Robust Simultaneous Stabilization Using Derivative State Feedback

2020 ◽  
Vol 15 (5) ◽  
Author(s):  
Venkatesh Suresh Deshmukh
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Diophantine Equations ◽  
Initial Conditions ◽  
Numerical Study ◽  
External Disturbance ◽  
Multiple Input Multiple Output ◽  
Simultaneous Stabilization ◽  
Switched Linear System ◽  
Single Input Single Output

Abstract In simultaneous stabilization of continuous time switched linear system models of inertially coupled dynamic systems with bounded persistent external disturbance and internal parameter variations, the generalized proportional integral derivative (PID) controller suffers from a serious drawback. It loses the ability to guarantee exponential stability of the closed-loop error response, which is the difference between the actual and the desired closed-loop responses. The high value of the hardware gain has no control over the situation. On the contrary, the derivative state feedback (DSF) controller effectively employs the hardware gain in diminishing the effects of external and internal disturbances. These facts are proved and illustrated by suitable examples. The proposed method of simultaneous stabilization is shown to be an easier alternative to solve Diophantine equations encountered. The method for single input single output (SISO) systems is also shown to extend seamlessly to the control of multiple input multiple output (MIMO) square models with equal number of inputs and outputs. The shortcoming of the method is pointed out when the models are not square. The advantages of the proposed methodology over the existing methods are outlined. Finally, an efficient time domain simulation scheme is presented for the numerical study of such models in time and transfer function domain with nonzero initial conditions.

Observer-Based Control of a Class of Switched Fuzzy Systems

2014 ◽  
Vol 945-949 ◽  
pp. 2539-2542
Author(s):  
Hong Yang ◽  
Huan Huan Lü ◽  
Le Zhang
Keyword(s):  
Fuzzy System ◽  
Fuzzy Systems ◽  
Function Method ◽  
State Feedback ◽  
Closed Loop ◽  
External Disturbance ◽  
Asymptotically Stable ◽  
Closed Loop System ◽  
Lyapunov Function Method ◽  
Switching State

For the non-measurable states, a control of switched fuzzy systems is presented based on observer. Using switching technique and multiple Lyapunov function method, the fuzzy observer is built to ensure that for all allowable external disturbance the relevant closed-loop system is asymptotically stable. Moreover, switching strategy achieving system global asymptotic stability of the switched fuzzy system is given. In this model, a switching state feedback controller is presented. A simulation shows the feasibility and the effectiveness of the method.

scholarly journals Boundary stabilization and disturbance rejection for an unstable time fractional diffusion-wave equation

2022 ◽  
Author(s):  
Hua-Cheng Zhou ◽  
Ze-Hao Wu ◽  
Bao-Zhu Guo ◽  
Yangquan Chen
Keyword(s):  
Output Feedback ◽  
Disturbance Rejection ◽  
State Feedback ◽  
Closed Loop ◽  
External Disturbance ◽  
Fractional Diffusion ◽  
Loop System ◽  
Boundary Stabilization ◽  
Closed Loop System ◽  
Diffusion Wave

In this paper, we study boundary stabilization and disturbance rejection problem for an unstable time fractional diffusion-wave equation with Caputo time fractional derivative. For the case of no boundary external disturbance, both state feedback control and output feedback control via Neumann boundary actuation are proposed by the classical backstepping method. It is proved that the state feedback makes the closed-loop system Mittag-Leffler stable and the output feedback makes the closed-loop system asymptotically stable. When there is boundary external disturbance, we propose a disturbance estimator constructed by two infinite dimensional auxiliary systems to recover the external disturbance. A novel control law is then designed to compensate for the external disturbance in real time, and rigorous mathematical proofs are presented to show that the resulting closed-loop system is Mittag-Leffler stable and the states of all subsystems involved are uniformly bounded. As a result, we completely resolve, from a theoretical perspective, two long-standing unsolved mathematical control problems raised in [Nonlinear Dynam., 38(2004), 339-354] where all results were verified by simulations only.

scholarly journals Robust Position Control of a Two-Sided 1-DoF Impacting Mechanical Oscillator Subject to an External Persistent Disturbance by Means of a State-Feedback Controller

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Firas Turki ◽  
Hassène Gritli ◽  
Safya Belghith
Keyword(s):  
State Feedback ◽  
Position Control ◽  
External Disturbance ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Mechanical Oscillator ◽  
Impact Oscillator ◽  
State Feedback Controller ◽  
The Impact

This paper proposes a state-feedback controller using the linear matrix inequality (LMI) approach for the robust position control of a 1-DoF, periodically forced, impact mechanical oscillator subject to asymmetric two-sided rigid end-stops. The periodic forcing input is considered as a persistent external disturbance. The motion of the impacting oscillator is modeled by an impulsive hybrid dynamics. Thus, the control problem of the impact oscillator is recast as a problem of the robust control of such disturbed impulsive hybrid system. To synthesize stability conditions, we introduce the S-procedure and the Finsler lemmas by only considering the region within which the state evolves. We show that the stability conditions are first expressed in terms of bilinear matrix inequalities (BMIs). Using some technical lemmas, we convert these BMIs into LMIs. Finally, some numerical results and simulations are given. We show the effectiveness of the designed state-feedback controller in the robust stabilization of the position of the impact mechanical oscillator under the disturbance.

