On-Line Analysis of a Non-Linear Control System Using Correlation Methods

Abstract

In non-linear control processes the application of optimal control generally leads to a solution which is difficult to implement. The problem is approached here by the use of a correlation method of continual tracking of the working point on the static and dynamic characteristics of the control system. A hybrid computer is utilised to compute the correlation functions and continually to identify and reoptimise about the working point using quasi-linearisation techniques. The non-linear system considered is a hyrdaulic servomotor of a type used in aircraft flight control systems. The three-level m-sequences used as test signals are injected into the system during normal operation and, since they are uncorrelated with any other signal, may have an extremely small amplitude compared with the normal working input signal. Optimal control in this instance is applied by the use of a phase compensation network with a variable bandwidth. The change of bandwidth required to satisfy the performance criterion is calculated on-line and used to optimise the system. A brief summary of correlation methods is presented together with the equation's governing identification and optimisation. The hybrid computer arrangement is described and a selection of typical results is shown and discussed. A note on the stability of the overall system as a system with time delays is included. In conclusion, the problems of time-variant dynamics on non-linear systems are considered. A proposed hybrid computer scheme is presented for this purpose in which the characteristics of the m-sequences are up-dated to match the identified time constants of the system.