4Adaptive Control and Robust Control

In this chapter, we consider the RST (where RST is R (regulation), S (sensitivity) and T (tracking)) polynomial system structure introduced in section 3.3 for the case where the parameters and the structure of the mathematical model (polynomials images are variable over time. In these conditions, the dynamic performance of the closed-loop system needs to be guaranteed using an adaptive or robust strategy [LAN 89, LAN 97, DUG 91, BIT 93, AST 93, AST 95, BES 98, LEF 14].

In the adaptive strategy, the estimation of the model parameters and the design of the control law iteratively succeed one another in real time. Considering the polynomial RST control strategy, the design of its adaptive implementation is based on the recursive estimation of the new parameters in the closed-loop system and on its redesign at every sampling period (of the parameters of the RST polynomials) using recursive adaptation mechanism.

The structure of the nominal system (NS) can vary as well because of nonlinear process behavior or/and uncertainties that occur after the model estimation. In this case, we consider that the discrepancy between the model and the process was due to the time variation both in the structure and the model parameters. Thus, we propose a robust control strategy that ensures tolerance of the system to structural and parametric disturbances of the process. ...

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