disturbances of the controlled object, reduces system complexity and analysis difficulty, and balances robust performance and disturbance resistance performance.
Smart Images
Figure CN122063884A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of automatic control system design, and in particular to a design method for a robust controller with zero-pole cancellation between inner and outer loops. Background Technology
[0002] In the field of control engineering, multi-loop feedback control is a very common and important control strategy, widely used in many practical systems. Taking servo systems as an example, the current loop, speed loop, and position loop are typical manifestations of multi-loop feedback control. Through the coordinated work of multiple control loops, multi-loop feedback control can provide more precise and comprehensive control of the system, meeting the stringent performance requirements of different application scenarios.
[0003] Among the many multi-loop feedback control schemes, dual-loop control is a relatively basic and widely used structure. In a dual-loop control system, both the inner and outer loop controllers are typically of at least first order. Specifically, the inner and outer loop controllers are connected in series with the controlled object, and then together form a closed-loop structure in the form of unity negative feedback. This closed-loop structure allows the system to sense the deviation between the output and the desired input in real time, and to reduce the deviation through the adjustment of the controllers, thereby achieving precise control of the controlled object.
[0004] Compared to single-loop feedback control systems, dual-loop feedback control systems exhibit significant advantages. In terms of robustness, dual-loop feedback control systems are better able to handle uncertainties such as changes in system parameters and external disturbances, maintaining relative stability in system performance. For example, when the parameters of the controlled object change due to environmental variations or component aging, the dual-loop feedback control system can maintain stable system output through the coordinated adjustment of the inner and outer loop controllers, while a single-loop feedback control system may experience a significant performance degradation due to parameter changes. Dual-loop feedback control systems also perform better in terms of disturbance rejection. They can more effectively suppress the impact of various external disturbances on the system output, enabling the system to recover to a stable state more quickly when disturbed.
[0005] However, dual-loop feedback control systems are not without their flaws. Because their structure involves at least two controllers connected in series with the controlled object to form a closed loop, the system order is typically higher than that of a single-loop control system. While the increased system order brings performance improvements, it also significantly increases system complexity. This means that more factors and parameters need to be considered during system design, analysis, and debugging, increasing the difficulty of design and implementation. For example, analyzing the stability and dynamic response performance indicators of a dual-loop feedback control system requires more complex mathematical tools and methods, making the analysis process more cumbersome and prone to errors compared to a single-loop control system. This increased complexity and analytical difficulty not only places higher demands on the professional knowledge and skills of control engineers but also, to some extent, limits the application of dual-loop feedback control systems in scenarios with strict constraints on system complexity and design difficulty.
[0006] Therefore, dual-loop feedback control systems hold an important position in control engineering. Although their robustness and disturbance rejection performance are superior to single-loop feedback control systems, the increased system complexity and analytical difficulty are key issues that need to be overcome in their application. Thus, how to fully leverage the advantages of dual-loop feedback control systems while reducing their complexity and analytical difficulty has become one of the important research directions in the field of control engineering. Summary of the Invention
[0007] The technical problem to be solved by this invention is to provide a design method for a robust controller with zero-pole cancellation between inner and outer loops, which can solve the problem that multi-loop feedback control systems cannot simultaneously achieve robust performance, disturbance rejection performance and system complexity.
[0008] To achieve the above-mentioned objectives, this invention provides a design method for a robust controller with inner and outer loop zero-pole cancellation, comprising the following steps:
[0009] S1. Define the system composition of the dual-loop closed-loop system, wherein the dual-loop closed-loop system includes an inner loop controller, an outer loop controller, and a controlled object; the inner loop controller is configured to cancel zeros and poles that are not needed by the controlled object, and the outer loop controller is configured to introduce the desired dominant poles of the closed-loop system. S2. Establish and solve the transfer function model of the controlled object to obtain the rational fractional transfer function of the controlled object; S3. Connect the inner loop controller in series with the controlled object and form an inner closed loop system with unity negative feedback. Establish the transfer function model of the inner loop controller and obtain the transfer function of the inner loop controller based on the dominant pole of the introduced closed loop system. S4. Connect the outer loop controller and the inner closed loop system in series and form a dual-loop closed loop system with unity negative feedback. Establish the transfer function model of the outer loop controller and obtain the transfer function of the outer loop controller based on the dominant pole of the introduced closed loop system. Complete the construction of the inner and outer loop dual-layer controller.
