Model Reference Adaptive Control For A Time-delay System With A Relative Order Of Two

The phenomenon of time-delay is a natural component of dynamic processes in many engineering fields.Even if the process itself does not include delays in its inner dynamics,delays are usually introduced through actuators,sensors,and transmission lines.On the one hand,time delay usually leads to unsatisfactory performances and is frequently a source of instability.On the other hand,in many dynamic processes,the parameters of the plant are unknown due to linearization approximation,modeling errors,measurement errors,and so on.Therefore,the control problem of uncertain dynamical systems with time-delays has attracted considerable attention over the past years.However,less study has been given to the topic of output adaptive control of continuous time-delay systems,and only a few results deal with output feedback model reference adaptive control of systems with state delays.This paper in view of the single-input single-output linear systems with the assumption that the relative degree of the system with the known state-delay be two.For the current reference and research results,there are errors in the process of the derivation.Therefore,on the basis of the results,we further studied the output feedback model reference adaptive control for the system.Therefore,the main contents of this paper are:(1)For the processing of linear state time-delay system,the main idea of this paper is to use the time-delay state of the reference model to compensate the time-delay state of the system.For the system's state-delay term,do not treat it as part of the system,but rather as an input to a system with no time delay.For the analysis of system time-delay item,we adopt a new method,that is,using the definition of general solution of generalized inverse matrix and using the measurable vector to represent the partial state of non-minimum state space of reference model.(2)The design of the structure of the system adaptive controller is divided into two control components: the output feedback control component and the feedforward control component.The structure of the output feedback control component is the same as the standard model reference adaptive control of a linear system without time-delay.The presence of the state-delay term promotes the use of an additional feedforward control component,which is a function of the delayed states of the reference model,and is formed by a special adaptively adjusted prefilter.The control component attempts to anticipate future outputs using a reference model.