FEEDBACK SYNCHRONIZATION USING POLE-PLACEMENT CONTROL

2000 ◽  
Vol 10 (11) ◽  
pp. 2611-2617 ◽  
Author(s):  
ROBERTO TONELLI ◽  
YING-CHENG LAI ◽  
CELSO GREBOGI
Keyword(s):  
Chaotic Systems ◽  
Pole Placement ◽  
Active Area ◽  
High Dimensions ◽  
Mutual Synchronization ◽  
Numerical Examples ◽  
Placement Method ◽  
Pole Placement Control

Synchronization in chaotic systems has become an active area of research since the pioneering work of Pecora and Carroll. Most existing works, however, rely on a passive approach: A coupling between chaotic systems is necessary for their mutual synchronization. We describe here a feedback approach for synchronizing chaotic systems that is applicable in high dimensions. We show how two chaotic systems can be synchronized by applying small feedback perturbations to one of them. We detail our strategy to design the control based on the pole-placement method, and give numerical examples.

scholarly journals Comparative Controlling of the Lorenz Chaotic System Using the SMC and APP Methods

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Ercan Köse ◽  
Aydın Mühürcü
Keyword(s):  
Chaotic System ◽  
Sliding Mode ◽  
Nonlinear Behavior ◽  
Taylor Series Expansion ◽  
Pole Placement ◽  
Control Technique ◽  
Placement Method ◽  
Feedback Matrix ◽  
Lorenz Chaotic System ◽  
Pole Placement Control

The Lorenz chaotic system is based on a nonlinear behavior and this causes the system to be unstable. Therefore, two different controller models were developed and named as the adaptive pole placement and sliding mode control (SMC) methods for the establishment of continuous time nonlinear Lorenz chaotic system. In order to achieve this, an improved controller structure was developed first theoretically for both the controller methods and then tested practically using the numerical samples. During the establishment of adaptive pole placement method for the Lorenz chaotic system, various stages were applied. The nonlinear chaotic system was also linearized by means of Taylor Series expansion processes. In addition, the feedback matrix of the adaptive pole placement method was determined using linear Jacobian matrix. The chaotic system reached an equilibrium point by using both the SMC and adaptive pole placement methods; however the simulation results of the SMC had better success than adaptive pole placement control technique.

Development of a fuzzy-state feedback regulator for stabilizing a flexible inverted pendulum system

2021 ◽  
pp. 107754632110429
Author(s):  
Pouriya Pourgholam ◽  
Hamid Moeenfard
Keyword(s):  
Fuzzy System ◽  
State Feedback ◽  
Equations Of Motion ◽  
Pole Placement ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Reduced Order Observer ◽  
Pole Placement Control ◽  
Fuzzy State

Accurate modeling and efficient control of inverted pendulums have always been a challenge for researchers. So, the current research aims to achieve the following objectives: (I) proposing a comprehensive dynamic model for the inverted pendulums which accounts for the flexibility of the pendulum bar and (II) suggesting an appropriate supervisory fuzzy-pole placement control strategy for stabilizing the pendulum system. Using a Lagrangian formulation, the equations of motion are derived and linearized. Then, a state feedback controller with a reduced-order observer is designed to stabilize the system. Closed-loop simulations reveal that at least six modes shall be considered in the dynamic equations. To improve the quality of the transient response, a novel fuzzy system is developed for real-time assignment of the controller poles. Simulation results demonstrate that the control quality is significantly improved by adding a supervisory fuzzy system to the control loop. The developed approach for dynamic modeling of the system, and the idea of multi-level fuzzy-pole placement control architecture developed in this paper, may be successfully applied to improve the response specifications in other dynamic systems.

Improved Pole-placement Control with Feed-forward Dead Zone Compensation for Position Tracking of Electro-Pneumatic Actuator System Improved Pole-placement Control with Feed-forward Dead Zone Compensation for Position Tracking of Electro-Pneumatic Actuato

2021 ◽  
Vol 20 (2) ◽  
pp. 25-32
Author(s):  
Noorhazirah Sunar ◽  
Mohd Fua’ad Rahmat ◽  
Ahmad ‘Athif Mohd Fauzi ◽  
Zool Hilmi Ismail ◽  
Siti Marhanis Osman ◽  
...  
Keyword(s):  
Dead Zone ◽  
Pneumatic Actuator ◽  
Pole Placement ◽  
Position Tracking ◽  
Zone Model ◽  
Feed Forward ◽  
The Dead ◽  
Chattering Effect ◽  
Pole Placement Controller ◽  
Pole Placement Control

Dead-zone in the valve degraded the performances of the Electro-Pneumatic Actuator (EPA) system.  It makes the system difficult to control, become unstable and leads to chattering effect nearest desired position.  In order to cater this issue, the EPA system transfer function and the dead-zone model is identified by MATLAB SI toolbox and the Particle Swarm Optimization (PSO) algorithm respectively.  Then a parametric control is designed based on pole-placement approach and combine with feed-forward inverse dead-zone compensation.  To reduce chattering effect, a smooth parameter is added to the controller output.  The advantages of using these techniques are the chattering effect and the dead-zone of the EPA system is reduced.  Moreover, the feed-forward system improves the transient performance.  The results are compared with the pole-placement control (1) without compensator and (2) with conventional dead-zone compensator.  Based on the experimental results, the proposed controller reduced the chattering effect due to the controller output of conventional dead-zone compensation, 90% of the pole-placement controller steady-state error and 30% and 40% of the pole-placement controller with conventional dead-zone compensation settling time and rise time.

scholarly journals Symmetric Oscillator: Special Features, Realization, and Combination Synchronization

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2142
Author(s):  
Victor Kamdoum Tamba ◽  
Janarthanan Ramadoss ◽  
Viet-Thanh Pham ◽  
Giuseppe Grassi ◽  
Othman Abdullah Almatroud ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Numerical Examples ◽  
Combination Synchronization ◽  
Significant Attention

Researchers have recently paid significant attention to special chaotic systems. In this work, we introduce an oscillator with different special features. In addition, the oscillator is symmetrical. The features and oscillator dynamics are discovered through different tools of nonlinear dynamics. An electronic circuit is designed to mimic the oscillator’s dynamics. Moreover, the combined synchronization of two drives and one response oscillator is reported. Numerical examples illustrate the correction of our approach.

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