[0010] According to one aspect of the invention, in step S3, the numerator and denominator of the obtained inner-loop controller transfer function respectively contain polynomials that can cancel out the numerator and denominator of the rational fractional transfer function of the controlled object.
[0011] According to one aspect of the invention, in step S3, the denominator of the obtained inner loop controller transfer function includes a polynomial such that the order of the denominator is not less than the order of the numerator.
[0012] According to one aspect of the present invention, in step S4, the numerator and denominator of the obtained outer loop controller transfer function respectively include polynomials for canceling the numerator and denominator of the inner loop system transfer function formed by the inner loop controller and the controlled object.
[0013] According to one aspect of the invention, in step S4, the numerator of the obtained outer loop controller transfer function includes constant terms of the system's desired characteristic polynomial, the denominator includes a polynomial whose order is not less than that of the numerator, and a non-constant term of the system's desired characteristic polynomial.
[0014] According to one aspect of the present invention, in step S2, the transfer function model of the control object is represented as follows:
[0015] in, The transfer function model of the controlled object is about The molecule polynomial, The transfer function model of the controlled object is about The denominator polynomial.
[0016] According to one aspect of the present invention, in step S3, the transfer function model of the inner loop controller is expressed as follows:
[0017] in, The transfer function model of the inner loop controller is expressed with respect to... The molecule polynomial, The transfer function model of the inner loop controller is expressed with respect to... The denominator polynomial; In step S3, the step of obtaining the inner-loop controller transfer function based on the introduced dominant pole of the closed-loop system, wherein the introduced dominant pole of the closed-loop system is either a pair of conjugate complex poles or a single dominant pole, wherein if the dominant pole of the closed-loop system is a pair of conjugate complex poles, it is expressed as:
[0018] in, Represents the imaginary unit. and All are positive real numbers; If the dominant pole of the closed-loop system is a single dominant pole, then it is expressed as:
[0019] in, It is a positive real number; The obtained inner-loop controller transfer function is expressed as:
[0020] in, Indicates the transfer function used to ensure the inner loop controller. A polynomial whose numerator and denominator have the same order.
[0021] According to one aspect of the present invention, in step S4, the transfer function model of the outer loop controller is expressed as follows:
[0022] in, The transfer function model of the outer loop controller is expressed with respect to... The molecule polynomial, The transfer function model of the outer loop controller is expressed with respect to... The denominator polynomial; In step S4, the step of obtaining the outer-loop controller transfer function based on the introduced dominant pole of the closed-loop system, wherein the introduced dominant pole of the closed-loop system is either a pair of conjugate complex poles or a single dominant pole, wherein if the dominant pole of the closed-loop system is a pair of conjugate complex poles, it is expressed as:
[0023] in, Represents the imaginary unit. and All are positive real numbers; The obtained outer loop controller transfer function is expressed as:
[0024] in, Indicates the function used to ensure the transfer of the outer loop controller. A polynomial whose numerator and denominator have the same order; If the dominant pole of the closed-loop system is a single dominant pole, then it is expressed as:
[0025] in, It is a positive real number; The obtained outer loop controller transfer function is expressed as:
[0026] in, Indicates the function used to ensure the transfer of the outer loop controller. A polynomial whose numerator and denominator have the same order.
[0027] According to one aspect of the invention, in the transfer function of the inner loop controller, the polynomial The constant term is 1; In the transfer function of the outer loop controller, the polynomial The constant term is 1.
[0028] According to one aspect of the present invention, in step S2, the step of establishing the transfer function model of the controlled object, the controlled object is a first-order inertial element, and the transfer function model of the controlled object is obtained by modeling the controlled object, power amplifier, actuator and sensor as a whole.
[0029] According to one aspect of the present invention, this approach can improve the robustness of the system to perturbations of the controlled object parameters and external disturbances without increasing the order of the closed-loop system.
