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.

End Point Position Control of Multi-Link Flexible Manipulators Using SDRE Method

2004 ◽  
Author(s):  
Jamil M. Renno ◽  
Woosoon Yim ◽  
Sahjendra N. Singh
Keyword(s):  
Equilibrium State ◽  
Closed Loop ◽  
Position Control ◽  
Loop System ◽  
Suboptimal Control ◽  
Flexible Manipulator ◽  
Flexible Manipulators ◽  
Closed Loop System ◽  
End Point ◽  
Elastic Modes

This paper treats end point regulation of multi-link light-weight flexible manipulators using the State Dependent Riccati Equation: SDRE method. It is well known that end point trajectory control using widely used feedback linearization techniques is not possible when the equilibrium state of the zero dynamics of the system is unstable or weakly stable. 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 for a multi-link flexible manipulator and suboptimal control laws are designed using the SDRE method. For the purpose of control, pseudo joint angles and elastic modes of each link are regulated to their equilibrium values which correspond to the target end point. Weighting matrices in the quadratic performance index provide flexibility in shaping the pseudo angles and elastic modes trajectories. In the closed-loop system, the equilibrium state is asymptotically stable, and vibration is suppressed. Simulation results are presented for a two-link flexible manipulator, which show that in the closed-loop system, end point trajectory tracking is accomplished even with constraints on the control torque. Results also show that the transient characteristics of the pseudo angles and elastic modes can be easily shaped by the choice of the performance criterion.

scholarly journals Adaptive Stabilization Control for a Class of Complex Nonlinear Systems Based on T-S Fuzzy Bilinear Model

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Jinsheng Xing ◽  
Naizheng Shi
Keyword(s):  
Adaptive Control ◽  
Nonlinear Systems ◽  
Complex Systems ◽  
Closed Loop ◽  
Loop System ◽  
Asymptotically Stable ◽  
Bilinear Model ◽  
Closed Loop System ◽  
Fuzzy Modelling ◽  
Control Scheme

This paper proposes a stable adaptive fuzzy control scheme for a class of nonlinear systems with multiple inputs. The multiple inputs T-S fuzzy bilinear model is established to represent the unknown complex systems. A parallel distributed compensation (PDC) method is utilized to design the fuzzy controller without considering the error due to fuzzy modelling and the sufficient conditions of the closed-loop system stability with respect to decay rateαare derived by linear matrix inequalities (LMIs). Then the errors caused by fuzzy modelling are considered and the method of adaptive control is used to reduce the effect of the modelling errors, and dynamic performance of the closed-loop system is improved. By Lyapunov stability criterion, the resulting closed-loop system is proved to be asymptotically stable. The main contribution is to deal with the differences between the T-S fuzzy bilinear model and the real system; a global asymptotically stable adaptive control scheme is presented for real complex systems. Finally, illustrative examples are provided to demonstrate the effectiveness of the results proposed in this paper.

On the control of a single flexible arm robot via Youla-Kucera parameterization

Robotica ◽  
2014 ◽  
Vol 34 (1) ◽  
pp. 150-172 ◽  
Author(s):  
Habib Esfandiar ◽  
Saeed Daneshmand ◽  
Roozbeh Dargahi Kermani
Keyword(s):  
Closed Loop ◽  
Optimization Techniques ◽  
Loop System ◽  
Flexible Manipulator ◽  
Order System ◽  
Flexible Beam ◽  
Closed Loop System ◽  
Stabilizing Controller ◽  
Main Challenge ◽  
Tip Mass

SUMMARYIn this paper, based on the Youla-Kucera (Y-K) parameterization, the control of a flexible beam acting as a flexible robotic manipulator is investigated. The method of Youla parameterization is the simple solution and proper method for describing the collection of all controllers that stabilize the closed-loop system. This collection comprises function of the Youla parameter which can be any proper transfer function that is stable. The main challenge in this approach is to obtain a Youla parameter with infinite dimension. This parameter is approximated by a subspace with finite dimensions, which makes the problem tractable. It is required to be generated from a finite number of bases within that space and the considered system can be approximated by an expansion of the orthonormal bases such as FIR, Laguerre, Kautz and generalized bases. To calculate the coefficients for each basis, it is necessary to define the problem in the form of an optimization problem that is solved by optimization techniques. The Linear Quadratic Regulator (LQR) optimization tool is employed in order to optimize the controller gains. The main aim in controller design is to merge the closed-loop system and the second order system with the desirable time response characteristic. The results of the Youla stabilizing controller for a planar flexible manipulator with lumped tip mass indicate that the proposed method is very efficient and robust for the time-continuous instances.

