H_∞ Optimal Performance Design of an Unstable Plant under Bode Integral Constraint

Abstract

This paper proposed the H ∞ state feedback and H ∞ output feedback design methods for unstable plants, which improved the original H ∞ state feedback and H ∞ output feedback. For the H ∞ state feedback design of unstable plants, it presents the complete robustness constraint which is based on solving Riccati equation and Bode integral. For the H ∞ output feedback design of unstable plants, the medium-frequency band should be considered in particular. Besides, this paper presents the method to select weight function or coefficients in the H ∞ design, which employs Bode integral to optimize the H ∞ design. It takes a magnetic levitation system as an example. The simulation results demonstrate that the optimal performance of perturbation suppression is obtained with the design of robustness constraint. The presented method is of benefit to the general H ∞ design.

Robust Controller Design for Multi-Input Multi-Output Systems Using Coefficient Diagram Method

“…Here, the compensator (31) designed in [27] is compared with the method in this paper. Table 5 summarizes the results of evaluating the compensators (30) and (31) using formula (12). Table 5 shows that the decoupling effect of the compensator designed by the method in this paper is better.…”

“…For the four-tank system of the controlled object (33), the frequency ω 0 = 0.34 is selected, and the precompensator is obtained. Use the evaluation formula (12) to evaluate the decoupling system Q(s) after the compensator formula (34) acts on the controlled object formula (33), and the result is 0.000013. It shows that after the decoupling design, the interaction of the controlled object (33) is weak, and the decoupling effect is well.…”

“…Using the method in this paper, select the angular frequency ω 0 = 0.28 and obtain the compensator. Use Equation (12) to evaluate the effect of the compensator (Equation (36)) on the controlled object (Equation ( 35)) to obtain the decoupling system Q(s), and the result is 0.000000057. It shows that the system interaction effect of using compensator decoupling is minimal, and the decoupling effect is good.…”

Structured H∞ Control of an Electric Power Steering System

“…e stability of the system is the distance of the transfer function from the critical stability point. It is also the upper limit of the gain toward the sensitivity function [19,20]. It required the following:…”

Robust H∞ Control for the Spacecraft with Flexible Appendages

“…e research shows that it is difficult to use classical control to balance the multiple performance requirements for the integrated control of flexible spacecraft with multiple performance requirements [8]. However, H ∞ control theory is a synthetic control theory, which can include multiple performance requirements in the design [9][10][11][12][13][14][15][16][17][18], and it solves the control problems with multiple performance requirements and takes into account the multiple performance requirements of the system under the premise of ensuring the robustness of the system. In recent years, H ∞ control theory has been widely used in the control of the spacecraft.…”