scholarly journals Backstepping Synthesis for Feedback Control of First-Order Hyperbolic PDEs with Spatial-Temporal Actuation

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Xin Yu ◽  
Chao Xu ◽  
Huacheng Jiang ◽  
Arthi Ganesan ◽  
Guojie Zheng
Keyword(s):  
Feedback Control ◽  
Integral Transformation ◽  
Original System ◽  
Open Loop ◽  
Hyperbolic Partial Differential Equations ◽  
Target System ◽  
Control Law ◽  
Hyperbolic Pde ◽  
First Order ◽  
Boundary Control Problems

This paper deals with the stabilization problem of first-order hyperbolic partial differential equations (PDEs) with spatial-temporal actuation over the full physical domains. We assume that the interior actuator can be decomposed into a product of spatial and temporal components, where the spatial component satisfies a specific ordinary differential equation (ODE). A Volterra integral transformation is used to convert the original system into a simple target system using the backstepping-like procedure. Unlike the classical backstepping techniques for boundary control problems of PDEs, the internal actuation can not eliminate the residual term that causes the instability of the open-loop system. Thus, an additional differential transformation is introduced to transfer the input from the interior of the domain onto the boundary. Then, a feedback control law is designed using the classic backstepping technique which can stabilize the first-order hyperbolic PDE system in a finite time, which can be proved by using the semigroup arguments. The effectiveness of the design is illustrated with some numerical simulations.

Optimal Control of a Distributed Parameter, Time-Lagged River Aeration System

1975 ◽  
Vol 97 (2) ◽  
pp. 164-171 ◽  
Author(s):  
M. K. O¨zgo¨ren ◽  
R. W. Longman ◽  
C. A. Cooper
Keyword(s):  
Optimal Control ◽  
Feedback Control ◽  
Open Loop ◽  
Optimal Feedback Control ◽  
Distributed Parameter ◽  
Control Law ◽  
Optimal Controls ◽  
Distributed Parameter System ◽  
Parameter System ◽  
Characteristic Lines

The control of artificial in-stream aeration of polluted rivers with multiple waste effluent sources is treated. The optimal feedback control law for this distributed parameter system is determined by solving the partial differential equations along characteristic lines. In this process the double integral cost functional of the distributed parameter system is reduced to a single integral cost. Because certain measurements are time consuming, the feedback control law is obtained in the presence of observation delay in some but not all of the system variables. The open loop optimal control is then found, showing explicity the effect of changes in any of the effluent sources on the aeration strategy. It is shown that the optimal strategy for a distribution of sources can be written as an affine transformation upon the optimal controls for sources of unit strength.

scholarly journals Swing-up control of inverted pendulum systems

Robotica ◽  
1996 ◽  
Vol 14 (4) ◽  
pp. 397-405 ◽  
Author(s):  
Alan Bradshaw ◽  
Jindi Shao
Keyword(s):  
Feedback Control ◽  
State Feedback ◽  
Inverted Pendulum ◽  
Open Loop ◽  
State Feedback Control ◽  
Control Law ◽  
Inverted Position ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Partial State

SUMMARYIn Part I a technique for the swing-up control of single inverted pendulum system is presented. The requirement is to swing-up a carriage mounted pendulum system from its natural pendent position to its inverted position. It works for all carriage balancing single inverted pendulum systems as the swing-up control algorithm does not require knowledge of the system parameters. Comparison with previous swing-up controls shows that the proposed swing-up control is simpler, eaiser. more efficient, and more robust.In Part II the technique is extended to the case of the swing-up control of double inverted pendulum systems. Use is made of a novel selective partial-state feedback control law. The nonlinear, open-loop unstable, nonminimum-phase. and interactive MIMO pendulum system is actively linearised and decoupled about a neutrally stable equilibrium by the partial-state feedback control. This technique for swing-up control is not at all sensitive to uncertainties such as modelling error and sensor noise, and is both reliable and robust.

scholarly journals Decentralized Finite-TimeH∞Connective Control for a Class of Large-Scale Systems with Different Structural Forms

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Xiaohua Li ◽  
Yang Liu ◽  
Xiaoping Liu
Keyword(s):  
Feedback Control ◽  
Finite Time ◽  
Large Scale ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Original System ◽  
State Feedback Control ◽  
Control Law ◽  
Interconnected System ◽  
The One

Decentralized finite-timeH∞connective control problem for a class of large-scale interconnected systems is studied in this paper. The research aims at two structural forms, namely, the interconnected structure and the one with expanding construction. A new method is proposed to design a decentralized state feedback control law for a large-scale interconnected system so that the closed-loop system is finite-timeH∞connectively bounded. The sufficient conditions for the existence of such a decentralized control law are deduced by using LMI method. Another method is presented for a large-scale interconnected system with expanding construction which can be used without changing the decentralized state feedback control law of the original system to design a controller for the newly added subsystem so that both the new subsystem and the resulting expanded system are finite-timeH∞connectively bounded. The feasibility and effectiveness of the proposed method are verified by some simulation results.

