Magnetic suspension robust control system

Abstract

The invention discloses a magnetic suspension robust control system, which realizes comprehensive optimization of a magnetic suspension motor by adopting a hybrid sensitivity control method of robust control, and effectively inhibits low-frequency disturbance and high-frequency noise by the system through the design of a sensitivity function and a complementary sensitivity function. The system can show excellent robustness in a wide frequency band, and the capability of resisting model uncertainty and external interference is enhanced; by optimizing the transfer function of the control quantity, the amplitude of a control signal is limited, and the problems of saturation and damage of an actuator are avoided; the dynamic performance and the steady-state performance of the motor are remarkably improved by combining high precision and quick response characteristics of model predictive control, so that the system has higher response speed, smaller overshoot and nearly zero steady-state error, and finally high-precision, high-robustness and high-stability control of the magnetic suspension motor under complex working conditions is realized. And the practical application requirements of a new generation of magnetic suspension motors are met.

Description

Technical Field

[0001] The present invention relates to the technical field of control systems, and more specifically, to a magnetic levitation robust control system. Background Art

[0002] The traditional PID control method is based on the deviation between the actual value and the target value. It controls the system through linear adjustment, accumulation of historical deviations, and the rate of change of deviations. It has been widely used in the field of industrial control. However, its control method is relatively simple and it is difficult to deal with various nonlinear and uncertain problems in complex systems.

[0003] With the continuous development of magnetic levitation motor technology, the new generation of magnetic levitation motors exhibit more complex dynamic characteristics during operation, such as large parameter changes, obvious dynamic characteristic conversion, excessive sensor load, and unpredictable external interference. These problems make it difficult for traditional PID control methods to meet actual needs in terms of control accuracy and dynamic response performance. Especially in the face of model uncertainty and external interference, the system is prone to performance degradation or even instability. At the same time, it is difficult for traditional methods to coordinately optimize the sensitivity function, complementary sensitivity function and control signal transfer function, resulting in insufficient performance of the system in low-frequency disturbance suppression, high-frequency noise suppression and control signal amplitude limitation. Therefore, there is an urgent need for a robust control method that can be jointly optimized based on the sensitivity function, complementary sensitivity function and control quantity transfer function to improve the robustness, dynamic performance and steady-state accuracy of the magnetic levitation motor system under complex working conditions.

[0004] Therefore, in view of the above technical problems, it is necessary to provide a magnetic levitation robust control system. Summary of the invention

[0005] The object of the present invention is to provide a magnetic levitation robust control system to solve the above-mentioned problems.

[0006] In order to achieve the above purpose, the technical solution provided by an embodiment of the present invention is as follows:

[0007] A robust magnetic suspension control system using mixed sensitivity H ∞ Control method, the method steps are as follows:

[0008] S1: Establish the open-loop transfer function G and robust controller K of the system, where G is the open-loop transfer function of the system, describing the dynamic characteristics of the system, and K is the robust controller of the system;

[0009] S2: Calculate the sensitivity function S, which is the transfer function of the system from the reference input r to the tracking error e;

[0010] S3: Calculate the complementary sensitivity function T, where the complementary sensitivity function T is the transfer function of the system from the reference input r to the output y;

[0011] S4: Calculate the control quantity transfer function R, where the control quantity transfer function R is the transfer function of the system from the reference input r to the control quantity u;

[0012] S5: Design a robust controller K based on the joint optimization of the sensitivity function S, the complementary sensitivity function T and the control variable transfer function R;

[0013] The transfer functions of the reference input r of the system to the tracking error e, the system output y and the control quantity u are:

[0014] Transfer function from r to e:

[0015] Transfer function from r to y:

[0016] Transfer function from r to u:

[0017] Among them, S and T are the sensitivity function and complementary sensitivity function of the system respectively, and S+T=I;

[0018] The closed-loop transfer function matrix P of the system from the reference input r to the evaluation signal z is expressed as:

[0019]

[0020] Among them, W1 is a sensitivity weighting function, which is used to optimize the sensitivity function S. Specifically, W1 is:

[0021] Among them, a>0, b>0;

[0022] The parameters of the weighting function W1 are finally selected as:

[0023]

[0024] W2 is a linear weighted function used to limit the amplitude of the control variable u. Specifically, W2 is:

[0025] W2=c, where c>0;

[0026] The parameters of the weighting function W2 are finally selected as:

[0027] W2=10 -5 ;

[0028] W3 is the complementary sensitivity weighting function, which is used to optimize the complementary sensitivity function T. Specifically, W3 is:

[0029] Among them, m>0, n>0, k>0;

[0030] The parameters of the weighting function W3 are finally selected as:

[0031]

[0032] The evaluation signals after weighting W1, W2, and W3 are z1, z2, and z3 respectively.

