Sliding Mode Control and Elastic Mode Stabilization of a Robotic Arm With Flexible Links

1991 ◽  
Vol 113 (4) ◽  
pp. 669-676 ◽  
Author(s):  
P. J. Nathan ◽  
S. N. Singh
Keyword(s):  
Closed Loop ◽  
Joint Angle ◽  
Sliding Mode ◽  
Variable Structure ◽  
Terminal State ◽  
Loop System ◽  
Robotic Arm ◽  
Closed Loop System ◽  
Elastic Mode ◽  
Mode Stabilization

This paper treats the question of control of an elastic robotic arm of two links based on variable structure system (VSS) theory and pole assignment technique for stabilization. A discontinuous joint angle control law, based on VSS theory, is designed which accomplishes asymptotic decoupled joint angle trajectory tracking. In the closed-loop system, the trajectories are attracted toward a chosen hypersurface in the state space and then slide along it. Although, joint angles are controlled using variable structure control (VSC) law, the flexible modes of the links are excited. Using center manifold theory, it is shown that the closed-loop system, including the sliding mode controller, is stable. Based on a linearized model about the terminal state, a stabilizer is designed using pole assignment technique to control the elastic oscillations of the links. A control logic is included which switches the stabilizer at the instant when the joint angle trajectory enters a specified neighborhood of the terminal state. Simulation results are presented to show that in the closed-loop system, accurate joint angle trajectory tracking, and elastic mode stabilization are accomplished in the presence of payload uncertainty.

scholarly journals Adaptive Robust Quadratic Stabilization Tracking Control for Robotic System with Uncertainties and External Disturbances

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Jinzhu Peng ◽  
Yan Liu
Keyword(s):  
Closed Loop ◽  
Robot Manipulator ◽  
Variable Structure ◽  
Robotic System ◽  
Loop System ◽  
Closed Loop System ◽  
Hybrid Scheme ◽  
External Disturbances ◽  
Control Approach ◽  
Quadratic Stabilization

An adaptive robust quadratic stabilization tracking controller with hybrid scheme is proposed for robotic system with uncertainties and external disturbances. The hybrid scheme combines computed torque controller (CTC) with an adaptive robust compensator, in which variable structure control (VSC) andH∞optimal control approaches are adopted. The uncertain robot manipulator is mainly controlled by CTC, the VSC is used to eliminate the effect of the uncertainties and ensure global stability, andH∞approach is designed to achieve a certain tracking performance of closed-loop system. A quadratic stability approach, which allows separate treatment of parametric uncertainties, is used to reduce the conservatism of the conventional robust control approach. It can be also guaranteed that all signals in closed-loop system are bounded. The validity of the proposed control scheme is shown by computer simulation of a two-link robotic manipulator.

scholarly journals Efficient and Novel voltage control method using DC-DC Cuk Converter under Load Variation

2019 ◽  
Vol 3 (2) ◽  
Author(s):  
Syed Mujtaba Mahdi Mudassir ◽  
Faheem Ahmed Khan ◽  
Shaziya Sultana
Keyword(s):  
Control System ◽  
Closed Loop ◽  
Sliding Mode ◽  
Loop System ◽  
Control Mode ◽  
System Response ◽  
Switching Function ◽  
Sliding Modes ◽  
Closed Loop System ◽  
Cuk Converter

A control system is a set of mechanical or electronic devices that regulates other devices or systems by way of control loops. Typically, control systems are computerized. The mode of operation in a Control System where controlling variables is a function of the system and the structure is changed knowingly according to set of rules, which are already declared: for example a sensor based  system, is called as sliding control mode where the feedback control system response is limited and revolves around surface in the space to a point of equilibrium. In this mode of schemes, a switching variable dictates which form of control is to be used at a given instant, depending on the position of the state from the surface. First a set of points for which the switching function is null is used called as sliding surface. Sliding Mode Control (SMC) is a very robust technique which can handle sudden and large changes in dynamics of the system which can be applied to many areas like controlling of motor, aircraft and spacecraft, process control and power systems. SMC is one of the best tool in the industry to design controllers for the systems which has variable values, and provides robust properties against matched uncertainties, However,this use of SMC can only be achieved after the occurrence of the sliding mode. Before the occurrence of the switching function as null i.e. during the reaching phase, the system is affected by even matched ones. Several first order SMC applications for linear and nonlinear systems can be found in the literature [1]. Hence to eliminate the reaching phase and to make sure the ruggedness of the system throughout the entire closed-loop system response Integral Sliding Modes are used. In this paper a design procedure for sliding mode controllers for better control of voltage is applied, and then the ideas implemented are extended to all integral sliding modes in order to ensure optimum operation of entire system response[2]. Necessary conditions for the existence of sliding modes are also given. The closed-loop system is also proved to be exponentially stable. Simulation and experimental tests using the prototype of controlled DC-DC  CUK converter were performed to validate the proposed control approach.

