Adaptive Feedforward and Anti-windup Compensation for Amplitude and Rate Saturation with Application to Precision Control

Precision motion systems have stringent error tolerance and are subject to different sources of disturbances. These disturbances can be periodic or non-periodic, wide band or narrow band and concentrate at different frequency ranges. Moreover, actuators are subject to saturation problems, which can lead to degraded servo performance and even instability when the controllers are commanding over the physical limits of the actuators. In order to investigate the precision motion control strategies for disturbance rejection as well as saturation compensation, we study the vibration control and anti-windup compensation for the amplitude and rate saturations for the hard disk drive servo system, especially for the dual-stage system.The decoupled sensitivity design is presented to separate the dual-stage system into two single-input-single-output systems. Then the baseline controllers are designed using the Linear Quadratic Gaussian/ Loop Transfer Recovery to shape the overall sensitivity function. First, in order to reject periodic disturbances, two repetitive disturbance observers (RDOBs) are added. The additional RDOBs are proven to be add-on components to the overall sensitivity, thus extending repetitive narrow notches at the harmonic frequencies. As a result, the stability of the system is not influenced. And the two actuators are limited to operate at different frequencies for repetitive disturbance rejection.Second, the adaptive feed-forward control is designed to reject the low frequency wide-band vibrations. Two structures are proposed, in which pre-identification of either the plant model or the sensitivity model is performed. The inﬁnite impulse response (IIR) ﬁlter is adapted, which is different from the conventional method using a ﬁnite impulse response filter. Besides, the error convergence is proven rigorously with assumptions. Therefore, the adaptive feed-forward control can approximate more complex unknown vibration transfer dynamics.Third, the saturation problem of the secondary actuator in the dual-stage hard disk drive system is discussed. To address this, the linear conditioning structure is exploited. The anti-windup controllers for the amplitude saturation are synthesized by formulating linear matrix inequality (LMI) optimizations. Robustness of the system is also analyzed. We combine the existing theorems and mathematical tools such as integral quadratic constraints, Schur complement, S-procedure, etc. and present procedural steps to formulate the LMI optimization problem for control synthesis. It is different from the method that utilizing the Lyapunov theory, thus does not involve the difficulty to come up with a feasible Lyapunov function.Finally, both amplitude and rate saturations are considered together. A generalized anti-windup controller is synthesized by formulating the saturation problem into a robust control problem. With additional loop transformation, the anti-windup controller is synthesized by µ-synthesis. This technique is less conservative and generalizable to systems with multiple different saturations. Note that, all the proposed techniques are add-on controls, which means the original baseline controls remain unmodified. This brings flexibility into design and implementation.