[0033] As a further improvement of the present invention, the design process of the robust controller K includes:

[0034] Establish the state space model of the magnetic levitation system and obtain the open-loop transfer function G;

[0035] Calculate the optimal robust controller K using the MATLAB / Simulink environment and the Robust Control Toolbox;

[0036] The controller algorithm is transplanted to the digital signal processor (DSP) through the S-Function module to achieve real-time control.

[0037] Compared with the prior art, the advantages of the present invention are:

[0038] This scheme achieves comprehensive optimization of the magnetic levitation motor by adopting a hybrid sensitivity control method of robust control. Through the design of sensitivity function and complementary sensitivity function, the system effectively suppresses low-frequency disturbances and high-frequency noise, so that the system can show excellent robustness in a wide frequency band and enhance the ability to resist model uncertainty and external interference; by optimizing the transfer function of the control quantity, the control signal amplitude is limited to avoid the problems of actuator saturation and damage; combined with the high precision and fast response characteristics of model predictive control, the dynamic performance and steady-state performance of the motor are significantly improved, so that the system has a higher response speed, smaller overshoot and close to zero steady-state error, and finally realizes high-precision, high-robustness and high-stability control of the magnetic levitation motor under complex working conditions, meeting the practical application needs of the new generation of magnetic levitation motors. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 The system of the present invention adopts mixed sensitivity H ∞ Schematic diagram of control method;

[0040] Figure 2 is the mixed sensitivity H of the present invention ∞ Schematic diagram of control standard box;

[0041] Figure 3 is the robustness H of the system of the present invention ∞ Flowchart of the control algorithm. DETAILED DESCRIPTION

[0042] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention; it is obvious that the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments, and all other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making creative work are within the scope of protection of the present invention.

[0043] Example:

[0044] See also Figure 1-3 , a robust magnetic suspension control system using mixed sensitivity H ∞ Control method, mixed sensitivity H ∞ The control method steps are as follows:

[0045] S1: Establish the open-loop transfer function G and robust controller K of the system, where G is the open-loop transfer function of the system, describing the dynamic characteristics of the system, and K is the robust controller of the system;

[0046] S2: Calculate the sensitivity function S, which is the transfer function of the system from the reference input r to the tracking error e;

[0047] S3: Calculate the complementary sensitivity function T, which is the transfer function of the system from the reference input r to the output y;

[0048] S4: Calculate the control quantity transfer function R, which is the transfer function of the system from the reference input r to the control quantity u;

[0049] S5: Design a robust controller K based on the joint optimization of the sensitivity function S, the complementary sensitivity function T and the control variable transfer function R;

[0050] The transfer functions of the system's reference input r to the tracking error e, system output y and control quantity u are:

[0051] Transfer function from r to e:

[0052] Transfer function from r to y:

[0053] Transfer function from r to u:

[0054] Among them, r is the reference input, e is the tracking error, u is the control quantity, and y is the system output.

[0055] Among them, S is the transfer function from the reference input r to the tracking error e, and is the sensitivity function of the system, which represents the influence of the reference input r on the tracking error e. By optimizing the sensitivity function S, low-frequency disturbances and model uncertainties can be effectively suppressed, thereby reducing the tracking error of the system and improving the steady-state accuracy of the system.

[0056] T is the transfer function from the reference input r to the system output y, and is the system's complementary sensitivity function, which represents the influence of the reference input r on the system output y. The complementary sensitivity function T is used to optimize the high-frequency characteristics, especially in the case of noise and high-frequency interference. By designing a suitable complementary sensitivity function T, the system's ability to suppress high-frequency noise can be improved, ensuring the stability and dynamic performance of the system output;

[0057] R is the transfer function from the reference input r to the control quantity u, and is the control quantity transfer function, which is used to describe the influence of the reference input r on the controller output u. The design of the optimized control quantity transfer function R can effectively limit the controller output amplitude, avoid control saturation, protect the normal operation of the actuator, and ensure that the system has a fast response capability.

[0058] In the above relationship, the sensitivity function S and the complementary sensitivity function T satisfy the relationship:

[0059] S+T=I, that is, the sensitivity function and the complementary sensitivity function complement each other and together constitute the closed-loop transfer characteristics of the system. The sensitivity function mainly optimizes the performance of the system in the low-frequency range, and the complementary sensitivity function focuses on the optimization of the high-frequency range, thereby achieving a robust design in the entire frequency band. The control quantity transfer function R is independently used to suppress the amplitude of the control signal to prevent instability caused by excessive controller output.

