Design of Low Order Controllers for Decoupled MIMO Systems With Time Response Specifications

2018 ◽  
pp. 90-128
Author(s):  
Maher Ben Hariz ◽  
Wassila Chagra ◽  
Faouzi Bouani
Keyword(s):  
Convex Optimization ◽  
Optimization Problem ◽  
Closed Loop ◽  
Mimo Systems ◽  
Design Method ◽  
Optimal Solution ◽  
Time Response ◽  
Convex Optimization Problem ◽  
Tito Systems ◽  
Low Order

The design of a low order controller for decoupled MIMO systems is proposed. The main objective of this controller is to guarantee some closed loop time response performances such as the settling time and the overshoot. The controller parameters are obtained by resolving a non-convex optimization problem. In order to obtain an optimal solution, the use of a global optimization method is suggested. In this chapter, the proposed solution is the GGP method. The principle of this method consists of transforming a non-convex optimization problem to a convex one by some mathematical transformations. So as to accomplish the fixed goal, it is imperative to decouple the coupled MIMO systems. To approve the controllers' design method, the synthesis of fixed low order controller for decoupled TITO systems is presented firstly. Then, this design method is generalized in the case of MIMO systems. Simulation results and a comparison study between the presented approach and a PI controller are given in order to show the efficiency of the proposed controller. It is remarkable that the obtained solution meets the desired closed loop time specifications for each system output. It is also noted that by considering the proposed approach the user can fix the desired closed loop performances for each output independently.

Synthesis of Controllers for MIMO Systems with Time Response Specifications

2014 ◽  
Vol 3 (3) ◽  
pp. 25-52 ◽  
Author(s):  
Maher Ben Hariz ◽  
Wassila Chagra ◽  
Faouzi Bouani
Keyword(s):  
Global Optimization ◽  
Optimization Problem ◽  
Closed Loop ◽  
Controller Design ◽  
Mimo Systems ◽  
Optimal Solution ◽  
Optimization Method ◽  
Time Response ◽  
Step Response ◽  
Global Optimization Method

This paper proposes the design of fixed low order controllers for Multi Input Multi Output (MIMO) decoupled systems. The simplified decoupling is used as a decoupling system technique due to its advantages compared to other decoupling methods. The main objective of the proposed controllers is to satisfy some desired closed loop step response performances such as the settling time and the overshoot. The controller design is formulated as an optimization problem which is non convex and it takes in account the desired closed loop performances. Therefore, classical methods used to solve the non convex optimization problem can generate a local solution and the resulting control law is not optimal. Thus, the thought is to use a global optimization method in order to obtain an optimal solution which will guarantee the desired time response specifications. In this work the Generalized Geometric Programming (GGP) is exploited as a global optimization method. The key idea of this method consists in transforming an optimization problem, initially, non convex to a convex one by some mathematical transformations. Simulation results and a comparison study between the presented approach and a Proportional Integral (PI) controller are given in order to shed light the efficiency of the proposed controllers.

Synthesis and Implementation of a Fixed Low Order Controller on an Electronic System

2016 ◽  
Vol 5 (4) ◽  
pp. 42-63 ◽  
Author(s):  
Maher Ben Hariz ◽  
Faouzi Bouani
Keyword(s):  
Convex Optimization ◽  
Optimization Problem ◽  
Electronic System ◽  
Optimization Method ◽  
Industrial Applications ◽  
Time Response ◽  
Control Law ◽  
Convex Optimization Problem ◽  
Proportional Integral ◽  
Low Order

