(568r) Compromise Optimization Tuning Strategy for Model Predictive Controllers

Model predictive controllers (MPC) are widely used in a variety of industries, and, in particular, in petrochemical and oil processing plants. The underlying ideas behind MPC formulations are: (i) using a model representation to predict the behavior of the outputs of a system and (ii) solving the control optimization problem at each sampling time to calculate optimum control moves. The MPC used here operates with an incremental state-space model to avoid output tracking offset. The control cost function incorporates two weighted sum terms; the first one considers the deviations between predicted output values and output setpoints over an infinite predictive horizon, weighted by a diagonal, positive matrix Qy , and the second one considers the control actions over the control horizon, m, weighted by a diagonal, positive-definite matrix R. The infinite horizon approach is used to ensure that the system achieves asymptotic stability in nominal scenarios, i.e. when the â??real plantâ?? model and the controller model are the same. The infinite summation term is addressed using a Lyapunov equation approach.
Parameters m, Qy , and R directly affect control performance. m is an integer variable and its value affects the controller in the following manner: small values leads to stable but conservative control actions while large values decrease robustness and increase aggressiveness. Choosing m between 3 and 5 is a successful rule-of-thumb in control literature. In this work, we will focus on obtaining optimum values for parameters Qy and R, to ensure that controller performance fulfills one or more desired characteristics.
Optimization problems with more than one objective are categorized as multiobjective optimization problems. It is usual to encounter conflicting objectives and a set of optimum solutions, named Pareto set, in which it is impossible to improve one objective without deteriorating another. In such scenarios, the Utopia solution is defined as the vector of individually calculated optimum objectives.
In the tuning strategy developed here, tuning goals are defined in terms of the sum of squared errors between the closed-loop system outputs and reference trajectories over a tuning horizon. Reference trajectories are defined either in terms of arbitrary desired closed-loop output performance or in terms of open-loop transfer function step
responses. The tuning decision vector is comprised of Qy
and R, along with slack
variables weighting matrices originated from the infinite horizon control formulation.
Once all goals are defined, we proceed by calculating the Utopia solution and subsequently minimizing the Euclidian distance between it the feasible solutions. The solution of the latter problem gives the optimum set of tuning parameters.
The tuning technique was successfully applied to an IHMPC running on a C3/C4 splitter model with 3 inputs and 3 outputs. We compare control performance to a similar multiobjective tuning technique from the literature. The major advantages of the strategy described here over the latter are that (i) our technique does not require the calculation of the whole Pareto set and (ii) the compromise solution does not require further decision-maker input in order to choose an arbitrary optimum solution within the Pareto set.