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.

scholarly journals Time-Delayed Feedback Control of a Hydraulic Model Governed by a Diffusive Wave System

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Boumediène Chentouf ◽  
Nejib Smaoui
Keyword(s):  
Flow Control ◽  
Closed Loop ◽  
Semigroup Theory ◽  
Loop System ◽  
Delayed Feedback Control ◽  
Feedback Gain ◽  
Wave System ◽  
Closed Loop System ◽  
Decay Of Solutions ◽  
Time Delayed Feedback

This paper is concerned with the feedback flow control of an open-channel hydraulic system modeled by a diffusive wave equation with delay. Firstly, we put forward a feedback flow control subject to the action of a constant time delay. Thereafter, we invoke semigroup theory to substantiate that the closed-loop system has a unique solution in an energy space. Subsequently, we deal with the eigenvalue problem of the system. More importantly, exponential decay of solutions of the closed-loop system is derived provided that the feedback gain of the control is bounded. Finally, the theoretical findings are validated via a set of numerical results.

scholarly journals Intelligent Swing-Up and Robust Stabilization via Tube-based Nonlinear Model Predictive Control for A Rotational Inverted-Pendulum System

2020 ◽  
Vol 45 (1) ◽  
pp. 49-64
Author(s):  
Alvaro Prado ◽  
Marco Herrera ◽  
Oswaldo Menéndez
Keyword(s):  
Predictive Control ◽  
Nonlinear Model ◽  
Closed Loop ◽  
Inverted Pendulum ◽  
Angular Position ◽  
Loop System ◽  
Invariant Sets ◽  
Closed Loop System ◽  
Pendulum System ◽  
Inverted Pendulum System

The purpose of this paper is to introduce a new robust nonlinear model-based predictive control scheme applied to a rotational inverted-pendulum system. The rotational pendulum is composed by a mechanical arm attached to a free-motion pendulum (orthogonal to the arm), namely Furuta Pendulum. In principle, a Fuzzy controller enables the robotic arm bar to lift the rotational pendulum through oscillatory swing-up motion up to automatically achieve the upper equilibrium position in a prescribed stabilizing operation range. After the pendulum reaches the operating range, an intelligent control bypass system allows the transition between the swing-up motion controller and a robust predictive controller to maintain the angular position of the pendulum around the upward critical position. To achieve robust performance, a centralized control framework combines a triplet of control actions. The first one compensates for disturbances using the regulation trajectory ?feedforward control. The second control action corrects errors produced by modelling mismatch. The third controller assures robustness on the closed-loop system whilst compensating for deviations of the state trajectories from the nominal ones (i.e, disturbance-free). The control strategy provides robust feasibility despite constraints on the arm bar and pendulum's actuators are met. Such constraints are calculated on-line based on robust positively invariant sets characterised by polytopic sets (tubes). The proposed controller is tested in a series of simulations, and experimentally validated on a high-fidelity simulation environment including a rotational inverted-pendulum built for educational purposes. The results show that robust control performance is strengthened against disturbances of the closed-loop system benchmarked to inherently-robust linear and nonlinear predictive controllers.

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.

Dissipative Control of Singular Systems by Proportional Plus Derivative State Feedback

2012 ◽  
Vol 246-247 ◽  
pp. 826-831
Author(s):  
Shuang Yun Xing ◽  
Xin Jing ◽  
Yang Cao
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Singular Systems ◽  
Uncertain System ◽  
Loop System ◽  
Descriptor Systems ◽  
Control Synthesis ◽  
Closed Loop System ◽  
Dissipative Control ◽  
Derivative Matrix

This article deals with the problem of dissipative control synthesis for a class of descriptor systems with uncertainties in the derivative matrix. Attention is focused on the design of a proportional plus derivative (PD) state feedback, which guarantees that the closed-loop system is robustly stable and strict dissipative. Firstly, a sufficient condition for the closed-loop system is robustly stable and strict dissipative is presented by using a simple idea of changing the problem to the corresponding problem of an augmented uncertain system. Then, a PD controller is constructed by solving LMIs. Finally, a numerical example is given to demonstrate that the proposed method is effective.

scholarly journals Optimal Pole Assignment of Linear Systems by the Sylvester Matrix Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Hua-Feng He ◽  
Guang-Bin Cai ◽  
Xiao-Jun Han
Keyword(s):  
Assignment Problem ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Pole Assignment ◽  
Loop System ◽  
Linear Matrix ◽  
Feedback Gain ◽  
Matrix Equations ◽  
Closed Loop System ◽  
Linear Matrix Equations

The problem of state feedback optimal pole assignment is to design a feedback gain such that the closed-loop system has desired eigenvalues and such that certain quadratic performance index is minimized. Optimal pole assignment controller can guarantee both good dynamic response and well robustness properties of the closed-loop system. With the help of a class of linear matrix equations, necessary and sufficient conditions for the existence of a solution to the optimal pole assignment problem are proposed in this paper. By properly choosing the free parameters in the parametric solutions to this class of linear matrix equations, complete solutions to the optimal pole assignment problem can be obtained. A numerical example is used to illustrate the effectiveness of the proposed approach.

Optimal Eigenvectors Design for Structural Noise Reduction Through Adaptive Sandwich Algorithm

2009 ◽  
Author(s):  
T. Y. Wu ◽  
Y. L. Chung
Keyword(s):  
Noise Reduction ◽  
Closed Loop ◽  
Active Noise Control ◽  
Optimal Combination ◽  
Loop System ◽  
Structural Vibration ◽  
Feedback Gain ◽  
Structural Noise ◽  
Closed Loop System ◽  
Left And Right

The purpose of this research is to investigate the feasibility of utilizing the adaptive sandwich algorithm to find the optimal left and right eigenvectors for active structural noise reduction. As depicted in the previous studies, the structural acoustic radiation depends on the structural vibration behavior, which is strongly related to both the left eigenvectors (concept of disturbance rejection capability) and right eigenvectors (concept of mode shape distributions) of the system, respectively. In this research, a novel adaptive sandwich algorithm is developed for determining the optimal combination of left and right eigenvectors of the structural system. The sound suppression performance index (SSPI) is defined by combining the orthogonality index of left eigenvectors and the modal radiation index of right eigenvectors. Through the proposed adaptive sandwich algorithm, both the left and right eigenvectors are adjusted such that the SSPI decreases, and therefore one can find the optimal combination of left and right eigenvectors of the closed-loop system for structural noise reduction purpose. The optimal combination of left-right eigenvectors is then synthesized to determine the feedback gain matrix of the closed-loop system. The result of the active noise control shows that the proposed method can significantly suppress the sound pressure radiated from the vibrating structure.

scholarly journals Parameters Design for Logarithmic Quantizer Based on Zoom Strategy

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Jingjing Yan
Keyword(s):  
Closed Loop ◽  
The State ◽  
Loop System ◽  
Invariant Sets ◽  
Time Varying ◽  
Closed Loop System ◽  
Comparison Results

This paper is concerned with the problem of designing suitable parameters for logarithmic quantizer such that the closed-loop system is asymptotic convergent. Based on zoom strategy, we propose two methods for quantizer parameters design, under which it ensures that the state of the closed-loop system can load in the invariant sets after some certain moments. Then we obtain that the quantizer is unsaturated, and thus the quantization errors are bounded under the time-varying logarithm quantization strategy. On that basis, we obtain that the closed-loop system is asymptotic convergent. A benchmark example is given to show the usefulness of the proposed methods, and the comparison results are illustrated.

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.

Sign in / Sign up

Export Citation Format

Share Document