Optimization approach to the constrained regulation problem for linear continuous-time fractional-order systems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Xindong Si ◽  
Hongli Yang
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
State Feedback Control ◽  
Invariant Sets ◽  
Linear Feedback ◽  
Control Law ◽  
Optimization Approach ◽  
Fractional Order Systems ◽  
Linear Feedback Control ◽  
Computational Point

AbstractThis paper deals with the Constrained Regulation Problem (CRP) for linear continuous-times fractional-order systems. The aim is to find the existence conditions of linear feedback control law for CRP of fractional-order systems and to provide numerical solving method by means of positively invariant sets. Under two different types of the initial state constraints, the algebraic condition guaranteeing the existence of linear feedback control law for CRP is obtained. Necessary and sufficient conditions for the polyhedral set to be a positive invariant set of linear fractional-order systems are presented, an optimization model and corresponding algorithm for solving linear state feedback control law are proposed based on the positive invariance of polyhedral sets. The proposed model and algorithm transform the fractional-order CRP problem into a linear programming problem which can readily solved from the computational point of view. Numerical examples illustrate the proposed results and show the effectiveness of our approach.

Open-loop adaptive feedback control of deposited zinc in hot-dip galvanizing

1993 ◽  
Vol 1 (5) ◽  
pp. 779-790 ◽  
Author(s):  
C. Fenot ◽  
F. Rolland ◽  
G. Vigneron ◽  
I.D. Landau
Keyword(s):  
Feedback Control ◽  
Open Loop ◽  
Adaptive Feedback ◽  
Adaptive Feedback Control

Semi-global output regulation for discrete-time singular linear systems with input saturation via composite nonlinear feedback control

2016 ◽  
Vol 39 (3) ◽  
pp. 352-360 ◽  
Author(s):  
Xiaoyan Lin ◽  
Dongyun Lin ◽  
Weiyao Lan
Keyword(s):  
Feedback Control ◽  
Linear Systems ◽  
Discrete Time ◽  
Input Saturation ◽  
Output Regulation ◽  
Control Law ◽  
Nonlinear Feedback Control ◽  
Nonlinear Feedback ◽  
Composite Nonlinear Feedback ◽  
Singular Linear Systems

The semi-global output regulation problem of multi-variable discrete-time singular linear systems with input saturation is investigated in this paper. A composite nonlinear feedback control law is constructed by using a low gain feedback technique for semi-global stabilisation of discrete-time singular linear systems with input saturation. The sufficient solvability conditions of the semi-global output regulation problem by composite nonlinear feedback control are established. When the composite nonlinear feedback control law is reduced to a linear control law, the solvability conditions are an exact discrete-time counterpart of the semi-global output regulation problem of continuous-time singular linear systems. With the extra control freedom of the nonlinear part in the composite nonlinear feedback control law, the transient performance of the closed-loop system can be improved by carefully choosing the linear feedback gain and the nonlinear feedback gain. The design procedure of the composite nonlinear feedback control law and the improvement of the transient performance are illustrated by a numerical example.

Feedback control law of solar sail with variable surface reflectivity at Sun-Earth collinear equilibrium points

2020 ◽  
Vol 106 ◽  
pp. 106144 ◽  
Author(s):  
Lorenzo Niccolai ◽  
Giovanni Mengali ◽  
Alessandro A. Quarta ◽  
Andrea Caruso
Keyword(s):  
Feedback Control ◽  
Equilibrium Points ◽  
Solar Sail ◽  
Control Law ◽  
Variable Surface ◽  
Surface Reflectivity

Passive optimal feedback control of an articulated flexible arm

2020 ◽  
pp. 107754632095676
Author(s):  
Raja Tebbikh ◽  
Hicham Tebbikh ◽  
Sihem Kechida
Keyword(s):  
Optimal Control ◽  
Feedback Control ◽  
Closed Loop ◽  
Open Loop ◽  
Optimal Feedback Control ◽  
Convolution Operators ◽  
High Frequencies ◽  
Zero Initial Condition ◽  
Flexible Arm ◽  
Euler Bernoulli Beam

This article deals with stabilization and optimal control of an articulated flexible arm by a passive approach. This approach is based on the boundary control of the Euler–Bernoulli beam by means of wave-absorbing feedback. Due to the specific propagative properties of the beam, such controls involve long-memory, non-rational convolution operators. Diffusive realizations of these operators are introduced and used for elaborating an original and efficient wave-absorbing feedback control. The globally passive nature of the closed-loop system gives it the unconditional robustness property, even with the parameters uncertainties of the system. This is not the case in active control, where the system is unstable, because the energy of high frequencies is practically uncontrollable. Our contribution comes in the achievement of optimal control by the diffusion equation. The proposed approach is original in considering a non-zero initial condition of the diffusion as an optimization variable. The optimal arm evolution, in a closed loop, is fixed in an open loop by optimizing a criterion whose variable is the initial diffusion condition. The obtained simulation results clearly illustrate the effectiveness and robustness of the optimal diffusive control.

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