Abstract
A model reference adaptive system for a linear system with transport delay is newly designed by using Lyapunov's stability theory. The process to be studied in this paper, consists of a linear lumped parameter system having unknown variations in parameters and a plug flow process having unknown variations in reaction coefficients. A reference model is described by time invariant ordinary differential equations and partial differential equations.
In order to study adaptive control law, the author introduces a error equation which can describe the difference between process and reference model. The problem of designing the adaptive control system can be formulated as that of determining the stable control law for this error system with transport delay.
For this error system with transport delay, a Lyapunov's functional is assumed. Then, the adaptive control equations that can make the time derivative of the Lyapunov's functional negative-definite, are derived. The proposed adaptive control is a feedback control of state variable errors about transport delay process as well as errors about the lumped parameter process. Stable control gains for adaptive controller can be obtained by solving the partial differential equations of a Lyapunov's type.
From the simulation results for a scalar system with transport delay, it is found that the proposed adaptive control system can adapt the process to the reference model in the presence of variations in the reaction coefficient of the transport delay as well as in the parameters of the lumped process.