[0030] According to one aspect of the present invention, the inner-loop controller of this embodiment includes a polynomial that balances the order of the numerator and denominator, which can ensure the physical realizability of the controller without affecting the system gain.
[0031] According to one aspect of the present invention, this approach fully solves the problem that commonly used multi-loop control system design methods in the field of automatic control cannot simultaneously consider robustness, disturbance rejection performance, and system complexity.
[0032] According to one aspect of the present invention, compared with the traditional single-loop control system, the order of the total system in this embodiment is not increased, which enables the embodiment to take into account the beneficial effects of robust performance, disturbance rejection performance and system complexity. Attached Figure Description
[0033] Figure 1 This is a flowchart illustrating the design steps of the robust controller for zero-pole cancellation in the inner and outer loops according to the present invention. Figure 2This is a schematic diagram of the robust zero-pole cancellation controller for the inner and outer loops of the present invention; Detailed Implementation To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the embodiments will be described in detail below.
[0034] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. The embodiments cannot be described in detail here, but the embodiments of the present invention are not limited to the following embodiments.
[0035] like Figure 1 As shown, according to one embodiment of the present invention, a method for designing a robust controller for inner and outer loop zero-pole cancellation includes the following steps: S1. Define the system composition of the dual-loop closed-loop system, wherein the dual-loop closed-loop system includes an inner loop controller, an outer loop controller, and a controlled object; the inner loop controller is configured to cancel zeros and poles that are not needed by the controlled object, and the outer loop controller is configured to introduce the desired dominant poles of the closed-loop system. S2. Establish and solve the transfer function model of the controlled object to obtain the rational fractional transfer function of the controlled object; S3. Connect the inner loop controller in series with the controlled object and form an inner closed loop system with unity negative feedback. Establish the transfer function model of the inner loop controller and obtain the transfer function of the inner loop controller based on the dominant pole of the introduced closed loop system. S4. Connect the outer loop controller and the inner closed loop system in series and form a dual-loop closed loop system with unity negative feedback. Establish the transfer function model of the outer loop controller and obtain the transfer function of the outer loop controller based on the dominant pole of the introduced closed loop system. Complete the construction of the inner and outer loop dual-layer controller.
[0036] like Figure 1 As shown, according to one embodiment of the present invention, in step S1, in the step of clarifying the system configuration of the dual-loop closed-loop system, the controlled object 3 is a first-order inertial element, and both the inner and outer loops of the dual-loop closed-loop system adopt first-order series correction controllers, and both the inner and outer loops are unity negative feedback. The inner loop controller 2 is configured to cancel out unwanted zeros and poles of the controlled object 3, while the outer loop controller 1 is configured to introduce the desired dominant pole of the closed-loop system.
[0037] like Figure 1 As shown, according to one embodiment of the present invention, in step S2, the step of establishing the transfer function model of the controlled object involves modeling the controlled object 3 as a whole, including the controlled object, power amplifier, actuator, and sensor, to obtain the transfer function model of the controlled object; in this embodiment, the transfer function model of the controlled object 3 is about s The rational fraction of (i.e., the independent variable in the transfer function) is then expressed as:
[0038] in, The transfer function model of control object 3 is shown below. The molecule polynomial, The transfer function model of control object 3 is shown below. The denominator polynomial.
[0039] like Figure 1 As shown, according to one embodiment of the present invention, in step S3, the transfer function model of the inner loop controller is established, and the transfer function of the inner loop controller is obtained based on the dominant poles of the introduced closed-loop system. The numerator and denominator of the obtained inner loop controller transfer function respectively contain polynomials in the denominator and numerator of the rational fractional transfer function of the controlled object. Further, the denominator of the obtained inner loop controller transfer function contains a polynomial whose order is not less than the order of the numerator.