Robust Generation of Limit Cycles in Nonlinear Systems: Application on Two Mechanical Systems

2017 ◽  
Vol 12 (4) ◽  
Author(s):  
Ali Reza Hakimi ◽  
Tahereh Binazadeh
Keyword(s):  
Nonlinear Systems ◽  
Limit Cycle ◽  
Limit Cycles ◽  
Closed Loop ◽  
Stable Limit Cycle ◽  
Additional Term ◽  
Loop System ◽  
Stable Limit ◽  
Closed Loop System ◽  
Robust Performance

This paper studies inducing robust stable oscillations in nonlinear systems of any order. This goal is achieved through creating stable limit cycles in the closed-loop system. For this purpose, the Lyapunov stability theorem which is suitable for stability analysis of the limit cycles is used. In this approach, the Lyapunov function candidate should have zero value for all the points of the limit cycle and be positive in the other points in the vicinity of it. The proposed robust controller consists of a nominal control law with an additional term that guarantees the robust performance. It is proved that the designed controller results in creating the desirable stable limit cycle in the phase trajectories of the uncertain closed-loop system and leads to induce stable oscillations in the system's output. Additionally, in order to show the applicability of the proposed method, it is applied on two practical systems: a time-periodic microelectromechanical system (MEMS) with parametric errors and a single-link flexible joint robot in the presence of external disturbances. Computer simulations show the effective robust performance of the proposed controllers in generating the robust output oscillations.

A Novel Delay-Independent Robust Adaptive Controller Design for Uncertain Nonlinear Systems With Time-Varying State Delay

2019 ◽  
Vol 15 (1) ◽  
Author(s):  
Hadi Azmi ◽  
Alireza Yazdizadeh
Keyword(s):  
Nonlinear Systems ◽  
Linear Matrix Inequality ◽  
Closed Loop ◽  
Controller Design ◽  
Loop System ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
System Delay ◽  
Closed Loop System

Abstract In this paper, two novel adaptive control strategies are presented based on the linear matrix inequality for nonlinear Lipschitz systems. The proposed approaches are developed by creatively using Krasovskii stability theory to compensate parametric uncertainty, unknown time-varying internal delay, and bounded matched or mismatched disturbance effects in closed-loop system of nonlinear systems. The online adaptive tuning controllers are designed such that reference input tracking and asymptotic stability of the closed-loop system are guaranteed. A novel structural algorithm is developed based on linear matrix inequality (LMI) and boundaries of the system delay or uncertainty. The capabilities of the proposed tracking and regulation methods are verified by simulation of three physical uncertain nonlinear system with real practical parameters subject to internal or state time delay and disturbance.

Direct Adaptive CMAC PI Control for Uncertain Nonlinear Systems with Measurable Output Feedback

2013 ◽  
Vol 479-480 ◽  
pp. 612-616
Author(s):  
Chun Sheng Chen
Keyword(s):  
Nonlinear Systems ◽  
Closed Loop ◽  
Control Structure ◽  
Loop System ◽  
Pi Control ◽  
Uncertain Nonlinear Systems ◽  
Closed Loop System ◽  
External Disturbances ◽  
Lyapunov Stability Criterion ◽  
System Output

A stable direct adaptive CMAC PI controller for a class of uncertain nonlinear systems is investigated under the constrain that only the system output is available for measurement. First, a state observer is used to estimate unmeasured states of the systems. Then, the PI control structure is used for improving robustness in the closed-loop system and avoiding affection of uncertainties and external disturbances. The global asymptotic stability of the closed-loop system is guaranteed according to the Lyapunov stability criterion. To demonstrate the effectiveness of the proposed method, simulation results indicate that the proposed approach is capable of achieving a good trajectory following performance without the knowledge of plant parameters.

