Stabilization of Mechanical Systems with Backlash by PI Loop Shaping

2016 ◽  
Vol 5 (3) ◽  
pp. 21-46 ◽  
Author(s):  
Ahmad Taher Azar ◽  
Fernando E. Serrano
Keyword(s):  
Control Design ◽  
Theoretical Background ◽  
System Behavior ◽  
Describing Function ◽  
Pendulum System ◽  
Loop Shaping ◽  
Control Gain ◽  
Different Types ◽  
Electrical Motors ◽  
Frequency Domain Approach

Backlash is one of several discontinuities found in different kinds of systems, it can be found in actuators of different types, such as mechanical and hydraulic, giving way to unwanted effects in the system behavior. PI loop shaping control design implementing a describing function to find the limit cycle oscillations and the appropriate control gain is developed. Therefore a frequency domain approach is implemented for the control of nonlinear system of any kind such as robotics, mechatronics, other kind of mechanisms, electrical motors etc. Finally, in order to corroborate the theoretical background explained in this article, the stabilization of a cart-pendulum system with the proposed control strategy is shown.

Proportional Integral Loop Shaping Control Design With Particle Swarm Optimization Tuning

2018 ◽  
pp. 24-57 ◽  
Author(s):  
Ahmad Taher Azar ◽  
Fernando E. Serrano ◽  
Sundarapandian Vaidyanathan
Keyword(s):  
Particle Swarm Optimization ◽  
Particle Swarm ◽  
Control Design ◽  
Theoretical Background ◽  
Swarm Optimization ◽  
Proportional Integral ◽  
Loop Shaping ◽  
Control Gain ◽  
Electrical Motors ◽  
Frequency Domain Approach

Backlash is one of several discontinuities found in different kinds of systems. It can be found in actuators of different types, such as mechanical and hydraulic, giving way to unwanted effects in the system behavior. Proportional integral (PI) loop shaping control design implementing a describing function to find the limit cycle oscillations and the appropriate control gain selection by particle swarm optimization is developed. Therefore, a frequency domain approach is implemented for the control of nonlinear system of any kind such as robotics, mechatronics, and other kind of mechanisms, electrical motors, etc. Finally, in order to corroborate the theoretical background explained in this chapter, the stabilization of a cart-pendulum system with the proposed control strategy is shown.

Stabilization and Control of Mechanical Systems with Backlash

2015 ◽  
pp. 1-60 ◽  
Author(s):  
Ahmad Taher Azar ◽  
Fernando E. Serrano
Keyword(s):  
Optimal Control ◽  
Mechanical Systems ◽  
Control Design ◽  
Optimal Controller ◽  
Joint Control ◽  
System Behavior ◽  
Describing Function ◽  
Control Approach ◽  
Control Gain ◽  
And Control

Backlash is one of several discontinuities found in different kinds of systems; it can be found in actuators of different types, such as mechanical and hydraulic, giving way to unwanted effects in the system behavior. In this chapter, three different control approaches are derived to stabilize mechanical systems in which this phenomenon is present in the actuators of the system. First, an independent joint control approach when backlash is found in the actuators is derived; then a PI loop shaping control design implementing a describing function to find the limit cycle oscillations and the appropriate control gain is developed. Finally, an optimal controller for mechanical systems with backlash is derived, obtaining the optimal control law and oscillations frequency when this nonlinearity is found implementing a describing function to model the backlash effects.

scholarly journals Neural feedback linearization adaptive control for affine nonlinear systems based on neural network estimator

2011 ◽  
Vol 8 (3) ◽  
pp. 307-323 ◽  
Author(s):  
Mohamed Bahita ◽  
Khaled Belarbi
Keyword(s):  
Neural Network ◽  
Nonlinear Systems ◽  
Feedback Linearization ◽  
Pendulum System ◽  
Rbf Network ◽  
Inverted Pendulum System ◽  
Neural Network Controller ◽  
Control Gain ◽  
On Line ◽  
Neural Feedback

In this work, we introduce an adaptive neural network controller for a class of nonlinear systems. The approach uses two Radial Basis Functions, RBF networks. The first RBF network is used to approximate the ideal control law which cannot be implemented since the dynamics of the system are unknown. The second RBF network is used for on-line estimating the control gain which is a nonlinear and unknown function of the states. The updating laws for the combined estimator and controller are derived through Lyapunov analysis. Asymptotic stability is established with the tracking errors converging to a neighborhood of the origin. Finally, the proposed method is applied to control and stabilize the inverted pendulum system.

