Multi-Objective Optimization of Tip Tracking Control Using LMI

2005 ◽  
Author(s):  
Bo Xie ◽  
Bin Yao
Keyword(s):  
Tracking Control ◽  
Controller Design ◽  
Robot Manipulator ◽  
System Model ◽  
Linear Matrix ◽  
Flexible Structure ◽  
Flexible Beam ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Lyapunov Matrix

This paper presented multi-objective optimization of tip tracking control for non-collocated flexible beam. The desired trajectory is specified at the tip displacement of the flexible structure, which undergoes translation base motion actuated by a linear motor. The system model is first formulated from modal truncation approach for the flexible structure representing a single Cartesian robot manipulator. The linear system model of the flexible structure always has structural uncertainties. Robust stability and robust performance on tip tracking can be expressed as H2/H∞ norm constraints, which are converted into the Linear Matrix Inequality (LMI). The multi-objective controller design is solved by the convex minimization. In order to reduce the conservatism generated when the same Lyapunov matrix is selected, the Lyapunov matrix is scaled for different norm constraints. Simulation results have demonstrated favorable tip tracking of the proposed robust controller.

Multi-Objective Optimization Model Development to Support Sizing Decisions for a Novel Reciprocating Steam Engine Technology

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
J. M. Hamel ◽  
Devin Allphin ◽  
Joshua Elroy
Keyword(s):  
Computational Model ◽  
Design Optimization ◽  
Kinematic Model ◽  
Operating Conditions ◽  
Steam Engine ◽  
System Model ◽  
System Level ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Crank Angle

A system-level computational model of a recently patented and prototyped novel steam engine technology was developed from first principles for the express purpose of performing design optimization studies for the engine's inventors. The developed system model consists of numerous submodels including a flow model of the intake process, a dynamic model of the intake valve response, a pressure model of the engine cylinder, a kinematic model of the engine piston, and an output model that determines engine performance parameters. A crank-angle discretization strategy was employed to capture the performance of engine throughout a full cycle of operation, thus requiring all engine design submodels to be evaluated at each crank angle of interest. To produce a system model with sufficient computational speed to be useful within optimization algorithms, which must exercise the system level model repeatedly, various simplifying assumptions and modeling approximations were utilized. The model was tested by performing a series of multi-objective design optimization case studies using the geometry and operating conditions of the prototype engine as a baseline. The results produced were determined to properly capture the fundamental behavior of the engine as observed in the operation of the prototype and demonstrated that the design of engine technology could be improved over the baseline using the developed computational model. Furthermore, the results of this study demonstrate the applicability of using a multi-objective optimization-driven approach to conduct conceptual design efforts for various engine system technologies.

Active vibration suppression of flexible structure using a LMI-based control patch

2011 ◽  
Vol 18 (9) ◽  
pp. 1375-1379 ◽  
Author(s):  
Hua Wang ◽  
Xian-Hai Shen ◽  
Liang-Xu Zhang ◽  
Xiao-Jin Zhu
Keyword(s):  
Vibration Suppression ◽  
Controller Design ◽  
Design Procedure ◽  
Linear Feedback ◽  
Linear Matrix ◽  
Flexible Structure ◽  
Active Vibration Suppression ◽  
Structure Simulation ◽  
Active Vibration ◽  
Control Patch

Based on the linear matrix inequality, a linear feedback control is presented to realize active vibration suppression of a class of flexible structure. By introducing an appropriate modal transformation, the controller design procedure can be simplified greatly. A specific Lyapunov function is adopted to induce the asymptotical stability of the flexible structure. Simulation results for flexible spacecraft are provided to illustrate the effectiveness of the proposed scheme.

scholarly journals Observer-Based Decentralized Tracking Control with Preview Action for a Class of Nonlinear Interconnected Systems

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Xiao Yu
Keyword(s):  
Tracking Control ◽  
Controller Design ◽  
Tracking Error ◽  
State Feedback Control ◽  
Control Action ◽  
Linear Matrix ◽  
Reference Trajectory ◽  
Integral Control ◽  
Control Approach ◽  
Output Tracking Control

In this paper, for the first time, the observer-based decentralized output tracking control problem with preview action for a class of interconnected nonlinear systems is converted into a regulation problem for N augmented error subsystems composed of the tracking error dynamics, the difference equation of the state observer, and the available future reference trajectory dynamics associated with each individual subsystem. The developed innovative formulation of an observer-based decentralized preview tracking control scheme consists of the integral control action, the observer-based state feedback control action, and the preview action of the desired trajectory. The controller design feasibility conditions are formulated in terms of a linear matrix inequality (LMI) by using the Lyapunov function approach to ensure the existence of the suggested observer-based decentralized control strategy. Furthermore, both decentralized observer gain matrices and decentralized tracking controller gain matrices can be efficiently and simultaneously computed through a one-step LMI procedure. Stability analysis of the closed-loop augmented subsystem is carried out to illustrate that all tracking errors asymptotically converge toward zero. Finally, a numerical example is provided to demonstrate the effectiveness of the suggested control approach.

Dynamic System Modeling of Flexible Beam System Using Multi-Objective Optimization Differential Evolution Algorithm

2014 ◽  
Vol 695 ◽  
pp. 605-608 ◽  
Author(s):  
Mohd Zakimi Zakaria ◽  
Mohd Sazli Mohd Saad ◽  
Hishamuddin Jamaluddin ◽  
Robiah Ahmad
Keyword(s):  
Mathematical Model ◽  
Differential Evolution ◽  
Dynamic System ◽  
System Modeling ◽  
Differential Evolution Algorithm ◽  
Flexible Beam ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Beam System ◽  
Flexible Beam System

This paper proposes an algorithm called multi-objective optimization using differential evolution (MOODE) for providing the optimal mathematical model of flexible beam system. The main reason of developing a flexible beam system is to find an appropriate controller to control the vibration produced by this system. This dynamic system is treated as a black box where the acquired input-output data is used in the modeling processes. Two objective functions are considered for optimization; minimizing the number of term of a model structure and minimizing the mean square error between actual and predicted outputs. Nonlinear auto-regressive with exogenous input (NARX) model is used to represent the mathematical model of the investigated system. To obtain an optimal model for representing the dynamic behavior of flexible beam system, the model validity tests have been applied.

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