On an internal multimodel control for nonlinear multivariable systems - A comparative study

Abstract

Abstract-An internal multimodel control designed for nonlinear multivariable systems, is proposed in this paper. This approach is based on the multi-modeling of nonlinear systems and the realization of a specific inversion of each model. A comparative study is presented between two structures of the internal multimodel control. The first one is based on switching models and the second on residues techniques as fusion method. The case of a second order nonlinear multivariable system shows the effectiveness of both structures.

Internal Model Control of A Class of Continuous Linear Underactuated Systems

“…In the case of multivariable fully-actuated systems, n is the number of the system inputs and outputs, r is a reference signal of a dimension (n 1), y is the process output vector of a dimension (n 1), y m is the model output vector of a dimension (n 1), v is a disturbance signal affecting the system and u c is the control input signal of a dimension (n 1) [2,4]. As shown in Fig.…”

“…In the case of linear multivariable fully-actuated systems, the process and its model can be presented by their square transfer matrices of dimension (n n) or their space state representations [2,4].…”

“…To remedy these problems, we propose firstly to modify the IMC basic structure so that it becomes applicable to underactuated systems. Secondly, we design an approximate inverse of the model plant which is inspired of studies of [1,7] in the case of SISO systems, and those of [2,4] in the case of multivariable fully-actuated systems. This proposed controller represents a remedy for NMP systems.…”

“…In 1982, it was defined for Single-Input Single-Output systems (SISO) by Morari and Garcia and extended to Multi-Input Multi-Output (MIMO) ones in 1985 [3,8]. Since then, several structures of continuous-time, discrete-time, linear and non-linear IMC have been proposed [1,2,4,5,6,7]. These studies have covered many classes of SISO systems and MIMO fully-actuated ones where the number of control inputs is equal to that of the outputs.…”

“…The use of this controller ensures a high level of robustness and system performance reservation even in the case of NMP systems and those with a time-delay [1,5]. A number of studies of this IMC structure have been applied to both linear and non-linear SISO systems [1,6,7] as well as multivariable fully-actuated ones [2,4]. The obtained results are very satisfactory which led us to extend the approach to a class of continuous linear multivariable underactuated systems.…”