scholarly journals Feedback control of chaotic systems using multiple shooting shadowing and application to Kuramoto–Sivashinsky equation

2020 ◽  
Vol 476 (2240) ◽  
pp. 20200322
Author(s):  
Karim Shawki ◽  
George Papadakis
Keyword(s):  
Feedback Control ◽  
Chaotic Systems ◽  
Adjoint Equation ◽  
Linear Quadratic Regulator ◽  
Multiple Shooting ◽  
Spatial Correlations ◽  
Linear Quadratic ◽  
Feedback Matrix ◽  
Standard Linear ◽  
Sivashinsky Equation

We propose an iterative method to evaluate the feedback control kernel of a chaotic system directly from the system’s attractor. Such kernels are currently computed using standard linear optimal control theory, known as linear quadratic regulator theory. This is however applicable only to linear systems, which are obtained by linearizing the system governing equations around a target state. In the present paper, we employ the preconditioned multiple shooting shadowing (PMSS) algorithm to compute the kernel directly from the nonlinear dynamics, thereby bypassing the linear approximation. Using the adjoint version of the PMSS algorithm, we show that we can compute the kernel at any point of the domain in a single computation. The algorithm replaces the standard adjoint equation (that is ill-conditioned for chaotic systems) with a well-conditioned adjoint, producing reliable sensitivities which are used to evaluate the feedback matrix elements. We apply the idea to the Kuramoto–Sivashinsky equation. We compare the computed kernel with that produced by the standard linear quadratic regulator algorithm and note similarities and differences. Both kernels are stabilizing, have compact support and similar shape. We explain the shape using two-point spatial correlations that capture the streaky structure of the solution of the uncontrolled system.

Controlling an Underactuated Two-Wheeled Mobile Robot: A Constraint-Following Approach

2019 ◽  
Vol 141 (7) ◽  
Author(s):  
Hui Yin ◽  
Ye-Hwa Chen ◽  
Dejie Yu
Keyword(s):  
Mobile Robot ◽  
Degrees Of Freedom ◽  
Control Design ◽  
Nonholonomic Constraints ◽  
Linear Quadratic Regulator ◽  
Wheeled Mobile Robot ◽  
Linear Quadratic ◽  
Control Goal ◽  
Standard Linear ◽  
Following Error

Controlling underactuated systems is a challenging problem in control engineering. This paper presents a novel constraint-following approach for control design of an underactuated two-wheeled mobile robot (2 WMR), which has two degrees-of-freedom (DOF) to be controlled but only one actuator. The control goal is to drive the 2 WMR to follow a set of constraints, which may be holonomic or nonholonomic constraints. The constraint is considered in a more general form than the previous studies on constraint-following control (hence including a wider range of constraints). No auxiliary variables or pseudo variables are required for the control design. The proposed control only uses physical variables. We show that the proposed control is able to deal with both holonomic and nonholonomic constraints by forcing the constraint-following error to converge to zero, even if the system is not initially on the constraint manifold. Using this control design, we investigate two cases regarding different constraints on the 2 WMR motion, one for a holonomic constraint and the other for a nonholonomic constraint. Simulation results show that the proposed control is able to drive the 2 WMR to follow the constraints in both cases. Furthermore, the standard linear quadratic regulator (LQR) control is applied as a comparison in the simulations, which reflects the advantage of the proposed control.

Robust Control and Synchronization of Chaotic Systems with Actuator Constraints

2015 ◽  
pp. 1-43 ◽  
Author(s):  
Kouamana Bousson ◽  
Carlos Velosa
Keyword(s):  
Robust Control ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Linear Part ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Aeroelastic System ◽  
Control Approach ◽  
Nonlinear Part ◽  
Actuator Constraints

This chapter proposes a robust control approach for the class of chaotic systems subject to magnitude and rate actuator constraints. The approach consists of decomposing the chaotic system into a linear part plus a nonlinear part to form an augmented system comprising the system itself and the integral of the output error. The resulting system is posteriorly seen as a linear system plus a bounded disturbance, and two robust controllers are applied: first, a controller based on a generalization of the Lyapunov function, then a Linear-Quadratic Regulator (LQR) with a prescribed degree of stability. Numerical simulations are performed to validate the approach applying it to the Lorenz chaotic system and to a chaotic aeroelastic system, and parameter uncertainties are also considered to prove its robustness. The results confirm the effectiveness of the approach, and the constraints are guaranteed as opposed to other control techniques which do not consider any kind of constraints.

