Geometric programming based robot control design

Jha, Nand K.

doi:10.1016/0360-8352(95)00146-r

Cited by 14 publications

(3 citation statements)

References 5 publications

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“…GGP problems are appeared in engineering design, management and chemical process industry (Nand, 1995;Choi & Dennis, 1996;Maranas & Floudas, 1997;Pörn et al, 2008;Tsai, 2009;Kheriji et al, 2011a, Ben Hariz et al, 2013.The particular feature of this method that it is dedicated to solve a class of non convex non linear programming problems with the objective function and the constraints are in polynomial forms. The mathematical formulation of a GGP problem with free variables is expressed as follows (Tsai et al, 2007):…”

Section: Mathematical Formulation Of the Ggp Methodsmentioning

confidence: 99%

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

Hariz

Bouani

2016

International Journal of System Dynamics Applications

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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.

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Section: Mathematical Formulation Of the Ggp Methodsmentioning

confidence: 99%

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

Hariz

Bouani

2016

International Journal of System Dynamics Applications

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“…GGP problems are commonly used in engineering design, management and chemical process industry (see e.g. Nand, 1995;Chul & Dennis, 1996;Maranas & Floudas, 1997;Porn, Bjork & Westerlund, 2008;Tsai, 2009;Kheriji, Bouani & Ksouri, 2011). The distinctive peculiarity of this method is that it is dedicated to solve a class of non convex non-linear programming problems with the objective function and constraints are in polynomial forms.…”

Section: Generalized Geometric Programming Methods Mathematical Formu...mentioning

confidence: 99%

Synthesis of Controllers for MIMO Systems with Time Response Specifications

Hariz

Chagra

Bouani

2014

International Journal of System Dynamics Applications

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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.

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“…As noted by [1,2], many nonlinear programming problems may be restated as geometric programming with little additional effort by simple techniques such as change of variables or by straightforward algebraic manipulation of terms. Additionally, (SGP) problem has found a wide range of applications in production planning, location, distribution contexts in risk management problems, various chemical process design and engineering design situations, and so on [3][4][5][6][7][8][9][10]. Hence, it is necessary to present good algorithms for solving (SGP).…”

Section: Introductionmentioning

confidence: 99%

A Global Optimization Algorithm for Signomial Geometric Programming Problem

Hou

Shen

Chen

2014

Abstract and Applied Analysis

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This paper presents a global optimization algorithm for solving the signomial geometric programming (SGP) problem. In the algorithm, by the straight forward algebraic manipulation of terms and by utilizing a transformation of variables, the initial nonconvex programming problem (SGP) is first converted into an equivalent monotonic optimization problem and then is reduced to a sequence of linear programming problems, based on the linearizing technique. To improve the computational efficiency of the algorithm, two range reduction operations are combined in the branch and bound procedure. The proposed algorithm is convergent to the global minimum of the (SGP) by means of the subsequent solutions of a series of relaxation linear programming problems. And finally, the numerical results are reported to vindicate the feasibility and effectiveness of the proposed method.

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Geometric programming based robot control design

Cited by 14 publications

References 5 publications

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

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

Synthesis of Controllers for MIMO Systems with Time Response Specifications

A Global Optimization Algorithm for Signomial Geometric Programming Problem

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