Fuzzy Mixed ${{H^{2}}/{H^{\infty}}}$ Optimization-Based Decentralized Model Reference Control and Application to Piezo-Driven XY Table Systems

Abstract

In this paper, a decentralized model reference control via fuzzy mixed 2 optimization design was developed. Each subsystem contained linear pulse transfer function systems (LPTFSs). The reference model for every LPTFS was first designed to shape the response of the th closed-loop subsystem. Then the 2 -norm of the output error (i.e., the difference between the output of the reference model and the system) and weighted control input of the th LPTFS was minimized to obtain a control such that smaller energy consumption with bounded tracking error of the th LPTFS was achieved. However, an output disturbance of the th LPTFS caused by the interactions among the LPTFSs, the interconnections among the subsystems, modeling errors, and external loads deteriorated system performance or even resulted in instability. In this situation, the -norm of weighted sensitivity between output disturbance and output error of the th LPTFS was minimized to attenuate its effect. A nonlinear control based on output error for every LPTFS was also established to improve robust performance. The stability of the overall system was then verified by Lyapunov stability criterion. The application to piezodriven XY table system (PD-XY-TS) was carried out to confirm the usefulness of the proposed control.Index Terms-Decentralized control, fuzzy linear model, mixed 2 optimization, nonlinear control, piezo-driven XY table system (PD-XY-TS), reference model.

Robust model reference control of linear parameter‐varying systems with disturbances

“…(3) Design the LPV reference model (4) and (5) according to (12), (31) and (32). (4) If the state vector x is available online, solve (19) for P, L s i and a minimum γ > 0.…”

“…Consider a single-link flexible-joint robot [36] in the LPV form The LPV reference model (4) and 5is designed by computing the matrix C r using (12) and by computing the matrix B r using (32) with Z b = 0 0 0 1 T . To obtain a quadratically stable LPV reference model, the matrix A r (ρ) is computed by designing the matrices Z a i in (31) using the method for designing the LPV state feedback controllers [34].…”

“…On the other hand, some of the recent studies have focused on the robust model reference non-adaptive control techniques. These techniques are applied to different types of systems such as multivariable linear systems subject to model uncertainties [8,9], descriptor linear systems subject to parametric uncertainties [10], polytopic uncertain systems [11], decentralised linear systems with interactions treated as disturbances [12], Markovian jump linear systems with unknown transition probabilities [13] and uncertain network-based control systems [14].…”