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.

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.

Global Stabilization for a class of nonlinear fractional-order systems

2019 ◽  
Vol 10 (01) ◽  
pp. 1941009 ◽  
Author(s):  
Taide Liu ◽  
Feng Wang ◽  
Wanchun Lu ◽  
Xuhuan Wang
Keyword(s):  
Lyapunov Function ◽  
Fractional Order ◽  
Closed Loop ◽  
The State ◽  
Loop System ◽  
Global Stabilization ◽  
Fractional Order Systems ◽  
Closed Loop System ◽  
Integer Order ◽  
Backstepping Algorithm

The problem of Mittag–Leffler stabilization (MLS) is studied for a class of nonlinear non-integer order systems. The stabilizer is constructed by using the Lyapunov function and backstepping algorithm. The continuous controller is designed to ensure that the state of the nonlinear fractional-order closed-loop system converges to the equilibrium. Two simulation examples are given to illustrate the effectiveness of the method.

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.

Output feedback boundary control of a flexible marine riser system

2017 ◽  
Vol 24 (16) ◽  
pp. 3617-3630 ◽  
Author(s):  
Yu Liu ◽  
Fang Guo
Keyword(s):  
Boundary Control ◽  
Closed Loop ◽  
Vibration Suppression ◽  
High Gain ◽  
Loop System ◽  
System State ◽  
Marine Riser ◽  
Closed Loop System ◽  
Observer Error ◽  
System States

This paper is concerned with the design of boundary control for globally stabilizing a flexible marine riser system. The dynamics of the riser system are represented in the form of hybrid partial–ordinary differential equations. Firstly, when the system state available for feedback is unmeasurable, an observer backstepping method is employed to reconstruct the system state and then design the boundary control for vibration suppression of the riser system. Subsequently, for the case that the system states in the designed control law cannot be accurately obtained, the high-gain observers are utilized to estimate those unmeasurable system states. With the proposed control, the uniformly ultimately bounded stability of the closed-loop system is demonstrated by the use of Lyapunov’s synthetic method and the state observer error is converged exponentially to zero as time approaches to infinity. In addition, the disturbance observer is introduced to track external environmental disturbance. Finally, the control performance of the closed-loop system is validated by carrying out numerical simulation.

scholarly journals Constrained Uncertain System Stabilization with Enlargement of Invariant Sets

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Walid Hamdi ◽  
Wissal Bey ◽  
Naceur Benhadj Braiek
Keyword(s):  
Closed Loop ◽  
Uncertain System ◽  
Loop System ◽  
Invariant Sets ◽  
Feedback Gain ◽  
Closed Loop System ◽  
Control Laws ◽  
Robust Model Predictive Control ◽  
Robust Model ◽  
Polyhedral Set

An enhanced method able to perform accurate stability of constrained uncertain systems is presented. The main objective of this method is to compute a sequence of feedback control laws which stabilizes the closed-loop system. The proposed approach is based on robust model predictive control (RMPC) and enhanced maximized sets algorithm (EMSA), which are applied to improve the performance of the closed-loop system and achieve less conservative results. In fact, the proposed approach is split into two parts. The first is a method of enhanced maximized ellipsoidal invariant sets (EMES) based on a semidefinite programming problem. The second is an enhanced maximized polyhedral set (EMPS) which consists of appending new vertices to their convex hull to minimize the distance between each new vertex and the polyhedral set vertices to ensure state constraints. Simulation results on two examples, an uncertain nonisothermal CSTR and an angular positioning system, demonstrate the effectiveness of the proposed methodology when compared to other works related to a similar subject. According to the performance evaluation, we recorded higher feedback gain provided by smallest maximized invariant sets compared to recently studied methods, which shows the best region of stability. Therefore, the proposed algorithm can achieve less conservative results.

Gain Scheduling Control of Gas Turbine Engines: Stability by Computing a Single Quadratic Lyapunov Function

2013 ◽  
Author(s):  
Mehrdad Pakmehr ◽  
Nathan Fitzgerald ◽  
Eric M. Feron ◽  
Jeff S. Shamma ◽  
Alireza Behbahani
Keyword(s):  
Lyapunov Function ◽  
Gas Turbine ◽  
Closed Loop ◽  
Equilibrium Points ◽  
Gain Scheduling ◽  
Gas Turbine Engine ◽  
Loop System ◽  
Closed Loop System ◽  
Quadratic Lyapunov Function ◽  
Turbine Engine

We develop and describe a stable gain scheduling controller for a gas turbine engine that drives a variable pitch propeller. A stability proof is developed for gain scheduled closed-loop system using global linearization and linear matrix inequality (LMI) techniques. Using convex optimization tools, a single quadratic Lyapunov function is computed for multiple linearizations near equilibrium and non-equilibrium points of the nonlinear closed-loop system. This approach guarantees stability of the closed-loop gas turbine engine system. Simulation results show the developed gain scheduling controller is capable of regulating a turboshaft engine for large thrust commands in a stable fashion with proper tracking performance.

scholarly journals Adaptive Tracking Control for a Class of Manipulator Systems with State Constraints and Stochastic Disturbances

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Wei Sun ◽  
Wenxing Yuan ◽  
Jing Zhang ◽  
Qun Sun
Keyword(s):  
Tracking Control ◽  
Closed Loop ◽  
State Constraints ◽  
Adaptive Controller ◽  
Compact Set ◽  
Closed Loop System ◽  
Stochastic Disturbances ◽  
Adaptive Tracking Control ◽  
Barrier Lyapunov Function ◽  
Control Scheme

An adaptive controller is constructed for a class of stochastic manipulator nonlinear systems in this paper. The states are constrained in the compact set. A tan-type Barrier Lyapunov Function (BLF) is employed to deal with state constraints. The proposed control scheme guarantees the output error convergence to a small neighbourhood of zero. All the signals in the closed-loop system are bounded. The simulation results illustrate the validity of the proposed method.

Autonomous Mission Management Based Nonlinear Flight Control Design for a Class of Hybrid Unmanned Aerial Vehicles

2021 ◽  
Vol 01 (02) ◽  
pp. 2150009
Author(s):  
Kemao Peng
Keyword(s):  
Flight Control ◽  
Closed Loop ◽  
Main Idea ◽  
Loop System ◽  
Control Law ◽  
Closed Loop System ◽  
Control Laws ◽  
Mission Management ◽  
Rotary Wing ◽  
Transition Flight

In this paper, a nonlinear flight control law is designed for a hybrid unmanned aerial vehicle (UAV) to achieve the advanced flight performances with the autonomous mission management (AMM). The hybrid UAV is capable of hovering like quadrotors and maneuvering as fixed-wing aircraft. The main idea is to design the flight control laws in modules. Those modules are organized online by the autonomous mission management. Such online organization will improve the UAV autonomy. One of the challenges is to execute the transition flight between the rotary-wing and fixed-wing modes. The resulting closed-loop system with the designed flight control law is verified in simulation and the simulation results demonstrate that the resulting closed-loop system can successfully complete the designated flight missions including the transition flight between the rotary-wing and fixed-wing modes.

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