[0040] Specifically, the transfer function model of the inner loop controller is expressed as follows:
[0041] in, The transfer function model of the inner loop controller is expressed with respect to... The molecule polynomial, The transfer function model of the inner loop controller is expressed with respect to... The denominator polynomial; In this embodiment, the transfer function model of the inner loop controller The dominant poles of the introduced closed-loop system can be calculated, including: Obtain the dominant pole of the introduced closed-loop system, wherein the dominant pole of the introduced closed-loop system is either a pair of conjugate complex poles or a single dominant pole. If the dominant pole of the closed-loop system is a pair of conjugate complex poles, it is expressed as:
[0042] in, Represents the imaginary unit. and All are positive real numbers; Furthermore, in the pair of conjugate complex poles, positive real numbers The larger the number, the shorter the system transition process; positive real numbers The larger the value, the greater the oscillation frequency during the system transition. The specific value is selected according to the system application scenario, functional requirements, and hardware system performance limitations, following a preset performance balance trade-off rule.
[0043] If the dominant pole of the closed-loop system is a single dominant pole, then it is expressed as:
[0044] in, It is a positive real number; Furthermore, at a dominant pole, the positive real number The larger the system, the shorter the transition process.
[0045] Therefore, based on the dominant poles of the closed-loop system, the transfer function of the inner-loop controller can be calculated from the transfer function model of the inner-loop controller, and the transfer function of the inner-loop controller is expressed as:
[0046] in, Indicates the transfer function used to ensure the inner loop controller. A polynomial whose numerator and denominator have the same order.
[0047] In this embodiment, the polynomial The constant term is 1, and the coefficients of other terms are much less than 1 (e.g., 0.01) or equal to 0.
[0048] like Figure 1 As shown, according to one embodiment of the present invention, in step S4, where the outer loop controller and the inner closed-loop system are connected in series and a dual-loop closed-loop system is formed using unity negative feedback, after the inner closed-loop system forms a closed loop according to unity feedback, the transfer function of the object controlled by the outer loop controller is equivalent to the transfer function of the inner closed-loop system. Furthermore, the numerator and denominator of the obtained outer loop controller transfer function respectively contain polynomials used to cancel out the numerator and denominator of the transfer function of the inner closed-loop system formed by the inner loop controller and the controlled object. The inner closed-loop system transfer function can be obtained from the transfer function of the controlled object and the transfer function of the inner loop controller, which will not be elaborated further here. Further, the numerator of the obtained outer loop controller transfer function contains a constant term of the system's desired characteristic polynomial, the denominator contains a polynomial whose order is not less than the numerator's order, and a non-constant term of the system's desired characteristic polynomial. The system's desired characteristic polynomial can be obtained after the system's desired closed-loop poles are determined, which will not be elaborated further here.
[0049] Specifically, the transfer function model of the outer loop controller is expressed as follows:
[0050] in, The transfer function model of the outer loop controller is expressed with respect to... The molecule polynomial, The transfer function model of the outer loop controller is expressed with respect to... The denominator polynomial; In this embodiment, the transfer function model of the outer loop controller The dominant poles of the introduced closed-loop system can be calculated, including: Obtain the dominant pole of the introduced closed-loop system, wherein the dominant pole of the introduced closed-loop system is either a pair of conjugate complex poles or a single dominant pole. If the dominant pole of the closed-loop system is a pair of conjugate complex poles, it is expressed as:
[0051] in, Represents the imaginary unit. and All are positive real numbers; Furthermore, in the pair of conjugate complex poles, positive real numbers The larger the number, the shorter the system transition process; positive real numbers The larger the value, the greater the oscillation frequency during the system transition. The specific value is selected according to the system application scenario, functional requirements, and hardware system performance limitations, following a preset performance balance trade-off rule.
[0052] If the dominant pole of the closed-loop system is a single dominant pole, then it is expressed as:
[0053] in, It is a positive real number; Furthermore, at a dominant pole, the positive real number The larger the system, the shorter the transition process.
[0054] Therefore, based on the dominant poles of the closed-loop system, the transfer function of the outer-loop controller can be calculated from the model of the outer-loop controller. If the dominant poles of the closed-loop system are conjugate complex pole pairs, then the transfer function of the outer-loop controller is expressed as:
[0055] in, Indicates the function used to ensure the transfer of the outer loop controller. A polynomial whose numerator and denominator have the same order; In this embodiment, the polynomial The constant term is 1, and the coefficients of other terms are much less than 1 (e.g., 0.01) or equal to 0.