Multi Observer-Based Sliding Mode Load Frequency Control With Input Delay Estimation

2021 ◽  
Vol 1 (4) ◽  
Author(s):  
Ark Dev ◽  
David Fernando Novella Rodríguez ◽  
Sumant Anand ◽  
Mrinal Kanti Sarkar
Keyword(s):  
Power Systems ◽  
Closed Loop ◽  
Sliding Mode ◽  
Time Delay Estimation ◽  
Loop System ◽  
Load Frequency Control ◽  
System Stability ◽  
Input Delay ◽  
Delay Estimation ◽  
Closed Loop System

Abstract The letter proposes frequency stability in power systems with input delay. A closed loop system can be oscillatory or even unstable without the exact knowledge of delay. Therefore, it is desirable to design a control scheme which is based on the estimation of unknown delay. The proposed design consists of an infinite dimensional observer with an adaptive time delay estimation and a sliding mode controller (SMC). The merit of the proposed concept lies in the fact that the unknown delay is valued by just estimating the smallest delay segment. The controller input is obtained from a set of sequential observers that predicts the system states and ensures asymptotic stability of the closed loop system with input delay estimation. The existence of sliding mode and the closed loop system stability is proved thanks to the Lyapunov and Lyapunov–Krasovskii candidate functionals, respectively. Simulation results confirm the effectiveness of the proposed design.

End Point Control of Nonlinear Flexible Manipulators With Control Constraint Using SDRE Method

2002 ◽  
Author(s):  
Woosoon Yim ◽  
Sahjendra N. Singh
Keyword(s):  
Nonlinear Systems ◽  
Closed Loop ◽  
Loop System ◽  
Suboptimal Control ◽  
Flexible Manipulator ◽  
Closed Loop System ◽  
Elastic Mode ◽  
Nonminimum Phase ◽  
End Point ◽  
Elastic Modes

The paper treats the question of end point regulation of multi-link light-weight manipulators using the state dependent Riccati equation (SDRE) method. It is assumed that each link is flexible and deforms when maneuvered. It is well known that end point trajectory control using widely used feedback linearization technique is not possible since the system is nonminimum phase. Furthermore, control saturation is a major problem in controlling nonlinear systems. In this paper, an optimal control problem is formulated for the derivation of control law with and without control constraints on the joint torques and suboptimal control laws are designed using the SDRE method. This design approach is applicable to minimum and as well as nonminimum phase nonlinear systems. For the purpose of control, psuedo joint angles and elastic modes of each link are regulated to their equilibrium values which correspond to the target end point under gravity. Weighting matrices in the quadratic performance index provide flexibility in shaping the psuedo angle and elastic mode trajectories. In the closed-loop system, the equilibrium state is asymptotically stable, and vibration is uppressed. Simulation results are presented for a single link flexible manipulator which shows that in the closed-loop system, end point regulation is accomplished even with hard bounds on the control torque, and that the transient characteristics of the psuedo angles and elastic modes are easily shaped by the choice of the the performance criterion.

scholarly journals Operational Space Control of a Lightweight Robotic Arm Actuated by Shape Memory Alloy (SMA) Wires

2016 ◽  
Author(s):  
Serket Quintanar-Guzmán ◽  
Somasundar Kannan ◽  
Miguel A. Olivares-Mendez ◽  
Holger Voos
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Closed Loop ◽  
Loop System ◽  
Robotic Arm ◽  
Control Law ◽  
Closed Loop System ◽  
End Effector ◽  
Position Regulation ◽  
The Stability

This paper presents the design and control of a two link lightweight robotic arm using a couple of antagonistic Shape Memory Alloy (SMA) wires as actuators. A nonlinear robust control law for accurate positioning of the end effector of the two-link SMA based robotic arm is developed to handle the hysteresis behavior present in the system. The model presented consists of two subsystems: firstly the SMA wires model and secondly the dynamics of the robotic arm itself. The control objective is to position the robotic arm’s end effector in a given operational plane position. For this regulation problem a sliding mode control law is applied to the hysteretic system. Finally a Lyapunov analysis is applied to the closed-loop system demonstrating the stability of the system under given conditions. The simulation results demonstrate the accurate and fast response of the control law for position regulation. In addition, the stability of the closed-loop system can be corroborated.

Observer-based sliding mode control for piezoelectric wing bending-torsion coupling flutter involving delayed output

2020 ◽  
pp. 107754632094912
Author(s):  
Da Li ◽  
Hui Yang ◽  
Na Qi ◽  
Jiaxin Yuan
Keyword(s):  
Time Delay ◽  
Sliding Mode Control ◽  
Linear Matrix Inequalities ◽  
Closed Loop ◽  
Sliding Mode ◽  
Loop System ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Piezoelectric Patch

