Impulse response parameter based internal model control for discrete-time LPV systems

This paper presents a novel impulse response parameter based solution for internal model control (IMC) within the linear parameter varying framework. First, based on a discrete-time state-space representation, a finite horizon vector autoregressive model with exogenous disturbance (VARX) is obtained to describe the I/O relationship of an affine LPV plant. In this paper, inversion of the VARX model w.r.t. control input directly leads to a IMC law where analytic solution can be derived for unconstrained and optimal reference tracking error minimization. When the bias term in the finite horizon I/O predictor is neglected, asymptotic properties of closed-loop IMC is analyzed. The VARX parameters of the I/O LPV model can be factorized into a scheduling dependent data matrix and a sequence of constant impulse response parameters (IRPs). The latter part can consistently be identified from data as a single least-squares problem. Without the need to build or identify an LPV state-space model, this methodology is able to address IMC tracking error minimization by using IRPs. The viability of the proposed method is numerically tested in simulation environment.