[0060] The derivation of the above transfer function is based on the system's open-loop transfer function G and robust controller K, and is obtained through the coupling effect of closed-loop feedback. The sensitivity function S describes the transfer relationship from the reference input to the error of the system. By designing a suitable S, the control error can be reduced and the tracking accuracy of the system can be improved; the complementary sensitivity function T describes the transfer relationship from the reference input to the output of the system. Its optimized design can ensure that the system output responds quickly to the reference input and is highly robust to noise interference. At the same time, the design of the control quantity transfer function R can limit the controller output and avoid overload or saturation problems of the actuator while initially ensuring the dynamic performance.

[0061] The closed-loop transfer function matrix P of the system from the reference input r to the evaluation signal z is expressed as:

[0062]

[0063] Hybrid sensitivity control H ∞It is necessary to find a real and rational controller K that makes the closed-loop system stable and makes H ∞ The norm is extremely small. The design process of mixed sensitivity control is mainly the selection process of weighted functions W1, W2 and W3 for S, R and T. The selection of weighted functions is the key to the design of mixed sensitivity controller. ∞ The difficulty of control design lies in the selection of weighting functions. Different weighting functions are required for different controlled objects and different design indicators. There is no specific rule to follow among the weighting functions, and they mainly depend on practical experience.

[0064] The sensitivity weighting function W1 is the weighting function of the sensitivity function S. S is the transfer function from the system reference input r to the tracking error e, and is also the transfer function from the system interference input to the system output. It reflects the system's ability to suppress output disturbances and is an important performance indicator. Since disturbances usually occur in the low-frequency region, in order to suppress disturbances and minimize the gain of the sensitivity function S, the weighting function in the low-frequency band should be as large as possible. The selected W1 is a real rational number function with low-pass characteristics, which reflects the spectral characteristics of the disturbance. ;

[0065] In this solution, a sensitivity weighting function W1 with a low-pass property is selected as the weight provided by the sensitivity function S to optimize the performance of the low-frequency band. The sensitivity weighting function W1 is specifically:

[0066] Among them, a>0, b>0;

[0067] Among them, by increasing the low-frequency gain through the numerator a, the system can more strongly suppress the influence of low-frequency disturbance on the tracking error e, and by controlling the frequency characteristics through the denominator s+b, the sensitivity weighting function shows a smooth characteristic in the transition process from low frequency to high frequency;

[0068] The selection of parameters a and b requires a comprehensive consideration of the balance between low-frequency disturbance suppression capability and system stability. After multiple experimental comparisons and analyses, the final selection is

[0069] The numerator 100 in the sensitivity weighting function W1 is used to increase the system gain for the low frequency band, thereby more effectively suppressing low-frequency interference. The denominator s+0.01 provides a weight for the low frequency band, so that the sensitivity function has a higher gain in the low frequency band and gradually weakens in the high frequency band, avoiding the amplification of high-frequency noise.

[0070] Satisfies |W1S|<1, that is, in the entire frequency range, the weighted gain of the sensitivity function is less than 1, thereby ensuring the system's robustness to low-frequency interference, reducing tracking errors, suppressing errors caused by external low-frequency disturbances and model uncertainties, and avoiding system instability caused by excessive gain.

[0071] The linear weighted function W2 is the weighted function of the control quantity transfer function R, where R is the transfer function of the system from the reference input r to the control quantity u. The introduction of W2 can limit the size of the control quantity u, prevent the system from producing serious saturation phenomena during actual operation, and avoid damage to the actuator caused by excessive control quantity.

[0072] In this scheme, in order not to increase the order of the controller, W2 is taken as a real constant, and the linear weighting function W2 is specifically:

[0073] W2=c, where c>0;

[0074] Among them, the strength of the weighting function is controlled by the constant c to limit the amplitude of the control signal u and ensure that the control signal is within the working range of the actuator;

[0075] In order to prevent the actuator from saturation or overload and ensure the stability of the control output, after multiple experimental comparisons and analyses, W2=10 was finally selected. -5 ;

[0076] Satisfying |W2R|<1, that is, the amplitude of the control signal is effectively limited, ensuring that the control amount is within the working range of the actuator, and preventing excessive control signals from having adverse effects on the system dynamic performance and actuator safety.

