Backstepping algorithm for linear SISO plants under structural uncertainties

Abstract

The robust algorithm is proposed for parametric and structurally uncertain linear plants under external bounded disturbances. The structural uncertainty is an unknown dynamic order of the model of plants. The developed algorithm provides plant output tracking for a smooth bounded reference signal with a required accuracy at a finite time. It is assumed that only scalar input and output of the plants are available for measurement, but not their derivatives. For the synthesis of the control algorithm we use a modified backstepping algorithm. The synthesis of control algorithm is separated into rsteps, where ris an upper bound of the relative degree of control plant model. At each step we synthesize auxiliary controls that stabilize each subsystem about a zero. At the last step we synthesize a basic control law, which provides output tracking for smooth reference signal. It is shown that for the implementation of the algorithm we need to use only one filter of the control signal and the simplified control laws obtained by application of the real derivative elements. It allows simplifying significantly the calculation and implementation of the control system. Numerical examples and results of computer simulation are given, illustrating the operation of the proposed scheme.