[0056] If the dominant pole of the closed-loop system is a single dominant pole, then the transfer function of the outer-loop controller is expressed as:
[0057] in, Indicates the function used to ensure the transfer of the outer loop controller. A polynomial whose numerator and denominator have the same order.
[0058] In this embodiment, the polynomial The constant term is 1, and the coefficients of other terms are much less than 1 (e.g., 0.01) or equal to 0.
[0059] To further illustrate this plan, further examples will be provided.
[0060] Example A dual-loop closed-loop system is formed by inner-loop controller 2, outer-loop controller 1, and controlled object 3 using unity negative feedback. Inner-loop controller 2 and outer-loop controller 1 are both first-order series correction controllers, while controlled object 3 is a first-order inertial element. In this embodiment, the original pole of controlled object 3 is -1, and the desired dominant pole of the closed-loop system is -4. The steady-state gain of the dual-loop closed-loop system remains consistent with the original steady-state gain of controlled object 3.
[0061] For controlled object 3, its steady-state gain is 1, and its characteristic polynomial is... Therefore, the rational fractional transfer function of controlled object 3 can be expressed as: .
[0062] Based on this, the obtained inner-loop controller transfer function can be expressed as: In this embodiment, after the inner closed-loop system forms a closed loop according to unit feedback, the transfer function of the object controlled by the outer loop controller 1 is equivalent to the transfer function of the inner closed-loop system, that is, it is... Its steady-state gain is 1, and its characteristic polynomial is .
[0063] Furthermore, the obtained outer loop controller transfer function can be expressed as: In this embodiment, the equivalent open-loop transfer function formed by connecting the outer loop controller 1 in series with the inner closed-loop system is: After the outer loop controller 1 and the inner closed loop system form a closed loop according to unity negative feedback, the overall closed-loop transfer function of the resulting dual-loop closed-loop system is: The design goals have been achieved.
[0064] In contrast, if this embodiment is designed using the well-known traditional single-loop unity negative feedback control method, the transfer function of the typically used series compensator controller is: After a single-loop system forms a closed loop using unity negative feedback, the overall closed-loop transfer function of the system is also... This also achieves the design goal of adjusting the dominant pole to -4 and keeping the gain unchanged.
[0065] In the embodiments, parameter perturbation adaptability simulations demonstrate that when the steady-state gain and time constant of the controlled object are perturbed, the inner and outer loop zero-pole cancellation dual-loop control system exhibits higher parameter perturbation robustness than the single-loop system. Furthermore, constant disturbance simulations demonstrate that when there is disturbance between the controlled object and the nearest controller, the inner and outer loop zero-pole cancellation dual-loop system is less sensitive to disturbances and exhibits better disturbance adaptability.
[0066] In the embodiment, the order of the total system does not increase compared with the single-loop control system, which is a dual-loop control system with zero-pole cancellation between the inner and outer loops. This demonstrates that the design method of robust controller with zero-pole cancellation between the inner and outer loops can balance robust performance, disturbance rejection performance and system complexity.
[0067] The above description is merely an example of a specific solution of the present invention. For any devices and structures not described in detail herein, it should be understood that they are implemented using common devices and methods already available in the art.
[0068] The above description is merely one embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for designing a robust controller with inner and outer loop zero-pole cancellation, characterized in that, Includes the following steps: S1. Define the system composition of the dual-loop closed-loop system, wherein the dual-loop closed-loop system includes an inner loop controller, an outer loop controller, and a controlled object; the inner loop controller is configured to cancel zeros and poles that are not needed by the controlled object, and the outer loop controller is configured to introduce the desired dominant poles of the closed-loop system. S2. Establish and solve the transfer function model of the controlled object to obtain the rational fractional transfer function of the controlled object; S3. Connect the inner loop controller in series with the controlled object and form an inner closed loop system with unity negative feedback. Establish the transfer function model of the inner loop controller and obtain the transfer function of the inner loop controller based on the dominant pole of the introduced closed loop system. S4. Connect the outer loop controller and the inner closed loop system in series and form a dual-loop closed loop system with unity negative feedback. Establish the transfer function model of the outer loop controller and obtain the transfer function of the outer loop controller based on the dominant pole of the introduced closed loop system. Complete the construction of the inner and outer loop dual-layer controller.
