Control of chaos in nonlinear systems with time-periodic coefficients

2006 ◽  
Vol 364 (1846) ◽  
pp. 2417-2432 ◽  
Author(s):  
S.C Sinha ◽  
Alexandra Dávid
Keyword(s):  
Nonlinear Systems ◽  
Periodic Orbit ◽  
Nonlinear Control ◽  
State Feedback ◽  
State Feedback Control ◽  
Control Technique ◽  
Periodic Coefficients ◽  
Full State ◽  
Full State Feedback ◽  
Time Periodic

In this study, some techniques for the control of chaotic nonlinear systems with periodic coefficients are presented. First, chaos is eliminated from a given range of the system parameters by driving the system to a desired periodic orbit or to a fixed point using a full-state feedback. One has to deal with the same mathematical problem in the event when an autonomous system exhibiting chaos is desired to be driven to a periodic orbit. This is achieved by employing either a linear or a nonlinear control technique. In the linear method, a linear full-state feedback controller is designed by symbolic computation. The nonlinear technique is based on the idea of feedback linearization. A set of coordinate transformation is introduced, which leads to an equivalent linear system that can be controlled by known methods. Our second idea is to delay the onset of chaos beyond a given parameter range by a purely nonlinear control strategy that employs local bifurcation analysis of time-periodic systems. In this method, nonlinear properties of post-bifurcation dynamics, such as stability or rate of growth of a limit set, are modified by a nonlinear state feedback control. The control strategies are illustrated through examples. All methods are general in the sense that they can be applied to systems with no restrictions on the size of the periodic terms.

Full-State Feedback Control of a Variable-Speed Wind Turbine: A Comparison of Periodic and Constant Gains

2001 ◽  
Vol 123 (4) ◽  
pp. 319-326 ◽  
Author(s):  
Karl Stol ◽  
Mark Balas
Keyword(s):  
Wind Turbine ◽  
Degrees Of Freedom ◽  
State Feedback ◽  
State Feedback Control ◽  
Variable Speed ◽  
Horizontal Axis Wind Turbine ◽  
Speed Regulation ◽  
Significant Difference ◽  
Full State ◽  
Full State Feedback

An investigation of the performance of a model-based periodic gain controller is presented for a two-bladed, variable-speed, horizontal-axis wind turbine. Performance is based on speed regulation using full-span collective blade pitch. The turbine is modeled with five degrees-of-freedom; tower fore-aft bending, nacelle yaw, rotor position, and flapwise bending of each blade. An attempt is made to quantify what model degrees-of-freedom make the system most periodic, using Floquet modal properties. This justifies the inclusion of yaw motion in the model. Optimal control ideas are adopted in the design of both periodic and constant gain full-state feedback controllers, based on a linearized periodic model. Upon comparison, no significant difference in performance is observed between the two types of control in speed regulation.

scholarly journals Frequency-Adaptive Current Controller Design Based on LQR State Feedback Control for a Grid-Connected Inverter under Distorted Grid

Energies ◽  
2018 ◽  
Vol 11 (10) ◽  
pp. 2674 ◽  
Author(s):  
Rizka Bimarta ◽  
Thuy Vi Tran ◽  
Kyeong-Hwa Kim
Keyword(s):  
Feedback Control ◽  
Discrete Time ◽  
State Feedback ◽  
State Feedback Control ◽  
Frequency Variation ◽  
Grid Voltage ◽  
Frequency Information ◽  
Full State ◽  
Full State Feedback ◽  
Grid Connected Inverter