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 Integral State Feedback Control Using Linear Quadratic Gaussian in DC-drive System

2021 ◽  
Vol 21 (2) ◽  
pp. 79
Author(s):  
Supriyanto Praptodiyono ◽  
Hari Maghfiroh ◽  
Joko Slamet Saputro ◽  
Agus Ramelan
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
Linear Quadratic Regulator ◽  
Dc Motor ◽  
Drive System ◽  
Load Test ◽  
State Feedback Control ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Dc Drive

The electric motor is one of the technological developments which can support the production process. DC motor has some advantages compared to AC motor especially on the easier way to control its speed or position as well as its widely adjustable range. The main issue in the DC motor is controlling the angular speed with uncertainty and disturbance. The alternative solution of a control method with simple, easy to design, and implementable in a multi-input multi-output system is integral state feedback such as linear quadratic Gaussian (LQG). It is a combination between linear quadratic regulator and Kalman filter. One of the advantages of this method is the usage of fewer sensors compared with the original linear quadratic regulator method which uses sensors as many as the state in the system model. The design, simulation, and experimental study of the application of LQG as state feedback control in a DC-drive system have been done. Both performance and energy were analyzed and compared with conventional proportional integral derivative (PID). The gain of LQG was determined by trial whereas the PID gain is determined from MATLAB autotuning without fine-tuning. The load test and tracking test were carried out in the experiment. Both simulation and hardware tests showed the same result which LQG is superior in integral absolute error (IAE) by up to 74.37 % in loading test compared to PID. On the other side, LQG needs more energy, it consumes higher energy by 6.34 % in the load test.

Ornithopter Trajectory Generation With Stabilization

2008 ◽  
Author(s):  
John M. Dietl ◽  
Ephrahim Garcia
Keyword(s):  
Feedback Control ◽  
Discrete Time ◽  
Trajectory Generation ◽  
Flight Dynamics ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Flight Stabilization ◽  
Rate Feedback ◽  
Periodic Linear ◽  
Time Periodic

Ornithopter flight dynamics and a method for developing flight trajectories are described. These are used to study the unstable modes in hovering ornithopter flight. Stabilization is accomplished through three strategies: pitch-rate feedback control, linear quadratic regulator, and discrete-time periodic linear quadratic regulator. The discrete time controller is the only controller tested that was capable of stabilizing position of the vehicle in hover.

A Control Scheme for an Opposed Recumbent Tandem Human-Powered Bicycle

1996 ◽  
Vol 12 (4) ◽  
pp. 480-492
Author(s):  
Scott O. Cloyd ◽  
Mont Hubbard ◽  
LeRoy W. Alaways
Keyword(s):  
Feedback Control ◽  
Linear Quadratic Regulator ◽  
Optimal Feedback Control ◽  
State Variables ◽  
Linear Quadratic ◽  
Lateral Deviation ◽  
Control Scheme ◽  
Control Schemes ◽  
Lean Angle ◽  
Human Powered

Feedback control of a human-powered single-track bicycle is investigated through the use of a linearized dynamical model in order to develop feedback gains that can be implemented by a human pilot in an actual vehicle. The object of the control scheme is to satisfy two goals: balance and tracking. The pilot should be able not only to keep the vehicle upright but also to direct the forward motion as desired. The two control inputs, steering angle and rider lean angle, are assumed to be determined by the rider as a product of feedback gains and “measured” values of the state variables: vehicle lean, lateral deviation from the desired trajectory, and their derivatives. Feedback gains are determined through linear quadratic regulator theory. This results in two control schemes, a “full” optimal feedback control and a less complicated technique that is more likely to be usable by an inexperienced pilot. Theoretical optimally controlled trajectories are compared with experimental trajectories in a lane change maneuver.

Ultra-wide bandgap in active metamaterial from feedback control

2021 ◽  
pp. 107754632110358
Author(s):  
Kamal K Bera ◽  
Arnab Banerjee
Keyword(s):  
Feedback Control ◽  
Low Frequency ◽  
Linear Quadratic Regulator ◽  
Mass Ratio ◽  
Linear Quadratic ◽  
Dispersion Diagram ◽  
Active Feedback ◽  
Frequency Regime ◽  
Active Feedback Control ◽  
Low Mass Ratio

To widen the attenuation bandwidth in a mass-in-mass metamaterial chain, active feedback control is employed within the unit cell. The optimal control via Linear Quadratic Regulator is used to ensure the stability of the solution as well as adaptive tuning of the system. The key concept is to obtain a wider bandwidth by reducing the displacement amplitude of the outer mass of each unit of the metamaterial. Transmittance for finite number of units and dispersion diagram for infinitely long metamaterial chain are obtained using the backward-substitution method and Bloch–Floquet’s theorem, respectively. Results evidenced that an ultra-wide uninterrupted attenuation band starting from very low free wave frequency can be obtained. The dispersion diagram primarily depends on the frequency ratio of the resonating unit with the external main unit. The effect of the mass ratio is insignificant while active feedback control is implemented. This unique phenomenon implies that for a very low mass ratio also a wider bandwidth can be achieved. This enables to design a lightweight structure having wider bandwidth in low-frequency regime.

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