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.

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.

Preferences, Utility Function, and Control Design of Complex Cultivation Process

2013 ◽  
pp. 174-198
Keyword(s):  
Optimal Control ◽  
Utility Function ◽  
Kinetic Models ◽  
Control Design ◽  
Monod Kinetics ◽  
Cultivation Process ◽  
Monod Kinetic ◽  
And Control

In the control design are overcome restrictions connected with the observability of the Monod kinetics and with the singularities of the optimal control of Monod kinetic models.

Optimal Control Design of a Bimorph Optical Beam Deflector

2001 ◽  
Author(s):  
Chang-Po Chao ◽  
Jeng-Sheng Huang ◽  
Ching-Lung Ou Yung ◽  
Rong-Fong Fung
Keyword(s):  
Optimal Control ◽  
Position Control ◽  
Angular Position ◽  
Control Design ◽  
Element Model ◽  
Optical Beam ◽  
Optimal Feedback Control ◽  
Central Position ◽  
Control Effort ◽  
And Control

Abstract The optical beam deflector is composed of two piezoelectric layers, one sandwiched brass layer in the middle with both ends clamped and a mirror attached to the upper surface of the top piezoelectric layer in the central position. This structure is designed to deflect the mirror to a certain angular position by applying external voltage supply to piezo-layers. This study proposes an optimal angular position control scheme of the attached mirror. The governing partial differential equations are first derived for the ensuing analysis and control design, which is followed by the establishment of finite element model in ten nodes specified at some longitudinal points of the optical beam deflector. In order to achieve a faster convergent rate for the deflector to reach the desired angular position, the optimal control of LQ regulator with final states fixed is employed to explore the possibility of shorter transient response and less cost of control effort and states. The optimal feedback control is obtained based on solving a dynamic Riccati equation backward in time. The numerical simulation results are finally provided to validate the theoretical control design.

Strongly consistent estimation in a controlled Markov renewal model

1982 ◽  
Vol 19 (03) ◽  
pp. 532-545 ◽  
Author(s):  
Michael Kolonko
Keyword(s):  
Optimal Control ◽  
Dynamic Models ◽  
Consistent Estimation ◽  
Unknown Parameters ◽  
Control Approach ◽  
Renewal Model ◽  
Countable State ◽  
Estimation And Control ◽  
And Control ◽  
Strongly Consistent

The optimal control of dynamic models which are not completely known to the controller often requires some kind of estimation of the unknown parameters. We present conditions under which a minimum contrast estimator will be strongly consistent independently of the control used. This kind of estimator is appropriate for the adaptive or ‘estimation and control' approach in dynamic programming under uncertainty. We consider a countable-state Markov renewal model and we impose bounding and recurrence conditions of the so-called Liapunov type.

A near-optimal decentralized control approach for polynomial nonlinear interconnected systems

2020 ◽  
pp. 014233122097743
Author(s):  
Mohamed Sadok Attia ◽  
Mohamed Karim Bouafoura ◽  
Naceur Benhadj Braiek
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Open Loop ◽  
System Stability ◽  
Gronwall Lemma ◽  
Interconnected System ◽  
Control Approach ◽  
State Dependent ◽  
And Control

This article tackles the decentralized near-optimal control problem for the class of nonlinear polynomial interconnected system based on a shifted Legendre polynomials direct approach. The proposed method converts the interconnected optimal control problems into a nonlinear programming one with multiple constraints. In light of the formulated NLP optimization, state and control coefficients are used to design a nonlinear decentralized state feedback controller. Overall closed-loop system stability sufficient conditions are investigated with the help of Grönwall lemma. The triple inverted pendulum case is considered for simulation. Satisfactory results are obtained in both open-loop and closed-loop schemes with comparison to collocation and state-dependent Riccati equation techniques.

Global inverse optimal exponential path-tracking control of mobile robots driven by Lévy processes

Robotica ◽  
2021 ◽  
pp. 1-27
Author(s):  
K. D. Do
Keyword(s):  
Optimal Control ◽  
Mobile Robots ◽  
Tracking Control ◽  
Lévy Processes ◽  
Control Design ◽  
Levy Processes ◽  
Path Tracking ◽  
Tracking Errors ◽  
Hamilton Jacobi Bellman ◽  
And Control

Abstract This paper formulates and solves a new problem of global practical inverse optimal exponential path-tracking control of mobile robots driven by Lévy processes with unknown characteristics. The control design is based on a new inverse optimal control design for nonlinear systems driven by Lévy processes and ensures global practical exponential stability almost surely and in the pth moment for the path-tracking errors. Moreover, it minimizes cost function that penalizes tracking errors and control torques without having to solve a Hamilton–Jacobi–Bellman or Hamilton–Jaccobi–Isaacs equation.

Sign in / Sign up

Export Citation Format

Share Document