A pole placement controller for non-linear dynamic plants

Abstract

In this study a control-oriented model is proposed to represent a wide range of non-linear discrete-time dynamic plants. As a testimony to the efficiency of the model structure for control system design, a pole placement controller is designed for non-linear discrete-time plants. Mathematically the solution of the controller output is converted into resolving a polynomial equation in the current control term u( t), which significantly reduces the difficulties encountered in non-linear control system synthesis and computational complexities. The integrated procedure provides a straightforward methodology to use in linear control system design techniques when designing non-linear control systems. For a demonstration of the effectiveness of the proposed methodology used to deal with practical problems, pole placement controllers are designed for three non-linear plants, including the Hammerstein model, a laboratory-scale liquid level system and a continuous stirred tank reactor. The simulation results are presented with graphical illustrations.

U-model based LMI robust controller design

“…The identification error and stability of the controller of the U-pole placement control system have been discussed in (Zhu and Guo, 2002). An enhanced Newton-Raphson algorithm is proposed to guarantee the stability of the controller in a minimum phase system (Zhu et al, 1999).…”

“…In some instances linearizing structures have been used but these suffer from 'local applicability' (Isidori, 1995) and therefore, are not very attractive. In order to simplify the control law synthesis part in nonlinear modelling, a new control-oriented model termed as the U-Model has recently been suggested (Zhu and Guo, 2002). The U-Model has a more general appeal as compared to other nonlinear models (NARMAX model and Hammerstein model).…”

“…Based on the U-Model, pole placement controllers (Zhu and Guo, 2002) for nonlinear plants with known parameters have been proposed. Some previous works methods of control system design enhanced by U-Model.…”

Adaptive feed-forward control of thermal heating process

“…The error due to measurement noise, model mismatch, uncertain dynamics, plant variations is represented by e(t). Now by expanding the nonlinear function f (·) of the above equation as a polynomial with respect to u(t − 1) we can obtain the model as [4]:…”

“…However, due to lack of maneuverable structure, controller design based on NARMAX model results into an inevitable computationally complex procedure. To reduce the design complexity, a control oriented model termed as the U-model is proposed in [4], where the nonlinear plant is represented as a polynomial in the current control term. Based on this model the plant inverse can be easily evaluated on-line using standard root solving algorithms such as the Newton-Raphson method.…”