The Feedforward Tracking Control for Linear Systems with Quadratic Performance

In this paper the tracking problem with reference tracking signals and input signals being written as the form of Fourier series is considered. A method of feedforward tracking control based on the frequency preserving property of stable linear system is proposed. A direct relationship between control input and reference output for linear system is given which can be expressed as the linear transformation of Fourier coefficients between them. A quadratic performance with combined constraints of tracking error and control input is presented and the equivalence between the optimal problem under this performance and the least mean square problem is established.