Session: 07-12-01: Optimization, Uncertainty and Probability

Paper Number: 112145

112145 - A Comparative Study of Different Optimization Techniques in Modelling and Predictive Controls 

Model Predictive Control (MPC) is an optimization-based control methodology that explicitly utilizes a dynamic mathematical model of a process to obtain a control signal by minimizing an objective function. MPC algorithm has been formulated based on a quadratic criterion. The quadratic criterion is so popular due to its mathematical and numerical simplicity and efficiently solved using dynamic programming. The general predictive control law is based on the solution of a quadratic cost function with most of the algorithms using this form, formulated as a least-squares problem with weighting factors on the manipulated variable moves. MPC algorithms use the combination of optimization techniques and dynamic models for process control offering the concept of optimal controls. This concept has been expanded to encompass nonlinear optimization and more advanced modeling techniques such as artificial neural network, fuzzy logic and genetic algorithms. Many algorithms are available but among them the most common one is known as dynamic matrix control DMC. The DMC is gained increasing attention during the last decade and is essentially due to the improvements in modeling and identification techniques and digital computers. The DMC technique is based on a step response model of the process. The great diversity of nonlinear systems is the primary reason why there is a big interest in using these approaches with existing industrial controllers such as MPC. Many optimization approaches are implemented in calculating the control moves of MPC algorithm depending on the conditionality of the system matrix and the choice of its cost-function. Newton, Modified Newton, Cauchy, Momentum, Steep, Polak, and Davidon-Fletcher-Powell optimization techniques were used in this comparative study. A nonlinear discrete model was used in simulation to conduct the comparison using the transient response performance parameters: risetime, settling time, and overshoot percentage as comparison indices. The control performances of these optimizers are compared using two systems that are slow and fast reacting. It was found that the optimization strategy that were specifically designed to reduce the system matrix ill-conditionality provided better control performance when compared to other optimization algorithms. The comparison is made on the basis of the conditionality of the system matrix, integral absolute error index (IAE) and closed-loop specifications. The analyses of the results that were obtained considered the structure of the controller and its corresponding tuning strategy. Each optimization algorithm has own distinguishing features that translate into different formulations of dynamic matrix in the cost functions, which may or may not have significant influence on the control performance. The main objective of this paper is to provide the fundamental theory of well-known optimization algorithms.

Presenting Author: Ma'moun Abu-Ayyad Penn State Harrisburg

Presenting Author Biography: Dr. Mamoun Abu-Ayyad received his B.ScE. in Mechanical Engineering from
Al-Mustansiryia University in 1995, his M.ScE. in Mechanical Engineering from Jordan
University of Science and Technology in 1998. He obtained his Ph.D. degree in Mechanical Engineering from the University of New Brunswick/Canada in April 2006. Dr. Abu-Ayyad worked as a Post Doctoral Fellow in the Department of Mechanical Engineering at the University of New Brunswick for two years where he was involved in developing advanced predictive controllers for industrial systems.

Dr. Abu-Ayyad joined the department of mechanical engineering at Penn State Harrisburg as an assistant professor in August 2008. Dr. Abu-Ayyad teaches wide range of courses in the area of applied mechanics such as Machine Dynamics, Advanced Mechanical Design, System Dynamics, Automatic Controls, and Finite Element Analysis for the undergraduate level. Dr. Abu-Ayyad currently is an associate professor and his area of research includes modeling of nonlinear processes, predictive control, optimization and advanced system identification techniques.

Authors:

Ma'moun Abu-Ayyad Penn State Harrisburg
Yash Lad Penn State Harrisburg
Anilchandra Attaluri Penn State Harrisburg