The development of microelectronic field and software allows researchers to implement some control law in miniaturized devices such as Field Programmable Gate Arrays (FPGA) and microcontroller. These control laws may be used in industrial applications. The key of this work is the design and the implementation of a fixed low order controller on a STM32 microcontroller in order to control an electronic system. The main objective of this controller is to ensure some time response performances as the settling time and the overshoot. The controller parameters are obtained by resolving a non convex optimization problem while considering the desired closed loop specifications. So, the use of a classical optimization method to resolve such kind of problems may lead to a local solution and then the obtained solution is not optimal. Therefore, it is suggested to apply a global optimization method in order to get an optimal control law that can ensure the specified time response performances. The proposed method in this work is the Generalized Geometric Programming (GGP) method. This method consists on transforming, by some mathematical transformations, a non convex optimization problem to a convex one. The implementation of a Proportional Integral (PI) controller, a Proportional Integral Derivate (PID) and a fixed low order controller, on a real electronic system, shows the efficiency of the latter one.

scholarly journals Heliostat Field Layout Optimization with Evolutionary Algorithms

10.29007/7p6t ◽  
2018 ◽  
Author(s):  
Pascal Richter ◽  
David Laukamp ◽  
Levin Gerdes ◽  
Martin Frank ◽  
Erika Ábrahám
Keyword(s):  
Power Plant ◽  
Convex Optimization ◽  
Evolutionary Algorithms ◽  
Convergence Rate ◽  
Evolutionary Algorithm ◽  
Computer Science ◽  
Energy Supply ◽  
Optimization Problem ◽  
Convex Optimization Problem ◽  
New Genotype

The exploitation of solar power for energy supply is of increasing importance. While technical development mainly takes place in the engineering disciplines, computer science offers adequate techniques for optimization. This work addresses the problem of finding an optimal heliostat field arrangement for a solar tower power plant.We propose a solution to this global, non-convex optimization problem by using an evolutionary algorithm. We show that the convergence rate of a conventional evolutionary algorithm is too slow, such that modifications of the recombination and mutation need to be tailored to the problem. This is achieved with a new genotype representation of the individuals.Experimental results show the applicability of our approach.

scholarly journals Reconstruction of the early Universe as a convex optimization problem

2003 ◽  
Vol 346 (2) ◽  
pp. 501-524 ◽  
Author(s):  
Y. Brenier ◽  
U. Frisch ◽  
M. Hénon ◽  
G. Loeper ◽  
S. Matarrese ◽  
...  
Keyword(s):  
Convex Optimization ◽  
Early Universe ◽  
Optimization Problem ◽  
Convex Optimization Problem

scholarly journals Minimizing Power Consumption of an Experimental HVAC System Based on Parallel Grid Searching

Energies ◽  
2020 ◽  
Vol 13 (8) ◽  
pp. 2083 ◽  
Author(s):  
Wangqi Xiong ◽  
Jiandong Wang
Keyword(s):  
Power Consumption ◽  
Graphics Processing Units ◽  
Optimization Problem ◽  
Search Algorithm ◽  
Experimental Studies ◽  
Optimal Solution ◽  
Hvac System ◽  
Convex Optimization Problem ◽  
The One ◽  
Graphics Processing

This paper proposes a parallel grid search algorithm to find an optimal operating point for minimizing the power consumption of an experimental heating, ventilating and air conditioning (HVAC) system. First, a multidimensional, nonlinear and non-convex optimization problem subject to constraints is formulated based on a semi-physical model of the experimental HVAC system. Second, the optimization problem is parallelized based on Graphics Processing Units to simultaneously compute optimization loss functions for different solutions in a searching grid, and to find the optimal solution as the one having the minimum loss function. The proposed algorithm has an advantage that the optimal solution is known with evidence as to the best one subject to current resolutions of the searching grid. Experimental studies are provided to support the proposed algorithm.

scholarly journals Multitarget Linear-Quadratic Control Problem: Semi-Infinite Interval

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
L. Faybusovich ◽  
T. Mouktonglang
Keyword(s):  
Convex Optimization ◽  
Control Problem ◽  
Optimization Problem ◽  
Infinite Interval ◽  
Linear Quadratic Control ◽  
Linear Quadratic ◽  
Convex Optimization Problem ◽  
Simple Convex ◽  
Linear Quadratic Control Problem

We consider multitarget linear-quadratic control problem on semi-infinite interval. We show that the problem can be reduced to a simple convex optimization problem on the simplex.

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