Abstract
The authors propose a design method of a model reference control for nonlinear one-input, one-output systems. These systems contain such nonlinear elements as a dead-zone or a backlash at the input and the output. It is supposed that nonlinearities f(u) and g(σ), which are contained at the input and the the output, are divided into a linear part and a bounded nonlinear part such that f(u)=f1u+f(u), g(σ)=g1σ+g(σ). And for the systems, it is assumed that the all states are available directly.
The design method is considered on the coordinates transformed by a diagonal matrix T=diag[1, α-1, …, α-n+1] where α is the positive design parameter. The feedback control system is constructed so that the object may follow the reference model. The signals utilized in the feedback system are the state deviation between the system and the model and the signal g(σ)(1-ε), where g(σ) is the nonlinear characteristics of the output yP(=g(σ)) and ε(1>ε>0) is the design parameter. In the control system, feedback gains of the state deviations are selected so that eigenvalues λi (i=1, …, n) of the linear part of the system may satisfy following conditions; 1) All real part of the eigenvalues λi are negative. 2) The real part λRi and the imaginary part λIi of an eigenvalue λi satisfies |λRi|-|λIi|≥0. For the control system above mentioned, it is shown that the norm of the output error converges to any vicinity of the origin with any degree of stability by increasing α and decreasing ε. Namely, it is shown that the output error is practical stable.
Finally, computer simulation results are presented to illustrate the effectiveness of the proposed method.
