Robust control in presence of parametric uncertainties: Observer-based feedback controller design

Abstract

This paper proposes a complete procedure for the design of a robust controller for a nonlinear process, taking into account the various issues arising in the design and using the main theoretical results from the Literature about this topic. An extended model is set up, linking performance and robustness to the control law: the H ∞ norm of the extended system in closed loop measures the achievement of the objectives. The result is a state feedback control law which guarantees robust performance. The problem of the design of an observer to estimate the state of the system is also addressed, as the complete knowledge of the state is required to calculate the control action; moreover, the implications of the use of the observer in the design of the controller are pointed out. The methodology is illustrated via simulation of a regulation problem in a continuous stirred tank reactor (CSTR). The application of this methodology to more complex systems will be discussed. ᭧

Robust control of a reverse-flow reactor

“…More details about the theoretical foundation of this result and about the details of the calculus can be found in Fissore (2008). As only three temperatures are measured (or better, three differences between the temperature and the desired steadystate values), an observer is required to get the estimation of the other states and to guarantee robust performance, i.e., the optimum observer in the worst disturbance condition has to be calculated.…”

“…As only three temperatures are measured (or better, three differences between the temperature and the desired steadystate values), an observer is required to get the estimation of the other states and to guarantee robust performance, i.e., the optimum observer in the worst disturbance condition has to be calculated. The procedure described by Fissore (2008) was followed, and thus no further details are given here. An example of the results obtained with the system observer + controller is given in Fig.…”

“…For the calculation of the controller gain K 1 the same requirements on the regulation and on the control activity previously posed are used, as well as the same range for the coefficients of the matrices, thus taking into account model uncertainties. Again, following the detailed procedure outlined by Fissore (2008) both the observer and the controller satisfying the condition on the norm of the multivariable operator arising from the extended model have been calculated. An example of the results obtained with the system observer + controller is given in Fig.…”

“…In a previous work (Fissore, 2008) a detailed description of this technique has been given, summarising the main results appeared in the Literature and introducing the concept of "extended system" for the control design, where performance requirements and model uncertainty are described. Nonlinear variables are linearised around a "nominal" state and the range of values that can be assumed by the nonlinear variable is considered as a range of uncertainty around the nominal state.…”

Trajectory tracking in a nonlinear CSTR. Controller design based on a linear algebra approach

“…Because of its importance, the CSTR control has been addressed with a variety of linear and nonlinear control techniques [8], e.g., classic control and its derivations [7,9,10,11], adaptive control [12,13], robust control [14], geometric control [15,16], among others [5,17,18].…”