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

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.

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

Dynamic Systems and Control ◽

10.1115/imece2002-33126 ◽

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.

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

Robotica ◽

10.1017/s0263574714001337 ◽

2014 ◽

Vol 34 (1) ◽

pp. 150-172 ◽

Cited By ~ 1

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.

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Absolute Stability Condition Derivation for Position Closed-Loop System in Hydraulic Automatic Gauge Control

Processes ◽

10.3390/pr7100766 ◽

2019 ◽

Vol 7 (10) ◽

pp. 766 ◽

Cited By ~ 16

Author(s):

Zhu ◽

Tang ◽

Wang ◽

Jiang ◽

Zhao ◽

...

Keyword(s):

Absolute Stability ◽

Information Transfer ◽

Closed Loop ◽

Position Control ◽

Block Diagram ◽

Metallurgical Industry ◽

Loop System ◽

Transfer Model ◽

Closed Loop System ◽

Automatic Gauge Control

In the metallurgical industry, hydraulic automatic gauge control (HAGC) is a core mechanism for thickness control of plates used in the rolling process. The stability of the HAGC system’s kernel position closed-loop is key to ensuring a process with high precision, speed and reliability. However, the closed-loop position control system is typically nonlinear, and its stability is affected by several factors, making it difficult to analyze instability in the system. This paper describes in detail the functioning of the position closed-loop system. A mathematical model of each component was established using theoretical analysis. An incremental transfer model of the position closed-loop system was also derived by studying the connections between each component. In addition, based on the derived information transfer relationship, a transfer block diagram of disturbance quantity of the system was established. Furthermore, the Popov frequency criterion method was introduced to ascertain its absolute stability. The results indicate that the absolute stability conditions of the position closed-loop system are derived in two situations: when spool displacement is positive or negative. This study lays a theoretical foundation for research on the instability mechanism of an HAGC system.

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Adaptive Boundary Control for a Flexible Manipulator With State Constraints Using a Barrier Lyapunov Function

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4039364 ◽

2018 ◽

Vol 140 (8) ◽

Cited By ~ 7

Author(s):

Tingting Jiang ◽

Jinkun Liu ◽

Wei He

Keyword(s):

Lyapunov Function ◽

Boundary Control ◽

Closed Loop ◽

State Constraints ◽

Lyapunov Stability Theory ◽

Loop System ◽

Flexible Manipulator ◽

Closed Loop System ◽

Control Laws ◽

Barrier Lyapunov Function

In this paper, the problem of state constraints control is investigated for a class of output constrained flexible manipulator system with varying payload. The dynamic behavior of the flexible manipulator is represented by partial differential equations. To prevent states of the flexible manipulator system from violating the constraints, a barrier Lyapunov function which grows to infinity whenever its arguments approach to some limits is employed. Then, based on the barrier Lyapunov function, boundary control laws are given. To solve the problem of varying payload, an adaptive boundary controller is developed. Furthermore, based on the theory of barrier Lyapunov function and the adaptive algorithm, state constraints and output control under vibration condition can be achieved. The stability of the closed-loop system is carried out by the Lyapunov stability theory. Numerical simulations are given to illustrate the performance of the closed-loop system.

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