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In this work, it is presented a new contribution to the design of a robust MPC with output feedback, input constraints, and uncertain model. Multivariable predictive controllers have been used in industry to reduce the variability of the process output and to allow the operation of the system near to the constraints, where it is usually located the optimum operating point. For this reason, new controllers have been developed with the objective of achieving better performance, simpler control structure, and robustness with respect to model uncertainty. In this work, it is proposed a model predictive controller based on a nonminimal state space model where the state is perfectly known. It is an infinite prediction horizon controller, and it is assumed that there is uncertainty in the stable part of the model, which may also include integrating modes that are frequently present in the process plants. The method is illustrated with a simulation example of the process industry using linear models based on a real process.

Model predictive control has achieved a remarkable popularity in the process industry with thousands of practical applications [

The main objective of this work is to extend the controller proposed in González and Odloak [

Consider the following discrete time-invariant model:

For control implementation, in order to better locate the uncertainties along the process model, it is adequate to divide the model in two separated parts. The first part of the model is related to the pure integrating outputs, and the second part is related to the stable outputs. Here, it is assumed that the process has no outputs related simultaneously with stable and integrating modes. Then, suppose that the model defined by (

Within the conventional MPC formulation, the control horizon

Then, after time step

It should be noted that, after time step

After time step

The system outputs need to be controlled through the manipulation of the

Equation (

The constraint (

One can now define the robust MPC with output feedback for systems with integrating and stable outputs. The controller is robust in a sense that it maintains stability even in the presence of uncertainty in the model related to the stable outputs. Assuming that

Consider the following objective function:

The constraint defined in (

The constraint defined in (

The proof of the stability of an MPC usually involves two ingredients: recursive feasibility of the control problem and the existence of a Lyapnvov function for the closed-loop system. The theorem below shows the recursive feasibility of Problem

If Problem

Suppose that at time

Since Problem

If the system defined in (

Suppose that, at time step

Consider the system represented in (

Suppose that the convergence of

The proposed control strategy was tested with a small dimension system of the process industry. The system is part of a distillation column where isobutene is separated from n-butane in the alkylation unit of an oil refinery. This system was studied in Carrapiço et al. [^{3}/d), and feed temperature deviation (

Process diagram for alkylation system.

From practical tests, for a sampling period

In the set point tracking problem simulated here, the desired value of the liquid level in the overhead drum (

Outputs of the distillation system. Nominal case.

Inputs of the distillation system. Nominal case.

Outputs of the distillation system. Uncertain case.

Inputs of the distillation system. Uncertain case.

In this paper, it was presented a new version of the robust infinitive horizon MPC with output feedback for systems with stable and integrating outputs. The adopted model formulation precludes the need to include a state observer, and the computer burden to run the controller may be reduced. To accommodate uncertainty in the process model, the state space model was built in two separate parts: one part is related to the integrating outputs and the other is related to the stable outputs. With this approach, it was possible to include the multiplant uncertainty in the model of stable outputs. The resulting optimization problem is a convex nonlinear program that can be easily solved with the available NLP packages. A simulation example shows that the implementation of the developed approach at real industrial systems may be achieved at least for systems of small to medium dimension.