An adaptive controller to realize smooth input for systems with relative degree less than 3

In this paper, the main attention is focused on transient of control input signal, and then, we propose a novel model reference adaptive controller for SISO systems with relative degree less than three. When we control real devices by using the elementally conventional adaptive controller, we have an experience that high frequency oscillations with large amplitude occur in the control input signals. This is one of serious problems in actual applications. To generate a control input signal without oscillation, a novel estimator using an observer for the output tracking error signal is proposed. Using the estimator, it is shown theoretically that the control input signal converges with any convergent rate to an ideal input signal given by adding the exact model matching input signal and a smooth exponential damping signal. From the property it can be expected that. oscillations are hard to occur in the control input signals. Moreover, it is also proved theoretically that. the transient output error responses can be specified by setting design parameters.