[0077] The complementary sensitivity weighting function W3 is the weighting function of the complementary sensitivity function T, which represents the norm bound of the multiplicative perturbation. The disturbance caused by model uncertainty in the system mainly affects the system in the high-frequency band. In order to make the system robust to model uncertainty, W3 should have a high-pass property, and its rising slope can be larger to ensure that the closed-loop system can suppress high-frequency disturbances.

[0078] In this solution, a complementary sensitivity weighting function W3 with a high-pass property is selected, and the complementary sensitivity weighting function W3 is specifically:

[0079] Among them, m>0, n>0, k>0;

[0080] Among them, the molecular part ms 2 +ns provides frequency-dependent characteristics;

[0081] m determines the high-frequency gain and enhances the system's ability to suppress high-frequency noise;

[0082] n Enhanced mid-frequency characteristics and improved dynamic performance;

[0083] The denominator k normalizes the entire weighting function to prevent the system from becoming unstable due to excessive gain. By properly adjusting the values ​​of m, n, and k, the system can be ensured to have good robustness in the high frequency band while avoiding excessive amplification of high-frequency noise.

[0084] The design of the complementary sensitivity weighting function W3 is to weight the complementary sensitivity function T, so that the system can optimize the suppression ability of high-frequency interference and noise, ensure the smoothness and stability of the output signal, and thus enhance the dynamic robustness of the system. After many experimental comparisons and analyses, the final selection

[0085] The molecular part of the complementary sensitivity weighting function W3 is 0.001s 2 +ns improves the system gain in the high and mid-frequency bands, making the system more responsive to high-frequency noise and rapidly changing input signals. The denominator 1000 is used to normalize the overall gain to prevent excessive high-frequency gain from causing system instability.

[0086] Satisfying |W3T|<1, that is, the weighted gain of the complementary sensitivity function is less than 1, suppressing high-frequency noise while ensuring the smoothness and dynamic performance of the output signal.

[0087] The joint design of three weighted functions comprehensively optimizes the system performance in the low-frequency, medium-frequency and high-frequency bands. The system performs well in steady-state accuracy, dynamic response speed and anti-interference ability.

[0088] See also Figure 2 , the weighted evaluation signals of W1, W2, and W3 are z1, z2, and z3 respectively. The closed-loop transfer function matrix P describes the transfer relationship from the reference input r to multiple evaluation signals z. In the system design, the evaluation signal z is obtained by weighting the sensitivity function S, the control quantity transfer function R, and the complementary sensitivity function T through the weighting functions W1, W2, and W3.

[0089] The composition of the closed-loop transfer function matrix P reflects the performance optimization design of the system in the full frequency band, and comprehensive considerations are given to low-frequency disturbances, high-frequency interference and control signal amplitude, thereby ensuring the stability, robustness and dynamic response performance of the system.

[0090] By adopting the design of the closed-loop transfer function matrix P, the system can achieve the following beneficial effects:

[0091] The sensitivity function S and the complementary sensitivity function T are designed with weights of W1 and W3 to optimize the steady-state accuracy and dynamic response of the system in the low-frequency band and high-frequency band respectively, while satisfying the full-band performance compensation relationship of S+T=I. The design of weighted functions W1, W2 and W3 significantly improves the system's ability to suppress low-frequency disturbances and high-frequency noise, enabling the system to demonstrate excellent robustness in a wide frequency band, ensuring stable operation in complex, changeable and highly uncertain environments. This method effectively constrains the amplitude of the control signal and prevents the actuator from being damaged or saturated due to signal overload. At the same time, it achieves comprehensive optimization of system performance, covering multiple core aspects such as low-frequency disturbance suppression, high-frequency noise protection and control signal amplitude management. This innovation not only stabilizes the closed-loop stability of the system, but also significantly improves the control accuracy and dynamic response speed, laying a solid theoretical foundation for the practical application of robust control systems and providing advanced technical support.

[0092] MathWorks of the United States has developed a robust control toolbox based on MATLAB, which enables H ∞ Control theory has truly become a practical engineering design theory. The optimal robust controller of the system can be obtained using the MATLBAB robust control toolbox.

