Two‐degree‐of‐freedom controller design for linear parameter‐varying systems

Abstract

A design strategy for linear parameter-varying (LPV) systems is considered in a two-degree-of-freedom (TDOF) control framework. First, a coprime factorization for LPV systems is introduced. Second, based on the coprime factorization, a TDOF control framework of linear timeinvariant systems is extended to that of LPV systems. Good tracking performance and good disturbance rejection are achieved by a feedforward controller and a feedback controller, respectively. Furthermore, each controller design problem can be formulated in terms of a linear matrix inequality related to the L2 gain performance. Finally, a simple design example is illustrated.

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

“…□ Remark 4: The non-singular matrix T in (22) is not unique. For example, it can be computed using (27) and (28).…”

“…The proposed LPV state-feedback model reference control system is compared with some similar design systems. For instance, the idea presented in [26][27][28][29] is used to design a feedforward controller after designing an H ∞ proportional-integral (PI) controller for the single-link flexible-joint robot system (63) and (64). Fig.…”

“…The above feedforward controller cannot be used to track the reference signal sin(3t) because the reference signal sin(3t) is not trackable by the H ∞ PI feedback system. Therefore, the feedforward controllers in [26][27][28][29] are useful for further improvement in the tracking performance provided that the desired reference signal is trackable by the feedback system.…”

“…In most of these studies, different types of feedforward controllers are designed for further improvement in the tracking performance that is achieved by the previously designed feedback system. For examples, static feedforward controllers using the Youla parameterisation method [26], LPV feedforward controllers using the model matching technique [27], linear time-invariant feedforward controllers using the inversion technique [28] and dynamic LPV feedforward controllers using the parameter-dependent Lyapunov function and the multi-convexity technique [29] are designed for LPV systems.…”

“…The two vertices of ρ 1 are Λ 1 = − 0.218 and Λ 2 = 1. The parameters of the single-link flexible-joint robot are the torsional spring constant K = 0.4 Nm/rad, link inertia J l = 0.033 kgm 2 , link mass m = 0.1 kg, motor inertia J m = 0.016 kgm 2 , gravity constant g = 9.8 m/s 2 , link length l = 0.1 m and the motor constantk τ = 1 Nm/V.The following matrices are computed using(27) and(28):The following full row rank matrix G is selected since the inequalities(29) are satisfied for some P = P T > 0 and the rank conditions (43) are also satisfied…”