On Lyapunov Stability Theory for Model Reference Adaptive Control

Model reference adaptive control which are capable of exhibiting simultaneously several kinds of feature (e.g., automatically adjusting the controller gain, stabilizing the system, flexibility, adaptability, and robustness, and the like) are of great current interest. In the present paper we firstly formulate a model for Model reference adaptive control which covers a very large class of systems and which is suitable for the qualitative analysis of such systems. Next, we introduce the Lyapunov function (e.g., generalized energy properties) of being based on the stability theory of Lyapunov and analyze its definiteness to establish the corresponding conclusions which judges the stability of the system .We then design the rotating speed control strategy of servo system which is well suited to the adaptive control method, being based on the characteristics and control requirements of the servo system, In accordance with the transfer function mathematical model, we design the reference model, Under adding the polynomial , we determine the state equation and filtering equation of the auxiliary signal generator, at the same time determining the signal vector and the adjustable parameter vector, in addition to the above, we select the Lyapunov function to achieve the adaptive parameter adjustment law. To verify the validity of the method, doing a simulation study and using numerical integration method carries out the test on the aforementioned servo system model under the environment of basing simulation tool of Matlab. The results of the simulation tests show that MRAC is an effective way to control the rotating speed of this kind of servo motor, giving the system good tracking ability. It is concluded that the system has strong capacities to resist interference and changes of parameters in process, it could also overcome the influence of the time-varying nonlinearity on the control performance.