scholarly journals Angle Estimation for MIMO Radar in the Presence of Gain-Phase Errors with One Instrumental Tx/Rx Sensor: A Theoretical and Numerical Study

2021 ◽  
Vol 13 (15) ◽  
pp. 2964
Author(s):  
Fangqing Wen ◽  
Junpeng Shi ◽  
Xinhai Wang ◽  
Lin Wang
Keyword(s):  
Numerical Study ◽  
Multiple Input Multiple Output ◽  
Mimo Radar ◽  
Phase Errors ◽  
Direction Of Departure ◽  
Multiple Input ◽  
Input Multiple Output ◽  
Angle Pair ◽  
Parallel Factor ◽  
Parafac Decomposition

Ideal transmitting and receiving (Tx/Rx) array response is always desirable in multiple-input multiple-output (MIMO) radar. In practice, nevertheless, Tx/Rx arrays may be susceptible to unknown gain-phase errors (GPE) and yield seriously decreased positioning accuracy. This paper focuses on the direction-of-departure (DOD) and direction-of-arrival (DOA) problem in bistatic MIMO radar with unknown gain-phase errors (GPE). A novel parallel factor (PARAFAC) estimator is proposed. The factor matrices containing DOD and DOA are firstly obtained via PARAFAC decomposition. One DOD-DOA pair estimation is then accomplished from the spectrum searching. Thereafter, the remainder DOD and DOA are achieved by the least squares technique with the previous estimated angle pair. The proposed estimator is analyzed in detail. It only requires one instrumental Tx/Rx sensor, and it outperforms the state-of-the-art algorithms. Numerical simulations verify the theoretical advantages.

State Feedback Robust H∞ Control for Generalized Discrete System and Simulation

2013 ◽  
Vol 467 ◽  
pp. 621-626
Author(s):  
Chen Fang ◽  
Jiang Hong Shi ◽  
Kun Yu Li ◽  
Zheng Wang
Keyword(s):  
Discrete System ◽  
State Feedback ◽  
Closed Loop ◽  
The State ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Robust Controller ◽  
Closed Loop Systems

For a class of uncertain generalized discrete linear system with norm-bounded parameter uncertainties, the state feedback robust control problem is studied. One sufficient condition for the solvability of the problem and the state feedback robust controller are obtained in terms of linear matrix inequalities. The designed controller guarantees that the closed-loop systems is regular, causal, stable and satisfies a prescribed norm bounded constraint for all admissible uncertain parameters under some conditions. The result of the normal discrete system can be regarded as a particular form of our conclusion. A simulation example is given to demonstrate the effectiveness of the proposed method.

The Swing Control of Cranes with Variable Rope Length Based on Linear Time Varying System Theory

2012 ◽  
Vol 461 ◽  
pp. 763-767
Author(s):  
Li Fu Wang ◽  
Zhi Kong ◽  
Xin Gang Wang ◽  
Zhao Xia Wu
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Linear Time ◽  
Feedback Stabilization ◽  
Time Varying ◽  
Closed Loop System ◽  
Overhead Cranes ◽  
Time Varying Systems ◽  
Time Invariant ◽  
Time Invariant System

In this paper, following the state-feedback stabilization for time-varying systems proposed by Wolovich, a controller is designed for the overhead cranes with a linearized parameter-varying model. The resulting closed-loop system is equivalent, via a Lyapunov transformation, to a stable time-invariant system of assigned eigenvalues. The simulation results show the validity of this method.

High-Performance Motion Control With Slosh: A Constrained Sliding Mode Approach

2008 ◽  
Author(s):  
Hanz Richter ◽  
Kedar B. Karnik
Keyword(s):  
High Speed ◽  
High Performance ◽  
Design Methodology ◽  
Closed Loop ◽  
Sliding Mode ◽  
Initial Conditions ◽  
Rectilinear Motion ◽  
Industrial Setting ◽  
Open Container ◽  
Nominal Performance

The problem of controlling the rectilinear motion of an open container without exceeding a prescribed liquid level and other constraints is considered using a recently-developed constrained sliding mode control design methodology based on invariant cylinders. A conventional sliding mode regulator is designed first to address nominal performance in the sliding mode. Then an robustly-invariant cylinder is constructed and used to describe the set of safe initial conditions from which the closed-loop controller can be operated without constraint violation. Simulations of a typical transfer illustrate the usefulness of the method in an industrial setting. Experimental results corresponding to a high-speed transfer validate the theory.

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