Robust model following controllers guaranteeing zero-tracking error for uncertain systems including delayed state perturbations

2002 ◽  
Author(s):  
Hansheng Wu
Keyword(s):  
Uncertain Systems ◽  
Tracking Error ◽  
Model Following ◽  
Robust Model

Design of a Linear Controller for Robust Tracking and Model Following

1990 ◽  
Vol 112 (4) ◽  
pp. 552-558 ◽  
Author(s):  
T. H. Hopp ◽  
W. E. Schmitendorf
Keyword(s):  
Uncertain Systems ◽  
Feedforward Control ◽  
Tracking Error ◽  
Control Law ◽  
Time Varying ◽  
Robust Tracking ◽  
Matching Conditions ◽  
Nonlinear Controllers ◽  
Model Following ◽  
Tracking And Model Following

We consider a class of linear systems in which there is time-varying uncertainty. These linear uncertain systems can be divided into two types. Systems in which the structure of the uncertainty satisfies certain matching conditions are called matched, and those systems in which the uncertainty does not satisfy the matching conditions are called mismatched. A linear control law is determined which produces tracking of dynamic inputs. The tracking error does not asymptotically decrease to zero because the systems are uncertain, instead the error is bounded. In the case of matched systems this error bound can be made arbitrarily small, and the system is said to practically track the input. In mismatched systems, the tracking error cannot be made arbitrarily small, and the system is said to ε-track the input. Previously published theory requires nonlinear controllers for practical tracking. Here, we derive a linear feedforward control law. Several examples illustrate the results.

Robust model reference control for second-order descriptor linear systems subject to parameter uncertainties

2021 ◽  
pp. 014233122110450
Author(s):  
Guang-Tai Tian ◽  
Guang-Ren Duan
Keyword(s):  
Linear Systems ◽  
Tracking Error ◽  
Sufficient Conditions ◽  
Second Order ◽  
Parameter Uncertainties ◽  
Robust Controller ◽  
Model Reference ◽  
Robust Model ◽  
Robust Compensation ◽  
Descriptor Linear Systems

This paper is devoted to designing the robust model reference controller for uncertain second-order descriptor linear systems subject to parameter uncertainties. The parameter uncertainties are assumed to be norm-bounded. The design of a robust controller can be divided into two separate problems: a robust stabilization problem and a robust compensation problem. Based on the solution of generalized Sylvester matrix equations, we obtain some sufficient conditions to guarantee the complete parameterization of the robust controller. The parametric forms are expressed by a group of parameter vectors which reveal the degrees of freedom existing in the design of the compensator and can be utilized to solve the robust compensation problem. In order to reduce the effect of parameter uncertainties on the tracking error vector, the robust compensation problem is converted into a convex optimization problem with a set of linear matrix equation constraints. A simulation example is provided to illustrate the effectiveness of the proposed technique.

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