This paper proposes a frequency-adaptive current control design for a grid-connected inverter with an inductive–capacitive–inductive (LCL) filter to overcome the issues relating to both the harmonic distortion and frequency variation in the grid voltage. The current control scheme consists of full-state feedback control to stabilize the system and integral control terms to track the reference in the presence of disturbance and uncertainty. In addition, the current controller is augmented with resonant control terms to mitigate the harmonic component. The control scheme is implemented in the synchronous reference frame (SRF) to effectively compensate two harmonic orders at the same time by using only one resonant term. Moreover, to tackle the frequency variation issue in grid voltage, the frequency information which is extracted from the phase-locked loop (PLL) block is processed by a moving average filter (MAF) for the purpose of eliminating the frequency fluctuation caused by the harmonically distorted grid voltage. The filtered frequency information is employed to synthesize the resonant controller, even in the environment of frequency variation. To implement full-state feedback control for a grid-connected inverter with an LCL filter, all the state variables should be available. However, the increase in number of sensing devices leads to the rise of cost and complexity for hardware implementation. To overcome this challenge, a discrete-time full-state current observer is introduced to estimate all the system states. When the grid frequency is subject to variation, the discrete-time implementation of the observer in the SRF requires an online discretization process because the system matrix in the SRF includes frequency information. This results in a heavy computational burden for the controller. To resolve such a difficulty, a discrete-time observer in the stationary reference frame is employed in the proposed scheme. In the stationary frame, the discretization of the system model can be accomplished with a simple offline method even in the presence of frequency variation since the system matrix does not include the frequency. To select desirable gains for the full-state feedback controller and full-state observer, an optimal linear quadratic control approach is applied. To validate the practical effectiveness of the proposed frequency-adaptive control, simulation and experimental results are presented.

scholarly journals Full-State Feedback Control Design for Shape Formation using Linear Quadratic Regulator

2020 ◽  
Vol 2 (2) ◽  
pp. 83
Author(s):  
Muhamad Rausyan Fikri ◽  
Djati Wibowo Djamari
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
Linear Quadratic Regulator ◽  
State Feedback Control ◽  
Linear Quadratic ◽  
Shape Formation ◽  
Full State ◽  
Full State Feedback ◽  
Input Response ◽  
Agent Coordination

This study investigated the capability of a group of agents to form a desired shape formation by designing the feedback control using a linear quadratic regulator. In real application, the state condition of agents may change due to some particular problems such as a slow input response. In order to compensate for the problem that affects agent-to-agent coordination, a robust regulator was implemented into the formation algorithm. In this study, a linear quadratic regulator as the full-state feedback of robust regulator method for shape formation was considered. The result showed that a group of agents can form the desired shape (square) formation with a modification of the trajectory shape of each agent. The results were validated through numerical experiments.

scholarly journals Stability Control of Double Inverted Pendulum on a Cart Using Full State Feedback with H infinity and H 2 Controllers

2020 ◽  
Author(s):  
Mustefa Jibril ◽  
Messay Tadese ◽  
Reta Degefa
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
Inverted Pendulum ◽  
Stability Control ◽  
State Feedback Control ◽  
Superior Performance ◽  
Lagrange Equations ◽  
H Infinity ◽  
Full State ◽  
Full State Feedback

In this paper a full state feedback control of a double inverted pendulum on a cart (DIPC) are designed and compared. Modeling is based on Euler-Lagrange equations derived by specifying a Lagrangian, difference between kinetic and potential energy of the DIPC system. A full state feedback control with H infinity and H 2 is addressed. Two approaches are tested: open loop impulse response and a double inverted pendulum on a cart with full state feedback H infinity and H 2 controllers. Simulations reveal superior performance of the double inverted pendulum on a cart with full state feedback H infinity controller.

scholarly journals Stability Control of Double Inverted Pendulum on a Cart using Full State Feedback with H infinity and H 2 Controllers

2020 ◽  
Author(s):  
Mustefa Jibril ◽  
Messay Tadese ◽  
Reta Degefa
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
Inverted Pendulum ◽  
Stability Control ◽  
State Feedback Control ◽  
Superior Performance ◽  
Lagrange Equations ◽  
H Infinity ◽  
Full State ◽  
Full State Feedback

In this paper a full state feedback control of a double inverted pendulum on a cart (DIPC) are designed and compared. Modeling is based on Euler-Lagrange equations derived by specifying a Lagrangian, difference between kinetic and potential energy of the DIPC system. A full state feedback control with H infinity and H 2 is addressed. Two approaches are tested: open loop impulse response and a double inverted pendulum on a cart with full state feedback H infinity and H 2 controllers. Simulations reveal superior performance of the double inverted pendulum on a cart with full state feedback H infinity controller.

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