Deadbeat Response of Nonlinear Systems Described by Discrete-Time State Dependent Parameter Using Exact Linearization by Local Coordinate Transformation
E. M. Shaban
Mechanical Engineering Department, Jazan University, Saudi Arabia
Abstract: This paper considers State Dependent Parameter (SDP), Proportional-Integral-Plus (PIP) control of a wide class of nonlinear systems. Here, the system is modelled using the quasi-linear SDP model structure, in which the parameters are functionally dependent on other variables in the system. This formulation is then be used to design a PIP control law using linear system design strategies, such as pole assignment or suboptimal linear quadratic design. However, since not all feasible SDP model structures can be solved using the basic approach, the present paper develops an exact linearization by local coordinate transformation that returns the closed-loop system to a controllable state. Necessary and sufficient conditions are given such that nonlinear SDP systems are feedback equivalent to a controllable linear system. Finally, sufficient simulation examples are illustrated to verify the applicability of the approach. Similar or faster deadbeat response is achieved for nonlinear SDP models having one or more than one input terms respectively. Also, the equivalent linearized model leads to constant state feedback gains that control such nonlinear discrete-time SDP models.
[E. M. Shaban. Deadbeat Response of Nonlinear Systems Described by Discrete-Time State Dependent Parameter Using Exact Linearization by Local Coordinate Transformation. J Am Sci 2012;8(10):355-366]. (ISSN: 1545-1003). http://www.jofamericanscience.org. 53
Keywords: discrete-time nonlinear system, linearization by local coordinate transformation, state dependent parameter (SDP) model, proportional-integral-plus (PIP) control, deadbeat response. Full Text 53