scholarly journals Analysis of the stability of multi-mode systems with approximating nonlinear control laws

2021 ◽  
Vol 872 (1) ◽  
pp. 012010
Author(s):  
E A Shakhray ◽  
E V Lubentsova ◽  
V F Lubentsov ◽  
M V Meflekh
Keyword(s):  
Nonlinear Control ◽  
Control Laws ◽  
The Stability ◽  
Multi Mode

Stabilizing Feedback Controls for Nonlinear Hamiltonian Systems and Nonconservative Bilinear Systems in Elasticity

1982 ◽  
Vol 104 (1) ◽  
pp. 27-32 ◽  
Author(s):  
S. N. Singh
Keyword(s):  
Asymptotic Stability ◽  
Hamiltonian Systems ◽  
Attitude Control ◽  
Sufficient Conditions ◽  
Bilinear Systems ◽  
Feedback Controls ◽  
Control Laws ◽  
Nonlinear Maps ◽  
The Stability ◽  
Necessary And Sufficient

Using the invariance principle of LaSalle [1], sufficient conditions for the existence of linear and nonlinear control laws for local and global asymptotic stability of nonlinear Hamiltonian systems are derived. An instability theorem is also presented which identifies the control laws from the given class which cannot achieve asymptotic stability. Some of the stability results are based on certain results for the univalence of nonlinear maps. A similar approach for the stabilization of bilinear systems which include nonconservative systems in elasticity is used and a necessary and sufficient condition for stabilization is obtained. An application to attitude control of a gyrostat Satellite is presented.

scholarly journals Smooth enlargement of human standing sway by instability due to weak reaction floor and noise

2016 ◽  
Vol 3 (1) ◽  
pp. 150570 ◽  
Author(s):  
Tetsuro Funato ◽  
Shinya Aoi ◽  
Nozomi Tomita ◽  
Kazuo Tsuchiya
Keyword(s):  
Nonlinear Control ◽  
Neurological Disorders ◽  
System Model ◽  
Quiet Standing ◽  
Body Sway ◽  
Intermittent Control ◽  
Dynamic Reaction ◽  
Weak Reaction ◽  
Integral Control ◽  
The Stability

Human quiet standing is accompanied by body sway. The amplitude of this body sway is known to be larger than would be predicted from simple noise effects, and sway characteristics are changed by neurological disorders. This large sway is thought to arise from nonlinear control with prolonged periods of no control (intermittent control), and a nonlinear control system of this kind has been predicted to exhibit bifurcation. The presence of stability-dependent transition enables dynamic reaction that depends on the stability of the environment, and can explain the change in sway characteristics that accompanies some neurological disorders. This research analyses the characteristics of a system model that induces transition, and discusses whether human standing reflects such a mechanism. In mathematical analysis of system models, (intermittent control-like) nonlinear control with integral control is shown to exhibit Hopf bifurcation. Moreover, from the analytical solution of the system model with noise, noise is shown to work to smooth the enlargement of sway around the bifurcation point. This solution is compared with measured human standing sway on floors with different stabilities. By quantitatively comparing the control parameters between human observation and model prediction, enlargement of sway is shown to appear as predicted by the model analysis.

Stability of a Class of Piezoelectric State-Switching Methods

2000 ◽  
Author(s):  
Andrew J. Kurdila ◽  
William W. Clark ◽  
Weijian Wang ◽  
Dwayne E. McDaniel
Keyword(s):  
Lyapunov Functions ◽  
Closed Loop ◽  
Control Strategies ◽  
Short Circuit ◽  
Open Circuit ◽  
Hybrid Dynamical Systems ◽  
Multiple Lyapunov Functions ◽  
Control Laws ◽  
State Switching ◽  
The Stability

Abstract Experimental and anecdotal evidences have shown that state-switched control strategies for piezoelectric actuators can be advantageous. However, most discussions of the stability of these systems has relied on heuristic, or physically motivated, arguments. In this paper, we show that recent open-circuit/short-circuit state-switching control laws can be viewed as hybrid dynamical systems of Witsenhausen type. Within this framework, the closed-loop stability of OC/SC switching is rigorously established using the method of multiple Lyapunov functions.

scholarly journals Analysis of Robust Stability for a Class of Stochastic Systems via Output Feedback: The LMI Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Xin-rong Cong ◽  
Long-suo Li
Keyword(s):  
Linear Matrix Inequality ◽  
Robust Stability ◽  
Output Feedback ◽  
Stochastic Systems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Convex Optimization Problem ◽  
Control Laws ◽  
The Stability ◽  
And Control

This paper investigates the robust stability for a class of stochastic systems with both state and control inputs. The problem of the robust stability is solved via static output feedback, and we convert the problem to a constrained convex optimization problem involving linear matrix inequality (LMI). We show how the proposed linear matrix inequality framework can be used to select a quadratic Lyapunov function. The control laws can be produced by assuming the stability of the systems. We verify that all controllers can robustly stabilize the corresponding system. Further, the numerical simulation results verify the theoretical analysis results.

T-S Fuzzy observer and controller of Doubly-Fed Induction Generator

2016 ◽  
Vol 7 (3) ◽  
pp. 617
Author(s):  
Fouad Abdelmalki ◽  
Najat Ouaaline
Keyword(s):  
Induction Generator ◽  
Linear Matrix ◽  
Doubly Fed Induction Generator ◽  
Quadratic Lyapunov Function ◽  
Control Laws ◽  
Fuzzy Observer ◽  
Satisfactory Performance ◽  
Doubly Fed ◽  
The Stability ◽  
Theoretical Results

This paper aims to ensure a stability and observability of doubly fed induction generator DFIG of a wind turbine based on the approach of fuzzy control type T-S PDC (Parallel Distributed Compensation) which determines the control laws by return state and fuzzy observers. First, the fuzzy TS model is used to precisely represent a nonlinear model of DFIG proposed and adopted in this work. Then, the stability analysis is based on the quadratic Lyapunov function to determine the gains that ensure the stability conditions. The fuzzy observer of DFIG is built to estimate non-measurable state vectors and the estimated states converging to the actual statements. The gains of observatory and of stability are obtained by solving a set of linear matrix inequality (LMI). Finally, numerical simulations are performed to verify the theoretical results and demonstrate satisfactory performance.

scholarly journals Target Tracking in 3-D Using Estimation Based Nonlinear Control Laws for UAVs

Aerospace ◽  
2016 ◽  
Vol 3 (1) ◽  
pp. 5 ◽  
Author(s):  
Mousumi Ahmed ◽  
Kamesh Subbarao
Keyword(s):  
Nonlinear Control ◽  
Target Tracking ◽  
Control Laws

Modeling and Experimental Testing of Hoverboard Dynamic Behavior

2017 ◽  
Author(s):  
Arnoldo Castro ◽  
William Singhose ◽  
Xiaoshu Liu ◽  
Khalid Sorensen ◽  
Eun Chan Kwak
Keyword(s):  
Dynamic Model ◽  
Dynamic Behavior ◽  
Motion Capture ◽  
Environmental Conditions ◽  
Experimental Testing ◽  
Motion Capture Data ◽  
Control Laws ◽  
Operator Action ◽  
The Stability ◽  
Unexpected Behavior

Self-balancing human transporters are naturally unstable. However, when coupled with sophisticated control laws, these machines can provide mobility within a finite stability envelope. Challenging environmental conditions, or unanticipated operator action, can cause these machines to exhibit unexpected behavior. In an effort to better understand the behavior of these systems inside and outside the stability envelope, a dynamic model of a hoverboard is presented. Motion-capture data is also presented in which an operator’s interactions with the hoverboard were recorded.

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