Abstract
This paper presents a new model reference adaptive control system (MRACS) for Hammerstein systems, in which each system consists of a memoryless nonlinearity followed by a linear time invariant system. Such kind of systems is particularly simple, but can describe a class of nonlinear systems including nonlinear actuator. Although existing adaptive control schemes for Hammerstein systems have been developed in discrete-time case, we present the MRACS for continuous-time systems because many actual systems are continuous ones. First, we derive an adaptive control law by using only the input and output variables of the plant, which corresponds to MRACS for linear systems when the plant is linear. Second, we clarify that regularity of the signals in the closed loop is ensured when the relative degree of the plant is determined by the transfer function from the highest power of the input to the output. It is well known that regularity of the closed loop signals plays an important role to prove the stability of the system. By using the regularity conditions, we show that boundedness of all signals in the proposed control system and convergence of the output error are guaranteed in the case. Finally, the effectiveness of the proposed scheme is illustrated through numerical simulations.
