We study in this paper the theory and applications of a nonlinear control technique, i.e., the so-called composite nonlinear feedback control, for a class of linear systems with actuator nonlinearities. It consists of a linear feedback law and a nonlinear feedback law without any switching element. The linear feedback part is designed to yield a closed-loop system with a small damping ratio for a quick response, while at the same time not exceeding the actuator limits for the desired command input levels. The nonlinear feedback law is used to increase the damping ratio of the closed-loop system as the system output approaches the target reference to reduce the overshoot caused by the linear part. It is shown that the proposed technique is capable of beating the well-known time-optimal control in the asymptotic tracking situations. The application of such a new technique to an actual hard disk drive servo system shows that it outperforms the conventional method by more than 30%. The technique can be applied to design servo systems that deal with "point-and-shoot" fast targeting.

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In this paper, we propose new sequential randomized algorithms for convex optimization problems in the presence of uncertainty. A rigorous analysis of the theoretical properties of the solutions obtained by these algorithms, for full constraint satisfaction and partial constraint satisfaction, respectively, is given. The proposed methods allow to enlarge the applicability of the existing randomized methods to real-world applications involving a large number of design variables. Since the proposed approach does not provide a priori bounds on the sample complexity, extensive numerical simulations, dealing with an application to hard-disk drive servo design, are provided. These simulations testify the goodness of the proposed solution.

In a typical disk drive servo system, two or more types of controllers are used for track seeking, track following, and track settling modes. This leads to the problem of mode switching among these controllers. We present in this paper a unified control scheme, the discrete-time composite nonlinear feedback control, which can perform all the above functions in hard disk drive (HDD) servo systems with actuator saturation. The proposed scheme is composed by combining a linear feedback law and a nonlinear feedback law. The linear feedback law is designed to yield a fast response, while the nonlinear feedback law is used to increase the damping ratio of the closed-loop system as the system output approaches the command input. In the face of actuator saturation, this control law not only increases the speed of closed-loop response, but also improves the settling performance. Implementation results show that the proposed method outperforms the conventional proximate time-optimal servomechanism by about 30% in settling time.