Tracking Control of Linear Time-Invariant Nonminimum Phase Systems Using Filtered Basis Functions

Abstract

An approach for minimizing tracking errors in linear time-invariant (LTI) single-input single-output (SISO) discrete-time systems with nonminimum phase (NMP) zeros using filtered basis functions (FBF) is studied. In the FBF method, the control input to the system is expressed as a linear combination of basis functions. The basis functions are forward filtered using the dynamics of the NMP system, and their coefficients are selected to minimize the error in tracking a given desired trajectory. Unlike comparable methods in the literature, the FBF method is shown to be effective in tracking any desired trajectory, irrespective of the location of NMP zeros in the z-plane. The stability of the method and boundedness of the control input and system output are discussed. The control designer is free to choose any suitable set of basis functions that satisfy the criteria discussed in this paper. However, two rudimentary basis functions, one in time domain and the other in frequency domain, are specifically highlighted. The effectiveness of the FBF method is illustrated and analyzed in comparison with the truncated series (TS) approximation method.