IQC analysis of constrained MPC of large-scale systems

Technological advances have led to the widespread use of more complex systems in both industrial and academic practice. Model predictive control (MPC) is a strong and widely used control methodology. MPC has been first applied to the chemical process industries and now it is also used in microelectronics. The advantage of MPC is that it can exploit a model of the process and, using the concept of moving horizons, it can find the optimum path for the manipulated variables. However, it is not straightforward or even computationally
feasible to use MPC for distributed parameter systems consisting of systems of
Partial Differential Equations (PDEs). This work exploits the dissipative nature that many engineering systems exhibit, for model order reduction (MOR) purposes. Dissipativity is expressed as separation of eigenvalues in the spectrum of the linearized system and therefore separation of modes into slow and fast ones. These types of problems contain uncertainties that affect the controller’s stability. The stability and robustness of predictive control can be analyzed using the theory of integral quadratic constraints (IQCs). In this work we employ successive linearization off-line, constructing a model pool that consists
of reduced size linear models. A dissipation inequality is then used to compute an upper bound for the input/output gain when MPC is employed, exploiting the IQCs to consider the uncertainties of the closed loop system. The effectiveness of the proposed method is demonstrated through two chemical engineering case studies.