An observer-based sliding mode control scheme is proposed for suppressing bending-torsion coupling flutter motions of a wing aeroelastic system with delayed output by using the piezoelectric patch actuators. The wing structure is modeled as a thin-walled beam, and the aerodynamics on the wing are computed by the strip theory. For the implementation of the control algorithm, the piezoelectric patch is bonded on the top surface of the beam to act as the actuator. Ignoring the effect of piezoelectric actuators on structural dynamics, only considering the bending moments induced by piezoelectric effects, the corresponding dynamic motion equation is established by using the Lagrange method with the assumed mode method. The flutter speed and frequency of the closed-loop system with time delay are obtained by solving a polynomial eigenvalue problem. An observer-based controller that does not dependent on time delay is developed for suppressing the flutter, and the corresponding gain matrices are obtained by solving linear matrix inequalities. The sufficient condition for the asymptotic stability of the closed-loop system is derived in terms of linear matrix inequalities. The simulation results demonstrate that the proposed control strategy based on the piezoelectric actuator is effective in wing bending-torsion coupling flutter system with a delayed output.

scholarly journals Robust Sliding Control of SEIR Epidemic Models

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Asier Ibeas ◽  
Manuel de la Sen ◽  
Santiago Alonso-Quesada
Keyword(s):  
Sliding Mode Control ◽  
Closed Loop ◽  
Sliding Mode ◽  
A Priori ◽  
Vaccination Strategy ◽  
Loop System ◽  
Theoretic Approach ◽  
Closed Loop System ◽  
Sliding Control ◽  
Mode Control

This paper is aimed at designing a robust vaccination strategy capable of eradicating an infectious disease from a population regardless of the potential uncertainty in the parameters defining the disease. For this purpose, a control theoretic approach based on a sliding-mode control law is used. Initially, the controller is designed assuming certain knowledge of an upper-bound of the uncertainty signal. Afterwards, this condition is removed while an adaptive sliding control system is designed. The closed-loop properties are proved mathematically in the nonadaptive and adaptive cases. Furthermore, the usual sign function appearing in the sliding-mode control is substituted by the saturation function in order to prevent chattering. In addition, the properties achieved by the closed-loop system under this variation are also stated and proved analytically. The closed-loop system is able to attain the control objective regardless of the parametric uncertainties of the model and the lack ofa prioriknowledge on the system.

Design of Variable Structure Control with Bounded Inputs

2010 ◽  
Vol 29-32 ◽  
pp. 1175-1180
Author(s):  
Qing Kun Zhou ◽  
Sheng Jian Bai ◽  
Zhi Yong Zhang
Keyword(s):  
Closed Loop ◽  
Controller Design ◽  
Sliding Mode ◽  
Variable Structure ◽  
Closed Loop System ◽  
Variable Structure Systems ◽  
Structure Control ◽  
Variable Structure System ◽  
Lti System ◽  
The Stability

The design of variable structure system inputs which are constrained by saturation is studied. For a LTI system which satisfies some conditions, it is shown that appropriate bounded controllers guarantee the system’s global stability and maximize the sliding mode domain on the switching surfaces. Stability conditions of variable structure systems with constrained inputs are relaxed, and the stability of the closed-loop system is guaranteed by using passivity theory of linear passive systems. Moreover, nonlinear sliding surfaces are discussed for variable structure controller design, and a novel nonlinear switching surface is proposed. Finally, the proposed methods are applied to a 2nd order LTI system to show their usefulness.

scholarly journals Disturbance Observer-Based Continuous Finite-Time Sliding Mode Control against Matched and Mismatched Disturbances

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Ngo Phong Nguyen ◽  
Hyondong Oh ◽  
Yoonsoo Kim ◽  
Jun Moon
Keyword(s):  
Finite Time ◽  
Disturbance Observer ◽  
Closed Loop ◽  
Sliding Mode ◽  
Loop System ◽  
Time Varying ◽  
Time Stability ◽  
Closed Loop System ◽  
Finite Time Stability ◽  
Mismatched Disturbances

In this paper, we propose the disturbance observer-based continuous finite-time sliding mode controller (DOBCSMC) for input-affine nonlinear systems in which additive matched and mismatched disturbances exist. The objective is to show the robustness and disturbance attenuation performance of the closed-loop system with the proposed DOBCSMC subjected to general classes of matched and mismatched disturbances. The proposed DOBCSMC consists of three main features: (i) the nonlinear finite-time disturbance observer to obtain a fast and accurate estimation of matched and mismatched disturbances, (ii) the nonlinear sliding surface to ensure high precision in the steady-state phase of the controlled output, and (iii) the continuous supertwisting algorithm to guarantee finite-time convergence of the controlled output and reduce the chattering under the effect of matched and mismatched disturbances. It should be noted that the existing approaches cannot handle time-varying mismatched disturbances and/or cannot guarantee faster finite-time stability of the controlled output. We prove that the closed-loop system with the DOBCSMC guarantees both finite-time reachability to the sliding surface and finite-time stability of the controlled output to the origin. Various simulations are performed to demonstrate the effectiveness of the proposed DOBCSMC. In particular, the simulation results show that the DOBCSMC guarantees faster convergence of the closed-loop system to the origin, higher precision of the controlled output, and better robustness performance against various classes of (time-varying) matched and mismatched disturbances, compared with the existing approaches.

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