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.

Adaptive Contact Force Control of a Flexible Beam Using Output Feedback

2000 ◽  
Author(s):  
Woosoon Yim
Keyword(s):  
Contact Force ◽  
Contact Surface ◽  
Force Control ◽  
Closed Loop ◽  
Force Measurement ◽  
Transient Behavior ◽  
Loop System ◽  
Flexible Beam ◽  
Reference Trajectory ◽  
Closed Loop System

Abstract This paper presents an adaptive force trajectory control of a flexible beam using a piezoceramic actuator. Based on the adaptive backstepping method, a force control system using only force measurement is designed. For the derivation of the control law, it is assumed that parameters of the beam and contact surface stiffness are unknown. It is shown that in the closed-loop system, the contact force tracks a given reference trajectory and the beam vibration is suppressed as well. Digital simulations results show that the closed-loop system has good transient behavior and robust performance in the presence of uncertainties in the parameters of the flexible beam and the contact surface.

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.

Active Vibration Control of Beams by Combining Precompressed Layer Damping and ACLD Treatment: Performance Comparison of Various Robust Control Techniques

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Rajiv Kumar
Keyword(s):  
Robust Control ◽  
Closed Loop ◽  
Active Vibration Control ◽  
Flexible Structures ◽  
Performance Comparison ◽  
Loop System ◽  
Flexible Beam ◽  
Closed Loop System ◽  
Linear Quadratic ◽  
System Parameters

It is a well known fact that system parameters of the flexible structures keep on changing due to several reasons. Ordinary controllers lose their effectiveness in changed situations and do not guarantee the stability of the closed loop system. However, controllers designed based on robust control theory not only maintain the closed loop stability of the perturbed system with a large variation in system parameters but also maintain the best performance. H∞ loop shaping controller is designed and implemented experimentally on a smart flexible beam treated with precompressed layer damping and ACLD treatment. It outperforms linear quadratic Gaussian and standard H∞ controller both in terms of robust stability and robust performance. Relative merits and demerits of the μ-synthesis based controller are also discussed. Afterwards, these controllers were digitized at certain sampling frequencies and applied to the experimental flexible structure. Certain time domain parameters of the closed loop system discuss the relative superiority of these controllers which otherwise cannot be captured using frequency domain results alone.

scholarly journals Boundary Conditions for Transient and Robust Performance of a Reduced-Order Model-Based State Feedback Controller with PI Observer

Energies ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 2881
Author(s):  
Nebiyeleul Daniel Amare ◽  
Doe Hun Kim ◽  
Sun Jick Yang ◽  
Young Ik Son
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Loop System ◽  
Reduced Order Model ◽  
System Stability ◽  
Order System ◽  
Closed Loop System ◽  
Order Model ◽  
Reduced Order ◽  
Model Based

One common technique employed in control system design to minimize system model complexity is model order reduction. However, controllers designed by using a reduced-order model have the potential to cause the closed-loop system to become unstable when applied to the original full-order system. Additionally, system performance improvement techniques such as disturbance observers produce unpredictable outcomes when augmented with reduced-order model-based controllers. In particular, the closed-loop system stability is compromised when a large value of observer gain is employed. In this paper, a boundary condition for the controller and observer design parameters in which the closed-loop system stability is maintained is proposed for a reduced-order proportional-integral observer compensated reduced-order model-based controller. The boundary condition was obtained by performing the stability analysis of the closed-loop system using the root locus method and the Routh-Hurwitz criterion. Both the observer and the state feedback controller were designed using a reduced-order system model based on the singular perturbation theory. The result of the theoretical analysis is validated through computer simulations using a DC (direct current) motor position control problem.

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.

Adaptive Servoregulation of a Projectile Fin Using Piezoelectric Actuator

Aerospace ◽  
2005 ◽  
Author(s):  
Smitha Mani ◽  
Sahjendra N. Singh ◽  
Surya Kiran Parimi ◽  
Woosoon Yim
Keyword(s):  
Piezoelectric Actuator ◽  
Closed Loop ◽  
Angular Rate ◽  
Adaptive Controller ◽  
Loop System ◽  
Laboratory Model ◽  
Flexible Beam ◽  
Closed Loop System ◽  
Real Time Control ◽  
Aerodynamic Moment

This paper treats the question of adaptive control of a projectile fin using a piezoelectric actuator. The hollow projectile fin is rigid, within which a flexible cantilever beam with a piezoelectric active layer is mounted. The model of the fin-beam system includes the aerodynamic moment which is a function of angle of attack of the projectile. The rotation angle of the fin is controlled by deforming the flexible beam which is hinged at the tip of the rigid fin. It is assumed that the system parameters are completely unknown and that only the fin angle and its derivative are measured for synthesis. A linear combination of the fin angle and fin’s angular rate is chosen as the controlled output variable and an adaptive servoregulator is designed for the control of the fin angle and the rejection of the disturbance input (aerodynamic moment). In the closed-loop system, the fin angle asymptotically converges to the desired value and the elastic modes converges to their equilibrium values. Computer simulation is performed which shows that in the closed-loop system, the fin angle is precisely controlled in spite of uncertainties in the fin-beam parameters and the aerodynamic moment coefficients. Furthermore, a laboratory model of the projectile fin is developed and the adaptive controller is implemented for real-time control. Experimental results are presented which show that adaptive servoregulator accomplishes fin angle control.

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

2018 ◽  
Vol 140 (8) ◽  
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.

Design of a stabilizing controller for discrete-time switched delay systems with affine parametric uncertainties

2018 ◽  
Vol 41 (1) ◽  
pp. 14-22 ◽  
Author(s):  
NA Baleghi ◽  
MH Shafiei
Keyword(s):  
Discrete Time ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Loop System ◽  
Delay Systems ◽  
Linear Matrix ◽  
Parametric Uncertainties ◽  
Closed Loop System ◽  
Stabilizing Controller

This paper studies the stabilization problem of discrete-time switched systems in the presence of a time-varying delay and parametric uncertainties. The main goal is to provide a state feedback controller to guarantee the stability of the closed-loop system with an evaluated average dwell time. In this regard, an appropriate Lyapunov–Krasovskii functional is constructed and the sufficient conditions for stability of the closed-loop system are developed in terms of feasibility testing of proposed linear matrix inequalities. These conditions only depend on the upper bounds of the time delay and uncertain parameters. Additionally, a numerical example is provided to verify the theoretical results.

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