Robust Discrete-Time Output Tracking Controller Design for Nonminimum Phase Systems

An Efficient Robust Servo Design for Non-Minimum Phase Discrete-Time Systems with Unknown Matched/Mismatched Input Disturbances

“…Comparison with the results developed in [14], some extensions over [14] are summarized as follows: (i) The use of the past output measurements to estimate the system state with unknown matched input disturbances developed in [14] has been extended to the use of the current output measurements to estimate the system state and the EID principle for the unknown matched/mismatched input disturbances, so that the tracking performance can be rapidly improved; (ii) The restriction on the constant command input of reference model presented in [14] has been relaxed to time-varying command input of reference model, so that a more robust and flexible tracker can be achieved; (iii) The closed-loop poles of the observer error dynamic system presented in this paper are optimally assigned inside a circle with a pre-specified radius…”

“…but not just lying inside the unit circle ( 1 α = ) presented in [14], so that the transient response of the designed servo can be significantly improved.…”

“…Lemma 1 [14]: Suppose that ( ) d k is bounded and smooth and Assumption 3 holds, then ( ) d k satisfies the following equations:…”

“…To overcome this issue, Chang [13] constructed the discrete-time proportional-integral observer (PIO) to develop a state and disturbance estimator for the discrete-time system with an unknown external disturbance to improve its tracking performance. Consequently, an advanced algorithm on the robust discrete-time output tracking controller design for NMP systems has been proposed by Chang et al [14]. However, some restrictive conditions have been imposed on the existing design methodology in [14], namely: (i) The NMP plant has to be in square dimension; (ii) Only the matched input disturbance is considered; (iii) The variation of the disturbance in two consecutive sampling instants is not changed significantly; (iv) The model-following-based command generator which uses the constant input has to be constructed to generate the desired output; and (v) The use of the past output measurements to simultaneously estimate the system state and its equivalent input disturbance.…”

“…In the proposed approach, a variable input signal instead of the constant in [14] is used to generate a drastic command input. Then, a current-output observer-based LQDT with a high-gain property is developed to have the desired tracking performance.…”