scholarly journals Large-Scale Systems Control Design via LMI Optimization

2015 ◽  
Vol 44 (3) ◽  
pp. 247-253
Author(s):  
Branislav Rehak
Keyword(s):  
Decentralized Control ◽  
Large Scale ◽  
Expert Knowledge ◽  
Control Design ◽  
Large Scale Systems ◽  
Large Scale System ◽  
Lmi Optimization ◽  
Control Gain ◽  
Systems Control

A control design for a large-scale system using LMI optimization is proposed. The control is designed in a way such that the LQ cost in the case of the decentralized control  does not exceed a certain limit. The optimized quantity are the values of the control gain matrices. The methodology is useful even for finding a decomposition of the system, however, some expert knowledge is necessary in this case. The capabilities of the algorithm are illustrated by two examples.DOI: http://dx.doi.org/10.5755/j01.itc.44.3.6464

Comparison of Linear and Non-Linear Gas Turbine Performance Diagnostics

2003 ◽  
Author(s):  
Ph. Kamboukos ◽  
K. Mathioudakis
Keyword(s):  
Gas Turbine ◽  
Condition Monitoring ◽  
Theoretical Background ◽  
Diagnostic Methods ◽  
Turbine Performance ◽  
Different Types ◽  
Non Linear ◽  
Computational Procedures ◽  
Monitoring And Diagnostics ◽  
Performance Diagnostics

The features of linear performance diagnostic methods are discussed, in comparison to methods based on full non-linear calculation of performance deviations, for the purpose of condition monitoring and diagnostics. First, the theoretical background of linear methods is overviewed to establish a relationship to the principles used by non-linear methods. Then computational procedures are discussed and compared. The effectiveness of determining component performance deviations by the two types of approaches is examined, on different types of diagnostic situations. A way of establishing criteria to define whether non-linear methods have to be employed is presented. An overall assessment of merits or weaknesses of the two types of methods is attempted, based on the results presented in the paper.

scholarly journals A brief compendium of water entry results derived from laboratory tests of various types of wall assemblies

2019 ◽  
Vol 282 ◽  
pp. 02050
Author(s):  
Michael A. Lacasse ◽  
Nathan Van Den Bossche ◽  
Stephanie Van Linden ◽  
Travis V. Moore
Keyword(s):  
Numerical Simulation ◽  
Performance Evaluation ◽  
Laboratory Tests ◽  
Moisture Transfer ◽  
Control Design ◽  
Water Entry ◽  
Building Envelope ◽  
Test Results ◽  
Different Types ◽  
Wood Frame

There is an increase in the use of hygrothermal models to complete the performance evaluation of walls assemblies, either in respect to design of new assembles or the retrofit of existing wall assemblies. To this end there are guides available in which is provided information on moisture loads to wall assemblies. This includes, for example, Criteria for Moisture-Control Design Analysis in Buildings given in ASHRAE 160, Assessment of moisture transfer by numerical simulation provided in EN 15026, and NRC’s “Guidelines for Design for Durability of the Building Envelope”. The designer of a new assembly or evaluator of an existing wall is tasked with having to determine what moisture loads to apply to the wall and where to apply this load within the assembly. Typically there is little or no information that is readily available regarding moisture loads to walls and thus the suggested hourly moisture load, as given in ASHRAE 160, is 1% by weight of the total driving rain load to the wall (i.e. kg/m2-hr). In this paper, a brief compendium of water entry test results derived from laboratory tests of various types of wall assemblies is provided from which estimates of moisture loads to different types of wall can be developed. Water entry test results are given of wood frame walls typically used in housing, but also metal-glass curtain walls and other commercial wall assemblies, where possible, in terms of driving loads to the wall.

scholarly journals Multiple Bifurcations of a Cylindrical Dynamical System

2016 ◽  
Vol 46 (1) ◽  
pp. 33-52
Author(s):  
Ning Han ◽  
Qingjie Cao
Keyword(s):  
Dynamical System ◽  
Limit Cycles ◽  
Homoclinic Orbits ◽  
Complex Dynamic ◽  
Pendulum System ◽  
Sd Oscillator ◽  
Bistable State ◽  
Different Types ◽  
Coupling Dynamics ◽  
Dynamic Bifurcation

Abstract This paper focuses on multiple bifurcations of a cylindrical dynamical system, which is evolved from a rotating pendulum with SD oscillator. The rotating pendulum system exhibits the coupling dynamics property of the bistable state and conventional pendulum with the ho- moclinic orbits of the first and second type. A double Andronov-Hopf bifurcation, two saddle-node bifurcations of periodic orbits and a pair of homoclinic bifurcations are detected by using analytical analysis and nu- merical calculation. It is found that the homoclinic orbits of the second type can bifurcate into a pair of rotational limit cycles, coexisting with the oscillating limit cycle. Additionally, the results obtained herein, are helpful to explore different types of limit cycles and the complex dynamic bifurcation of cylindrical dynamical system.

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