Ph.D. received on: 16/4/1998

E-mail: magni@conpro.unipv.it

Tutor: Prof. R. Scattolini, Università degli Studi di Pavia
 
 

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Nonlinear receding horizon control: theory and application   ___________________________________________________________________________________________________________

Advisor:

Prof. R. Scattolini, Università degli Studi di Pavia
 

Summary:

Process industry is characterized by tighter and tighter product quality specifications, increasing productivity demands, new environmental regulations and fast changes in the economical market. In the last decades Model Based Predictive Control, also referred as Receding Horizon (RH) Control or Moving Horizon Control, has shown to respond in an effective way to these demands and is therefore widely accepted and used in many practical process control applications.
In this thesis a new nonlinear RH control algorithm is proposed. The RH control law is computed through the solution of a FH optimization problem with a terminal state penalty equal to the cost that would be incurred by applying a locally stabilizing linear control law thereafter. The main characteristics of this method are the following:
- the linear control law is never applied, but is just used to compute the terminal state penalty;
- assuming only stabilizability of the linearized system, the exponential stability of the equilibrium is guaranteed;
- as the length of the optimization horizon N goes from zero to infinity, the domain of attraction moves from the basin of attraction of the linear controller towards the basin of attraction of the infinite-horizon nonlinear controller;
- inequality constraints are allowed for;
- if the locally linearizing control law is computed by minimizing the same performance index (e.g. of LQ type) used in the solution of the FH problem, then the RH nonlinear control law is a consistent extension of the linear one (in the sense that the linear control law is tangent to the nonlinear one in the equilibrium point).
Stability robustness in the face of system perturbations is also established for discrete-time systems. For continuous-time systems, it is shown that different RH control laws, although based on an (open-loop) solution of a finite horizon optimal control problem, also yield a (feedback) solution of an associate infinite horizon optimal control problem. This inverse optimality result establishes an important robustness property of receding horizon control since the control laws are shown to possess stability margins of optimal control laws.
A way to directly consider disturbance attenuations specifications in the synthesis of the RH control law is then introduced by considering a game theoretic approach to nonlinear RH control. This approach can be seen also as a practical way to achieve a solution of nonlinear H infinity problems.
The last part of the thesis deals with two problems of crucial interest in the context of predictive control: the output feedback and tracking problems. First of all, the problem of tracking constant references for systems described by input/output NARX (Nonlinear AutoRegressive eXogenous) models which, typically, can be derived by means of black-box identification procedures is considered. Then it is shown how to deal with the general problem of tracking exogenous signals and asymptotically rejecting disturbances generated by a properly defined exosystem for systems described by state-space models with unmeasurable states.
The new multivariable predictive nonlinear controller is applied to solve a problem of interest for industry: the control of cement mills.

 

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