Hasmet Genceli

Brief Paper: Simultaneous Constrained Model Predictive Control and Identification of DARX Processes

In this paper, a procedure for the recursive approximation of the feasible parameter set of a linear model with a set membership uncertainty description is provided. Approximating regions of parallelotopic shape are considered. The new contribution of this paper consists in devising a general procedure allowing for block processing of q > 1 measurements at each recursion step. Based on this, several approximation strategies for polytopes are presented. Simulation experiments are performed, showing the effectiveness of the algorithm as compared to the original algorithm processing one measurement at each step.In this work, we formulate a new approach to simultaneous constrained model predictive control and identification (MPCI). The proposed approach relies on the development of a persistent excitation (PE) criterion for processes described by DARX models. That PE criterion is used as an additional constraint in the standard on-line optimization of MPC. The resulting on-line optimization problem of MPCI is handled by successively solving a series of semi-definite programming problems. Advantages of MPCI in comparison to other closed-loop identification methods are (a) Constraints on process inputs and outputs are handled explicitly, (b) Deterioration of output regulation is kept to a minimum, while closed-loop identification is performed. The applicability of the method is illustrated by a number of simulation studies. Theoretical and computational issues for further investigation are suggested.

Effect of on-line optimization techniques on model predictive control and identification (MPCI)

Model predictive control and identification (MPCI) is an adaptive MPC scheme that employs the persistent excitation condition to generate non-convex constraints on process inputs, in addition to conventional constraints of on-line optimization of MPC. This results in a non-convex problem, which has to be solved at each time instant k. In this work we rigorously show that a locally optimal solution of the above problem can be obtained by the successive semidefinite programming algorithm. We then develop a deterministic branch-and-bound approach, to obtain the global minimum of the MPCI optimization problem. Simulation results are presented to demonstrate the applicability of the proposed MPCI algorithms to small-scale systems.

Constrained model predictive control with simultaneous identification using wavelets

Abstract Model Predictive Control (MPC) often requires that a new process model be developed from data collected while the process remains under feedback control. How can a good model be obtained for a process under constrained MPC, without excessive perturbation of the process? We propose a novel approach, model predictive control and identification (MPCI), that relies on augmenting the standard on-line MPC optimization with a series of persistent excitation (PE) constraints that current and future process inputs must satisfy over a finite horizon. For linear processes, the resulting on-line optimization problem is solved by solving a series of semi-definite programming (SP) problems, for which efficient numerical methods with guaranteed convergence exist. The addition of the PE constraint to standard MPC paves the way for a number of different MPCI variants. A variant of MPCI involving time-frequency process identification with wavelets is proposed in the paper.

Analysis and Synthesis Methods for Robust Model Predictive Control

In this article we present a summary of our latest work on analysis and synthesis methods for robust constrained model predictive controllers. Processes modeled by multivariable linear time-invariant models as well as second-order Volterra series models are considered. Modeling uncertainty is characterized as upper and lower bounds on model parameters. Sufficient conditions for robust closed-loop stability with zero offset are presented for the kinds of processes mentioned above. In addition, robust performance bounds are discussed. Based on the robust stability and performance results, a tuning methodology for robust constrained model predictive control is developed. That methodology is elucidated through examples of linear and nonlinear model predictive control of a number of chemical processes.

Rigorous design of robust predictive controllers for processes with more inputs than outputs

Abstract In this paper we present a design methodology for multivariable Quadratic Dynamic Matrix Control (QDMC) systems with more manipulated variables than outputs. The algorithm requires the utilization of an end-condition and calculates low bounds on the move suppression coefficients in the on-line objective function. We show that these bounds are the solutions of an off-line constrained nonlinear minimization problem. The technique guarantees the robust stability of the closed-loop system, when both input and output constraints are present. The success of the method is illustrated through the application to an industrial case.

A New Approach to Model Predictive Control and Identification

Abstract We propose a novel approach to constrained model predictive control and identification (MPCI). This approach relies on augmenting the standard MPC on-line optimization with a persistent excitation constraint that current and future process inputs must satisfy over a finite moving horizon. For linear processes, the resulting online problem is transformed to a series of semi-definite (SP) programming problems, for which efficient numerical methods with guaranteed convergence can be used on-line. The effectiveness of the proposed new methodology is illustrated through simulations.