In this paper, the design of multivariable proportional-integral-derivative (PID) controllers for discrete-time systems based on linear matrix inequalities (LMIs) is studied. First the stability problem of the closed-loop system with the multivariable PID controller is investigated. To adjust the transient response of the resulting closed-loop system, the design method is extended to account for a pole clustering constraint. PID controller design methods that yield closed-loop systems with H_∞ and H₂ performance specifications are then investigated. Algorithms based on properly formulated LMIs are developed for the above different cases. Finally, the performance of the proposed controllers is experimentally evaluated in an adaptive optics system where it is desired to control the shape of a magnetic fluid deformable mirror. The experimental results indicate the proposed controllers can successfully provide the desired shape tracking performance in the closed-loop adaptive optics system.

The vibration caused by the multiple narrow band disturbances exists widely in the mechanical systems. In this paper, a Youla parameterized adaptive control approach is introduced for the rejection of unknown multiple narrow band disturbances. The adaptive notch filter weighted Q (Youla) parameter is adopted to the online internal model principle-based regulator, so that the disturbances can be fully attenuated and the robustness of the closed-loop system is improved. A central controller is first designed to obtain the desired baseline loop shape. Then, the controller is augmented by a notch filter weighted Q parameter to construct a series of stable controllers and the Q parameter in the stable controllers is tuned online to obtain the desired controller. The adaptive control method is applied in a data storage system to attenuate the flying height vibration and the experimental results illustrate the effectiveness of the proposed approach in rejecting unknown multiple narrow band disturbances.

With the improvement of the performance of optical equipment carried by on-orbit spacecraft, the requirements of vibration isolation are increasing. Passive isolation platforms are widely used, but the ability to suppress the low-frequency deterministic vibration disturbance is limited, especially near the system’s natural frequency. Therefore, an active vibration control strategy is proposed to improve passive isolation performance. In this paper, a Youla parameterized adaptive active vibration control system is introduced to improve the isolation performance of a piezo-actuated active–passive isolation structure. A linear quadratic Gaussian (LQG) central controller is first designed to shape the band-limited local loop of the closed-loop system. Then, the central controller is augmented into a Youla parameterized adaptive regulator with the recursive least square adaptive algorithm, and the Youla parameters (Q parameters) can be adjusted online to the desired value to suppress the unknown and time-varying multifrequency deterministic vibration disturbance. In the experiment, the residual vibration with respect to the combination of multiple frequencies is effectively suppressed by more than 20 dB on average, and a quick response time of less than 0.3 s is achieved when the deterministic residual vibration changes suddenly over time. The experimental results illustrate that the proposed adaptive active vibration control system can effectively suppress the low-frequency deterministic residual vibration.

In this paper, a new type of magnetic fluid deformable mirror (MFDM) with a two-layer layout of actuators is proposed to improve the correction performance for full-order aberrations with a high spatial resolution. The shape of the magnetic fluid surface is controlled by the combined magnetic field generated by the Maxwell coil and the two-layer array of miniature coils. The upper-layer actuators which have a small size and high density are used to compensate for small-amplitude high-order aberrations and the lower-layer actuators which have a big size and low density are used to correct large-amplitude low-order aberrations. The analytical model of this deformable mirror is established and the aberration correction performance is verified by the experimental results. As a new kind of wavefront corrector, the MFDM has major advantages such as large stroke, low cost, and easy scalability and fabrication.