Journal of The Society of Instrument and Control Engineers

A linearization technique of nonlinear control systems at each point on the state space trajectory is presented. This linearization which is often called the instantaneous linearization gives a good prospect on the system dynamic behavior. The characteristic equation and the state equation of the instantaneously linearized system are derived. The topology of the state space are revealed together with the stability of equilibrium states. The differences of the transient and frequency responses between the linear and nonlinear systems are explaind from the standpoint of the instantaneous linearization.

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This paper is concerned with the concept of parameter adjustability in model reference adaptive control systems. In this paper an adaptive system is said to be parameter adjustable when the dynamic characteristic of the basic feedback control system can be made identical to that of the reference model by adjusting the parameters in the controller, and it is said to be conditionally parameter adjustable when the dynamic characteristic of the basic system can be made approximately equal to that of the reference model. This paper considers conditions for an adaptive system to be parameter adjustable or conditionally parameter adjustable; some related questions are also considered. The conclusions obtained may be summarized as follows.
1) An adaptive system in which all the internal parameters vary is parameter adjustable only if the transefer function of the controlled system has no zeros, and the internal variables of the controlled system are accessible for measurement, or if the order of basic feedback system is not identical to that of the reference model.
2) In the conditionally parameter adjustable adaptive system if the parameters of the controlled system vary over very wide range of values, it is necessary to design the controller of the basic system so that the basic system is insensitive to parameter variations.
3) In the conditionally parameter adjustable adaptive system it is necessary to consider the concept of Lagrange stability rather than of Liapunov stability.

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