scholarly journals Discrete-Time Robust Control With an Anticipative Action for Preview Systems

2018 ◽  
Vol 141 (3) ◽  
Author(s):  
Asma Achnib ◽  
Tudor-Bogdan Airimitoaie ◽  
Patrick Lanusse ◽  
Sergey Abrashov ◽  
Mohamed Aoun ◽  
...  
Keyword(s):  
Robust Control ◽  
Discrete Time ◽  
Controller Design ◽  
Design Method ◽  
Reference Signal ◽  
Feedback Controller ◽  
Water Tank ◽  
Level Control ◽  
Model Uncertainties ◽  
Crone Control

A discrete-time robust controller design method is proposed for optimal tracking of future references in preview systems. In the context of preview systems, it is supposed that future values of the reference signal are available a number of time steps ahead. The objective is to design a control algorithm that minimizes a quadratic error between the reference and the output of the system and at the same time achieves a good level of the control signal. The proposed solution combines a robust feedback controller with a feedforward anticipative filter. The feedback controller's purpose is to assure robustness of the closed-loop system to model uncertainties. Any robust control methodology can be used (such as μ-synthesis, qft, or crone control). The focus of this paper will be on the design of the feedforward action in order to introduce the anticipative effect with respect to known future values of the reference signal without hindering the robustness achieved through the feedback controller. As such, the model uncertainties are taken into account also in the design of the feedforward anticipative filter. The proposed solution is validated in simulation and on an experimental water tank level control system.

scholarly journals Design of a Preview Controller for Discrete-Time Systems Based on LMI

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Li Li ◽  
Fucheng Liao
Keyword(s):  
Steady State ◽  
Discrete Time ◽  
Controller Design ◽  
Design Method ◽  
Reference Signal ◽  
Original System ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Discrete Time Systems ◽  
Time Systems

A preview controller design method for discrete-time systems based on LMI is proposed. First, we use the difference between a system state and its steady-state value, instead of the usual difference between system states, to transform the tracking problem into a regulator problem. Then, based on the Lyapunov stability theory and linear matrix inequality (LMI) approach, the preview controller ensuring asymptotic stability of the closed-loop system for the derived augmented error system is found. And an extended functional observer is designed in this paper which can achieve disturbance attenuation in the estimation process; as a result, the state of the system can be reconstructed rapidly and accurately. The controller gain matrix is obtained by solving an LMI problem. By incorporating the controller obtained into the original system, we obtain the preview controller of the system under consideration. To make sure that the output tracks the reference signal without steady-state error, an integrator is introduced. The numerical simulation example also illustrates the effectiveness of the results in the paper.

Application of CRONE Control to a Sampled Time Varying System With Periodic Coefficients

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Jocelyn Sabatier ◽  
Aitor Garcia Iturricha ◽  
Mathieu Moze ◽  
Alain Oustaloup
Keyword(s):  
Robust Control ◽  
Frequency Domain ◽  
Discrete Time ◽  
Time Varying ◽  
Periodic Coefficients ◽  
Crone Control ◽  
Time Varying Systems

An application of CRONE robust control extended to discrete-time-varying systems with periodic coefficients is presented. The application is carried out in the frequency domain through the representation of considered systems using time varying z-transforms and time varying pseudofrequency responses.

H∞ Preview Control for Discrete-Time Systems

1999 ◽  
Vol 123 (1) ◽  
pp. 117-124 ◽  
Author(s):  
Chintae Choi ◽  
Tsu-Chin Tsao
Keyword(s):  
Discrete Time ◽  
Controller Design ◽  
Problem Formulation ◽  
Strip Thickness ◽  
Feedback Controller ◽  
Algebraic Riccati Equation ◽  
Worst Case ◽  
The Future ◽  
Unknown Disturbances ◽  
Tandem Cold Mill

A preview controller to be able to prepare a plant with the future information for external disturbances will guarantee better performance to suppress their effects. A design approach for the optimal H∞ preview controller in the discrete-time domain is given. The preview and feedback controller are simultaneously designed to minimize the worst case RMS value of the regulated variables when the bounded unknown disturbances and the previewable disturbances hit the dynamic plants. Thus, a state feedback controller and the related preview controller are derived in this design, even though problem formulation and solving an algebraic Riccati equation are based on the full-information H∞ controller design scheme. The performance of the proposed preview controller is simulated with a rolling stand of the tandem cold mill in the steel-making works. The objective of the control system for the rolling stand is to minimize thickness error of the exit strip and tension variation between stands simultaneously. The entry strip thickness to the stand and the roll gap variation are considered as previewable disturbances, since they can be measured and estimated. The future informations of these physical variables are utilized in the preview controller to suppress their effects on the exit strip thickness and the inter-stand tension. The simulation results shows that the H∞ preview controller is effective to satisfy the requirements for the thickness and the tension.

Delay-Dependent Robust Control for Discrete-Time Uncertain Stochastic Systems With Time-Varying Delays

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Cheung-Chieh Ku ◽  
Guan-Wei Chen
Keyword(s):  
Robust Control ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Design Method ◽  
Sufficient Conditions ◽  
Jensen Inequality ◽  
Linear Matrix ◽  
Time Varying ◽  
Gain Scheduled Controller ◽  
Delay Dependent

This paper investigates a delay-dependent robust control problem of discrete-time uncertain stochastic systems with delays. The uncertainty considered in this paper is time-varying but norm-bounded, and the delays are considered as interval time-varying case for both state and input. According to the considerations of uncertainty, stochastic behavior, and time delays, the problem considered in this paper is more general than the existing works for uncertain stochastic systems. Via the proposed Lyapunov–Krasovskii function, some sufficient conditions are derived into the extended linear matrix inequality form. Moreover, Jensen inequality and free matrix equation are employed to reduce conservatism of those conditions. Through using the proposed design method, a gain-scheduled controller is designed to guarantee asymptotical stability of uncertain stochastic systems in the sense of mean square. Finally, two numerical examples are provided to demonstrate applicability and effectiveness of the proposed design method.

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