2. The design method for a robust controller with inner and outer loop zero-pole cancellation according to claim 1, characterized in that, In step S3, the numerator and denominator of the obtained inner loop controller transfer function respectively contain polynomials in the denominator and numerator of the rational fractional transfer function of the controlled object.
3. The design method for a robust controller with inner and outer loop zero-pole cancellation according to claim 2, characterized in that, In step S3, the denominator of the obtained inner loop controller transfer function contains a polynomial such that the order of the denominator is not less than the order of the numerator.
4. The design method for a robust controller with inner and outer loop zero-pole cancellation according to claim 3, characterized in that, In step S4, the numerator and denominator of the obtained outer loop controller transfer function respectively contain polynomials used to cancel out the numerator and denominator of the inner loop system transfer function formed by the inner loop controller and the controlled object.
5. The design method for a robust controller with inner and outer loop zero-pole cancellation according to claim 4, characterized in that, In step S4, the numerator of the obtained outer loop controller transfer function includes constant terms of the system's desired characteristic polynomial, the denominator includes a polynomial whose order is not less than the numerator's order, and a non-constant term of the system's desired characteristic polynomial.
6. The design method for a robust controller with inner and outer loop zero-pole cancellation according to claim 5, characterized in that, In step S2, the transfer function model of the control object is established as follows: in, The transfer function model of the controlled object is about The molecule polynomial, The transfer function model of the controlled object is about The denominator polynomial.
7. The design method for a robust controller with inner and outer loop zero-pole cancellation according to claim 6, characterized in that, In step S3, the transfer function model of the inner loop controller is established as follows: in, The transfer function model of the inner loop controller is expressed with respect to... The molecule polynomial, The transfer function model of the inner loop controller is expressed with respect to... The denominator polynomial; In step S3, the step of obtaining the inner-loop controller transfer function based on the introduced dominant pole of the closed-loop system, wherein the introduced dominant pole of the closed-loop system is either a pair of conjugate complex poles or a single dominant pole, wherein if the dominant pole of the closed-loop system is a pair of conjugate complex poles, it is expressed as: in, Represents the imaginary unit. and All are positive real numbers; If the dominant pole of the closed-loop system is a single dominant pole, then it is expressed as: in, It is a positive real number; The obtained inner-loop controller transfer function is expressed as: in, Indicates the transfer function used to ensure the inner loop controller. A polynomial whose numerator and denominator have the same order.
8. The design method for a robust controller with inner and outer loop zero-pole cancellation according to claim 7, characterized in that, In step S4, the transfer function model of the outer loop controller is established as follows: in, The transfer function model of the outer loop controller is expressed with respect to... The molecule polynomial, The transfer function model of the outer loop controller is expressed with respect to... The denominator polynomial; In step S4, the step of obtaining the outer-loop controller transfer function based on the introduced dominant pole of the closed-loop system, wherein the introduced dominant pole of the closed-loop system is either a pair of conjugate complex poles or a single dominant pole, wherein if the dominant pole of the closed-loop system is a pair of conjugate complex poles, it is expressed as: in, Represents the imaginary unit. and All are positive real numbers; The obtained outer loop controller transfer function is expressed as: in, Indicates the function used to ensure the transfer of the outer loop controller. A polynomial whose numerator and denominator have the same order; If the dominant pole of the closed-loop system is a single dominant pole, then it is expressed as: in, It is a positive real number; The obtained outer loop controller transfer function is expressed as: in, Indicates the function used to ensure the transfer of the outer loop controller. A polynomial whose numerator and denominator have the same order.
9. The design method for a robust controller with inner and outer loop zero-pole cancellation according to claim 8, characterized in that, In the transfer function of the inner loop controller, the polynomial The constant term is 1; In the transfer function of the outer loop controller, the polynomial The constant term is 1.
10. The design method for a robust controller with inner and outer loop zero-pole cancellation according to claim 1, characterized in that, In step S2, the step of establishing the transfer function model of the controlled object is that the controlled object is a first-order inertial element, and the transfer function model of the controlled object is obtained by modeling the controlled object, power amplifier, actuator and sensor as a whole.