Compensator-based approximate optimal control for affine nonlinear systems with input constraints and unmatched disturbances

2020 ◽  
Vol 42 (15) ◽  
pp. 3024-3034
Author(s):  
Ke Lu ◽  
Chunsheng Liu ◽  
Jingliang Sun ◽  
Chunhua Li ◽  
Chengcheng Ma
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Closed Loop ◽  
Control Method ◽  
Approximation Error ◽  
Loop System ◽  
Adaptive Dynamic Programming ◽  
Input Constraints ◽  
Closed Loop System ◽  
Additional Function

This paper develops a novel approximate optimal control method for a class of constrained continuous-time nonlinear systems in the presence of disturbances via adaptive dynamic programming (ADP) technique. First, an auxiliary dynamic compensator is introduced to deal with the input constraints. Through augmenting the original system with the designed auxiliary compensator, the design of constrained optimal controller is circumvented by stabilizing the equivalent augmented system. Then, the cost function is appropriately redefined by introducing an additional function connected with disturbances for the augmented nominal system in order to compensate the effect of unmatched disturbances. Next, the solution of associated Hamilton-Jacobi-Bellman (HJB) equation is solved online with weight adaptation law using neural networks (NNs). Furthermore, an additional robustifying term is utilized to compensate the effect of the approximation error of NNs, and thus the asymptotic stability of the closed-loop system is guaranteed. Finally, all signals of the closed-loop system are proved to be asymptotic convergence by using Lyapunov method. Simulation examples demonstrate the effectiveness of the proposed scheme.

scholarly journals Global Adaptive Control of Stochastic Nonlinear Systems with Linearly Bounded Unmeasurable States by Output Feedback

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Qiangde Wang ◽  
Chunling Wei
Keyword(s):  
Nonlinear Systems ◽  
Output Feedback ◽  
Closed Loop ◽  
Inverse Dynamics ◽  
Growth Conditions ◽  
Loop System ◽  
Stochastic Nonlinear Systems ◽  
Nonlinear Functions ◽  
Closed Loop System ◽  
Stochastic Stabilization

The problem of the output feedback stochastic stabilization is investigated for a class of stochastic nonlinear systems with linearly bounded unmeasurable states. Under the condition that the inverse dynamics is stochastic input-to-state stable and the nonlinear functions satisfy the linear growth conditions with unknown growth rate, an adaptive output feedback controller is proposed to make the closed-loop system globally stable in probability and the states of the closed-loop system converge to zero almost surely. A simulation example is provided to show the effectiveness of the theoretical results.

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.

Optimal Sliding Mode Control for a Class of Underactuated Nonlinear Systems

2011 ◽  
Author(s):  
Parham Ghorbanian ◽  
Sergey G. Nersesov ◽  
Hashem Ashrafiuon
Keyword(s):  
Nonlinear Systems ◽  
Sliding Mode Control ◽  
Closed Loop ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Domain Of Attraction ◽  
Loop System ◽  
Closed Loop System ◽  
Sliding Surfaces ◽  
Mode Control

In this paper, a general framework that provides sufficient conditions for asymptotic stabilization of underactuated nonlinear systems using an optimal sliding mode control in the presence of system uncertainties is presented. A performance objective is used to optimally select the parameters of the sliding mode control surfaces subject to state and input constraints. It is shown that the closed-loop system trajectories reach the optimal sliding surfaces in finite time and a constructive methodology to determine exponential stability of the closed-loop system on the sliding surfaces is developed which ensures asymptotic stability of the overall closed-loop system. The framework further provides the basis to determine an estimate of the domain of attraction for the closed-loop system with uncertainties. The results developed in this work are experimentally validated using a linear inverted pendulum testbed which show a good match between the actual domain of attraction of the upward equilibrium state and its analytical estimate.

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