(197c) Control Structure Adaptation for Linear Constrained Systems

Optimal operation of a chemical process as well as many other systems can generally be formulated as a dynamic optimization problem. Significant advances in computing technology and alogirthms allow the user to solve relatively large dynamic optimization problems efficiently. As far as implementation is concerned, a naive possibility is to solve the optimization problem off-line and implement the same. However, this strategy is clearly not robust or even feasible because of uncertainty (disturbances, measurement noise or model plant mismatch) Hence, it is necessary to introduce some kind of feedback from measurements. There are two main paradigms when it comes to implementation of the optimal solution [1].

Paradigm 1: On-line optimizing control where measurements are primarily used to update the model. With the arrival of new measurements, the optimization problem is resolved for the inputs. Examples of this approach are traditional implementation of Model Predictive Control, real-time optimization [2] and Model Predictive Control [3] are examples of Paradigm 1.

Paradigm 2: Pre-computed solutions based on offline optimization. Typically, the measurements are used to (indirectly) update the inputs using feedback control schemes. This is a relatively new approach and is best exemplied by the concept of self-optimizing control [4]. Other examples include explicit MPC [5].

The key idea behind self-optimizing control is that near optimal operation can be achieved without the need for re-optimization by using a constant setpoint policy [5]. Application of the concept of self-optimizing control to handle significantly large disturbances may require adapting the control structure. The problem of adapting a control structure to handle significantly large disturbances while maintaining optimality in a certain class of linear, constrained systems is addressed in this contribution. It is shown that the state can be determined completely by monitoring input constraints alone. Adaptation of the control structure, if necessary can be achieved by monitoring input constraints alone, without the need for online optimization. This is demonstrated through examples on a Heat Exchanger Network [6].

References

1. S. Narasimhan and S. Skogestad. Implementation of optimal operation using offline computations. In 8th International Symposium on Dynamics and Control of Process Systems, 2007.

2. J. V. Kadam and W. Marquardt. Sensitivity-based solution updates in closed-loop dynamic optimization. In 7th International Symposium on Dynamics and Control of Process Systems, 2004.

3. D.Q. Mayne, J.B. Rawlings, C.V. Rao and P.O.M. Scokaert. Constrained model predictive control: Stability and optimality. Automatica, 36:789.814, 2000

4. A. Bemporad, M. Morari, V. Dua and E.N. Pistikopoulos. The explicit linear quadratic regulator for constrained systems. Automatica, 38:3.20, 2002b.

5. S. Skogestad. Plantwide control: the search for the self-optimizing control structure. Journal of Process control, 10:487.507, 2000.

6. V. Lersbamrungsuk, S. Narasimhan, S. Skogestad and T. Srinophakun. Control structure design for optimal operation of heat exchanger networks. AIChE Journal, 54:150.162, 2008.