[0093] According to the weighting function selected above, the mixed sensitivity H of the magnetic suspension system is designed. ∞ The corresponding MATLAB program of the controller is as follows:

[0094] Clear;

[0095] %Establish the state space mathematical model of the system

[0096] A = [01; 956.05870];

[0097] B = [0; -24.3378];

[0098] C = [346.80];

[0099] D = 0;

[0100] G = ss(A,B,C,D);

[0101] % Determine the system's weighting functions W1, W2 and W3

[0102] W1 = [0100; 10.01]

[0103] W2=1e-5;

[0104] W3 = [0.00110; 00.1000];

[0105] % Generate the augmented state space of the system

[0106] G1=augtf(G,W1,E2,W3);

[0107] % Generate the transfer function mathematical model of the system

[0108] G = tf(G);

[0109] % Generate the transfer function of the system robust controller

[0110] GC = tf(hinf(G1));

[0111] % Generate impulse transfer function of robust controller of the system

[0112] GD=c2d(GC,0.0013,'tustin');

[0113] According to the above program calculation, the discrete pulse transfer function of the robust controller can be obtained. Therefore, this scheme establishes a simulation program for the magnetic levitation robust control system based on the MATLAB / Simulink environment. Finally, the S-Function module is used to write the robust H ∞ The control algorithm replaces the MATLAB program of the Robust Conreol Toolbox and transplants the controller algorithm to the digital signal processor (DSP). The real-time control of the magnetic levitation system is realized through the digital signal processor (DSP), the control quantity u is calculated in real time, and the system is dynamically adjusted through the actuator to quickly respond to changes in the input signal and dynamically adjust the control quantity to ensure the stability and dynamic performance of the system.

[0114] The magnetic levitation system in this scheme shows the following performance indicators in the robust control simulation:

[0115] 1. The overshoot of the system is less than 10%, which ensures the stability of the system when responding to the reference input and avoids system instability or actuator exceeding the safe working range due to excessive overshoot;

[0116] 2. The adjustment time is less than 0.15 seconds, which meets the design requirements of fast dynamic response and adapts to the demand of high dynamic performance of magnetic suspension system;

[0117] 3. The steady-state error is less than 1%, ensuring the high accuracy of the system output and meeting the requirements for high suspension height or position accuracy.

[0118] The best result of the experimental test is that the overshoot of the system is 7%, the adjustment time is 0.12 seconds, the steady-state error is 0.68%, and the steady-state error is close to zero, indicating that the system responds smoothly and quickly, with good dynamic performance and steady-state performance. Therefore, the robust controller H designed above ∞ It has better control effect.

[0119] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other specific forms without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations falling within the meaning and scope of the equivalent elements of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0120] In addition, it should be understood that although the present specification is described according to embodiments, not every embodiment contains only one independent technical solution. This narrative method of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation methods that those skilled in the art can understand.

Claims

1. A magnetic levitation robust control system, characterized in that: Using mixed sensitivity H ∞ Control method, the method steps are as follows: S1: Establish the open-loop transfer function G and robust controller K of the system, where G is the open-loop transfer function of the system, describing the dynamic characteristics of the system, and K is the robust controller of the system; S2: Calculate the sensitivity function S, which is the transfer function of the system from the reference input r to the tracking error e; S3: Calculate the complementary sensitivity function T, where the complementary sensitivity function T is the transfer function of the system from the reference input r to the output y; S4: Calculate the control quantity transfer function R, where the control quantity transfer function R is the transfer function of the system from the reference input r to the control quantity u; S5: Design a robust controller K based on the joint optimization of the sensitivity function S, the complementary sensitivity function T and the control variable transfer function R; The transfer functions of the reference input r of the system to the tracking error e, the system output y and the control quantity u are: Transfer function from r to e: Transfer function from r to y: Transfer function from r to u: Among them, S and T are the sensitivity function and complementary sensitivity function of the system respectively, and S+T=I; The closed-loop transfer function matrix P of the system from the reference input r to the evaluation signal z is expressed as: Among them, W1 is a sensitivity weighting function, which is used to optimize the sensitivity function S. Specifically, W1 is: Among them, a>0, b>0; The parameters of the weighting function W1 are finally selected as: W2 is a linear weighted function used to limit the amplitude of the control variable u. Specifically, W2 is: W2=c, where c>0; The parameters of the weighting function W2 are finally selected as: W2＝10 -5 ； W3 is the complementary sensitivity weighting function, which is used to optimize the complementary sensitivity function T. Specifically, W3 is: Among them, m>0, n>0, k>0; The parameters of the weighting function W3 are finally selected as: The evaluation signals after weighting W1, W2, and W3 are z1, z2, and z3 respectively.

2. A magnetic levitation robust control system according to claim 1, characterized in that: The design process of the robust controller K includes: Establish the state space model of the magnetic levitation system and obtain the open-loop transfer function G; Calculate the optimal robust controller K using the MATLAB / Simulink environment and the Robust Control Toolbox; The controller algorithm is transplanted to the digital signal processor (DSP) through the S-Function module to achieve real-time control.

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