A New Approach to Switching Robust Adaptive Control N.C. Quang, M.J. Tordon, and J. Katupitiya School of Mechanical and Manufacturing Engineering, University of New South Wales, Australia. Email: M.Tordon@unsw.edu.au Abstract— Comparison of advantages and disadvantages of control methods used in nonlinear systems is presented. To take advantage of both adaptive and robust control methods, a novel method which switches between the two is proposed. Robust control is used during transients and situations where parameters are uncertain. During steady state operations, adaptive control is used. Switching between the two methods is carried out based on the standard deviation of the estimated parameter vector. The method has been implemented on a 2 DOF articulated robot. Experimental results are presented to prove the robustness and the accuracy of the new control method. I. INTRODUCTION Systems in reality are uncertain. Two kinds of uncer- tainties exist; parametric uncertainties and uncertain non- linearities. In designing modern high performance systems, these two types of uncertainties must be accounted for and the successful elimination of their effects is of practical significance. So far numerous conventional methods such as PD, PID, computed torque control (CTC) as well as advanced control methods have been tried to solve the above mentioned problems. In general, the advanced methods are superior to the conventional control methods and the two principal categories are; the adaptive control (AC) and the robust control (RC). Adaptive control methods usually use parameter adapta- tion laws to update estimated model parameters of systems on-line. They use updated parameters in control laws to make systems adapt to parametric changes. Typically, in AC the transient performance is not considered. In order to make the systems perform well, nonlinearities of the systems must be known. Such controllers are described in [1]-[4]. In [5] the robustness of adaptive controllers applied to a robot manipulator is analyzed. As an improvement, the authors modified some adaptive control laws in an attempt to deal with unmodelled robot dynamics and external dis- turbances. Apart from the above, many other adaptive control methods have been developed to obtain better control per- formance. The results obtained with the adaptive control methods cited above indicate that transient errors are large in comparison to those in the steady state. This drawback results from the fact that adaptive controllers usually deal only with the ideal case of parametric uncertainties rather than disturbances. The process of parameter estimation takes some time to converge. Especially at the start, the parameters are poorly estimated, resulting in the poor tran- sient performance. In addition, when external disturbances are taken into account, while the robustness increases the decrease in asymptotic stability can not be avoided. The reason is that when external disturbances come into play, they affect the parameter adaptation laws. This leads to the parameter drift. As a consequence, if the external disturbances are large, they can cause systems to become unstable. These problems are well known and are described in [4]-[6]. Robust control methods, on the other hand, can success- fully deal with most of the weaknesses of the adaptive con- trol methods. Two of the popular robust control approaches are the Sliding Mode Control (SMC) [3], [7]-[9] and H ∞ optimal control [10], [11]. For linear systems, H ∞ controllers can be obtained in the state space by solving Riccati equation [10] or by using Linear Matrix Inequality (LMI) technique [11]. In nonlinear systems, H ∞ control problem becomes much more dif ficult since it seeks the solution of the very complex Hamilton-Jacobi (HJ) equation. In practice, different kinds of numerical approximation methods are suggested to solve the HJ equation. The SMC is preferably applied because of its simplicity. Many different versions of SMC have been suggested and developed [3], [7]-[9]. In the SMC, the tracking errors are forced to zero by applying nonlinear switching control inputs. That way, systems will slide along a manifold and reach the origin of the sliding space in spite of external disturbances and uncertain dynamics. As a result, at the transient stage when large uncertainties are present, systems are robust, i.e. have good transient performance. Due to the absence of parameter adaptation, RC in general and the SMC in particular, make no discrimination between external disturbances and parametric uncertainties during the transient or the steady state periods. Thus, the quality and performance at the transient and the steady state periods are similar. Consequently, tracking accuracy in the steady state shows no improvement. In the classical SMC methods, the switching control inputs cause chattering. To overcome this problem, fixed or time varying boundary layers are in- corporated in the control law, resulting in reduced switching