Gilberto Reynoso Meza

Background on Multiobjective Optimization for Controller Tuning

In this chapter a background on multiobjective optimization and a review on multiobjective optimization design procedures within the context of control systems and the controller tuning problem are provided. Focus is given on multiobjective problems where an analysis of the Pareto front is required, in order to select the most preferable design alternative for the control problem at hand.

Controller Tuning for Multivariable Processes

In this chapter, a multivariable controller is tuned by means of a multiobjective optimization design procedure. For this design problem, several specifications are given, regarding individual control loops and overall performance. Due to this fact, a many-objectives optimization problem is stated. In such problems, algorithms could face problems due to the dimensionality of the problem, since their mechanisms to improve convergence and diversity may conflict. Therefore, some guidelines to deal with this optimization process are commented. The aforementioned procedure will be used to tune a multivariable PI controller for the well known Wood and Berry distillation column process using different algorithms.

The 2012 IFAC Control Benchmark: An Industrial Boiler Process

In this chapter, a multiobjective optimization design procedure is applied to the multivariable version of the Boiler Control Problem, defined in 2nd IFAC Conference on Advances in PID Control, 2012. The chapter follows a realistic approach, closer to industrial practices: a nominal linear model will be identified and afterwards a constrained multiobjective problem with 5 design objectives will be stated. Such objectives will deal with overall robust stability, settling time performance and noise sensitivity. After approximating the Pareto Front and performing a multicriteria decision-making stage, the selected control system will be tested using the original nonlinear model.

Motivation: Multiobjective Thinking in Controller Tuning

Throughout this chapter, we intend to provide a multiobjective awareness of the controller tuning problem. Beyond the fact that several objectives and requirements must be fulfilled by a given controller, we will show the advantages of considering this problem in its multiobjective nature. That is, optimizing simultaneously several objectives and following a multiobjective optimization design (MOOD) procedure. Since the MOOD procedure provides the opportunity to obtain a set of solutions to describe the objectives trade-off for a given multiobjective problem (MOP), it is worthwhile to use it for controller tuning applications. Due to the fact that several specifications such as time and frequency requirements need to be fulfilled by the control engineer, a procedure to appreciate the trade-off exchange for complex processes is useful.

Comparing Control Structures from a Multiobjective Perspective

This chapter will illustrate the tools presented in previous chapters for the analysis and comparison of different design concepts. In particular, three different control structures (PI, PID and GPC) will be compared, analysing their benefits and drawbacks within a multiobjective approach. First, a two objective approach, where robustness and disturbance rejection are analyzed, will be developed. Later, a third objective will be added related to setpoint tracking. Since PI design concept has only two parameters to be tuned, the PID design concept will be set with a derivative gain \(K_d\) depending on other controller parameters for a fair comparison. Regarding the Generalized Predictive Controller (GPC) all parameters except prediction horizon and filter parameter will be fixed. Development of the example let the reader know how the tools can help to compare different control structures and how to choose the parameters for the best controller from the point of view of DM within a MOOD approach.

Tools for the Multiobjective Optimization Design Procedure

In this chapter, tools for the evolutionary multiobjective optimization process and the multicriteria decision making stage to be used throughout this book (as a reference) are presented. Regarding the optimization process, three different versions of a multiobjective evolutionary algorithm based on Differential Evolution will be commented; with those proposals, features such as convergence, diversity and pertinency are considered. Regarding the decision making stage, Level Diagrams will be introduced, due to their capabilities to analyze m-dimensional Pareto fronts.

Multiobjective Optimization Design Procedure for an Aircraft’s Flight Control System

In this chapter, the multiobjective optimization design procedure will be used to tune the autopilot controllers for an autonomous Kadett\(\copyright \) aircraft. For this aim, a multivariable PI controller is defined, and a many-objectives optimization instance is tackled using designer preferences. After the multicriteria decision making stage, the selected controller is implemented and evaluated in a real flight test.

Multiobjective Optimization Design Procedure for Controller Tuning of a TRMS Process

In this chapter, the multiobjective optimization design procedure will be used in order to tune the controller of a Twin Rotor MIMO System (TRMS). For such process, a many-objectives optimization instance is tackled using aggregate objective functions. Two different controllers are compared: a decentralized PID structure and a State Space feedback controller.

The ACC’1990 Control Benchmark: A Two-Mass-Spring System

In this chapter, controllers with different complexity for the control benchmark proposed in 1990 at the American Control Conference will be tuned using a multiobjective optimization design procedure. The aim of this chapter is two fold: on the one hand, to evaluate the overall performance of two different controller structures on such a benchmark by means of a design concepts comparison; on the other hand, to state MOP in order to have a more reliable measure of the expected controller’s performance.

The ABB’2008 Control Benchmark: A Flexible Manipulator

In this chapter, a digital controller is tuned for the control benchmark proposed in 2008 by the ABB group at the 17th IFAC World Congress via multiobjective optimization. In some instances, a more realistic evaluation of a controller performance is sought, that is, the expected performance of the controller when it will be implemented. For this benchmark, a digital controller with limited control actions is adjusted in order to control the end effector of a robotic arm.