Mathematical control of complex systems

Copyright © 2013 ZidongWang et al.This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

Optimisation of the weighting functions of an H_∞ controller using genetic algorithms and structured genetic algorithms

In this paper the optimisation of the weighting functions for an H<sub>∞</sub> controller using genetic algorithms and structured genetic algorithms is considered. The choice of the weighting functions is one of the key steps in the design of an H<sub>∞</sub> controller. The performance of the controller depends on these weighting functions since poorly chosen weighting functions will provide a poor controller. One approach that can solve this problem is the use of evolutionary techniques to tune the weighting parameters. The paper presents the improved performance of structured genetic algorithms over conventional genetic algorithms and how this technique can assist with the identification of appropriate weighting functions' orders

Genetic programming for the automatic design of controllers for a surface ship

In this paper, the implementation of genetic programming (GP) to design a contoller structure is assessed. GP is used to evolve control strategies that, given the current and desired state of the propulsion and heading dynamics of a supply ship as inputs, generate the command forces required to maneuver the ship. The controllers created using GP are evaluated through computer simulations and real maneuverability tests in a laboratory water basin facility. The robustness of each controller is analyzed through the simulation of environmental disturbances. In addition, GP runs in the presence of disturbances are carried out so that the different controllers obtained can be compared. The particular vessel used in this paper is a scale model of a supply ship called CyberShip II. The results obtained illustrate the benefits of using GP for the automatic design of propulsion and navigation controllers for surface ships

Evolutionary multi-objective optimisation with preferences for multivariable PI controller tuning

Multi-objective optimisation design procedures have shown to be a valuable tool for control engineers. They enable the designer having a close embedment of the tuning process for a wide variety of applica- tions. In such procedures, evolutionary multi-objective optimisation has been extensively used for PI and PID controller tuning; one reason for this is due to their flexibility to include mechanisms in order to en- hance convergence and diversity. Although its usability, when dealing with multi-variable processes, the resulting Pareto front approximation might not be useful, due to the number of design objectives stated. That is, a vast region of the objective space might be impractical or useless a priori, due to the strong degradation in some of the design objectives. In this paper preference handling techniques are incorpo- rated into the optimisation process, seeking to improve the pertinency of the approximated Pareto front for multi-variable PI controller tuning. That is, the inclusion of preferences into the optimisation process, in order to seek actively for a pertinent Pareto front approximation. With such approach, it is possible to tune a multi-variable PI controller, fulfilling several design objectives, using previous knowledge from the designer on the expected trade-off performance. This is validated with a well-known benchmark exam- ple in multi-variable control. Control tests show the usefulness of the proposed approach when compared with other tuning techniques.This work was partially supported by the fellowship BJT-304804/2014-2 from the National Council of Scientific and Technologic Development of Brazil (CNPq) and by EVO-CONTROL project (ref. PROMETEO/2012/028, Generalitat Valenciana - Spain).Reynoso Meza, G.; Sanchís Saez, J.; Blasco, X.; Freire, RZ. (2016). Evolutionary multi-objective optimisation with preferences for multivariable PI controller tuning. Expert Systems with Applications. 51:120-133. doi:10.1016/j.eswa.2015.11.028S1201335

Multiobjective H_2/H_∞-optimal control via finite dimensional Q-parametrization and linear matrix inequalities

The problem of multiobjective H_2/H_∞ optimal controller design is reviewed. There is as yet no exact solution to this problem. We present a method based on that proposed by Scherer (1995). The problem is formulated as a convex semidefinite program (SDP) using the LMI formulation of the H_2 and H_∞ norms. Suboptimal solutions are computed using finite dimensional Q-parametrization. The objective value of the suboptimal Q's converges to the true optimum as the dimension of and is increased. State space representations are presented which are the analog of those given by Khargonekar and Rotea (1991) for the H_2 case. A simple example computed using finite impulse response Qs is presented

Multiobjective control : an overview

An overview of a number of approaches to the multiobjective control problem is given. In practice, this problem usually boils down to a mixed-norm optimization, where traditionally the norms of interest are H2, H8 and l1. To capture different, often conflicting, design specifications a single-norm form is usually not enough and therefore a mixed-norm formalism combining these norms would be of considerable interest. Although it would be nice to have all three norms present, most approaches focus on the two-norm problem. Frequently encountered is the H2/H8 mixed-norm optimization problem, but combinations of l1 and the other two norms are starting to get more attention. It will be seen that the solution to the mixed-norm optimization problem has not yet reached a final shape, since most methods still exhibit problems, like not being able to find a solution if performance specifications are tight, or generating high-order or too conservative controllers, et

Performance-based control system design automation via evolutionary computing

This paper develops an evolutionary algorithm (EA) based methodology for computer-aided control system design (CACSD) automation in both the time and frequency domains under performance satisfactions. The approach is automated by efficient evolution from plant step response data, bypassing the system identification or linearization stage as required by conventional designs. Intelligently guided by the evolutionary optimization, control engineers are able to obtain a near-optimal ‘‘off-thecomputer’’ controller by feeding the developed CACSD system with plant I/O data and customer specifications without the need of a differentiable performance index. A speedup of near-linear pipelineability is also observed for the EA parallelism implemented on a network of transputers of Parsytec SuperCluster. Validation results against linear and nonlinear physical plants are convincing, with good closed-loop performance and robustness in the presence of practical constraints and perturbations

Controller tuning by means of multi-objective optimization algorithms: a global tuning framework

© 2013 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.A holistic multi-objective optimization design technique for controller tuning is presented. This approach gives control engineers greater flexibility to select a controller that matches their specifications. Furthermore, for a given controller it is simple to analyze the tradeoff achieved between conflicting objectives. By using the multi-objective design technique it is also possible to perform a global comparison between different control strategies in a simple and robust way. This approach thereby enables an analysis to be made of whether a preference for a certain control technique is justified. This proposal is evaluated and validated in a nonlinear multiple-input multiple-output system using two control strategies: a classical proportional- integral-derivative control scheme and a feedback state controller.This work was supported in part by the FPI-2010/19 Grant and the Project PAID-06-11 from the Universitat Politecnica de Valencia and in part by the Projects DPI2008-02133, TIN2011-28082, and ENE2011-25900 from the Spanish Ministry of Science and Innovation.Reynoso Meza, G.; García-Nieto Rodríguez, S.; Sanchís Saez, J.; Blasco, X. (2013). Controller tuning by means of multi-objective optimization algorithms: a global tuning framework. IEEE Transactions on Control Systems Technology. 21(2):445-458. https://doi.org/10.1109/TCST.2012.2185698S44545821

[[alternative]]Strong Stabilization and Stable Hinfinity Controller Design

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