Modular adaptive robust control of SISO nonlinear systems in a semi‐strict feedback form

Abstract

SUMMARYIn this paper, a modular modification of the adaptive robust control (ARC) technique is presented. The modular design has all of the original ARC properties with an estimation-based update law instead of a Lyapunov-based update law. In this design, the controller is divided into two modules: a control module and an identification module. A key new idea is to set a priori bounds on the time derivatives of the estimates to be maintained by the update law. As a result, their effects on the system tracking accuracy can be dominated by the control law. A modification is proposed for the standard gradient and least-square update laws to guarantee the bounds. This modification also makes the controller robust against the generalized (unparameterized) uncertainties considered in the ARC formulation while allowing asymptotic output tracking without the generalized uncertainties. Both the ARC and the modular ARC techniques are applied to a force control problem for an active suspension system. Simulations and experimental results are provided to show that the update law of the modular design is less sensitive to measurement noise which results in smaller force tracking error and smaller control gain.

Adaptive robust force control for vehicle active suspensions

“…In this paper, we studied the application of the newly developed modular ARC (MARC) controller [12,13] to the force control loop of an active suspension system. Experimental results show that the proposed MARC controller performs the force tracking task very well up to about 10 Hz; which is considerably higher than the 54 Hz results reported in the literature [4,5].…”

“…The main goal is to add flexibility to the identifier design without changing the properties of the ARC techniques. This technique has been illustrated in another paper [13] and is also available in Reference [12]. Details are thus omitted here.…”

“…In our laboratory, the estimated parameters usually diverge toward the upper or lower bound which commonly causes higher-than-necessary control gains, or even instability. In this paper, we present a modular ARC technique recently proposed by the authors [12,13]. The adaptation law is designed specifically for parameter convergence, and proven estimation schemes such as least-square update laws can be used.…”

Design of a mixed fuzzy controller for multiple-input multiple-output systems

“…Adaptive control and robust control methods have been developed in controlling SISO and MIMO systems to evaluate their control performance [24][25][26][27][28]. However, the applications of these control methods still require some knowledge about the system order and variation range of the parameters, and their output responses have oscillatory features during the initial learning interval.…”

“…The auxiliary subspace must be determined from Eqs. (8) and (24) to calculate the relative stability index I 2 of this closed-loop fuzzy control system, representing the system deviation tolerance.…”