Reference estimator in a discrete-time sliding mode controller

Abstract

A discrete-time sliding mode controller (SMC) controls the motion of mechanical apparatus such as a read head in a disk storage system. The overall control effort is generated by combining a linear control effort with a discrete-time sliding mode control effort generated by switching between gains in order to drive the system's phase states toward a sliding line trajectory. An estimate of a reference is generated and added to the control effort, thereby providing an approximation of the derivative of the reference signal. Estimating the reference signal may be performed by various methods, depending on whether the reference is known, unknown but repeatable, or completely unknown and non-repeatable. A least-mean-square (LMS) algorithm is employed to estimate the reference signal by computing coefficients of a function which minimizes a particular system parameter. If the reference is an unknown, repeatable sinusoid, such as the runout signal in a disk storage device, the coefficients of a synthesized sinusoid may be determined by minimizing the position error phase state. Alternatively, the coefficients of the synthesized sinusoid may be determined by minimizing the sliding mode variable &sgr;,which defines the position of the system phase states relative to the sliding line. For references that are unknown and non-repeatable, an estimate of the derivative of the reference signal is computed, weighted, and added to weighted derivatives of the estimate, where the weights or coefficients of this function are also determined by minimizing the sliding mode variable &sgr;,.