scholarly journals Design of an optimal preview controller for linear discrete-time periodic systems

2021 ◽  
pp. 014233122110025
Author(s):  
Mengyuan Sun ◽  
Fucheng Liao ◽  
Jiamei Deng
Keyword(s):  
Control Problem ◽  
Discrete Time ◽  
Tracking Control ◽  
Reference Signal ◽  
Periodic Systems ◽  
Augmented System ◽  
The Difference ◽  
System States ◽  
Ordinary Time ◽  
Time Periodic

In this paper, the preview tracking control problem for linear discrete-time periodic systems is considered. First, to overcome the difficulty arising from periodicity of the system, the linear discrete-time periodic system is transformed into an ordinary time-invariant system by lifting method. Secondly, the difference between a system state and its steady-state value is used to derive an augmented system instead of the usual difference between system states. Then, the preview controller for the augmented system is proposed by the preview control theory, which solves the preview tracking control problem for the periodic systems. Moreover, an integrator is introduced to ensure that the output can track the reference signal without static error. Finally, the obtained results are illustrated by the simulation examples.

Preview tracking control for discrete-time nonlinear Lur’e systems with sector-bounded nonlinearities

2018 ◽  
Vol 41 (10) ◽  
pp. 2726-2737 ◽  
Author(s):  
Xiao Yu ◽  
Fucheng Liao
Keyword(s):  
Discrete Time ◽  
Tracking Control ◽  
Tracking Error ◽  
Original System ◽  
Auxiliary Variable ◽  
Lur’E Systems ◽  
Reference Information ◽  
Lpv System ◽  
The Difference ◽  
System States

In this paper, the problem of preview tracking control for a class of discrete-time nonlinear Lur’e systems is investigated. To overcome the difficulty arising from the sector nonlinearity, the original system is transformed into a linear parameter varying (LPV) system, and a new auxiliary method is introduced. The difference between the state vector and the auxiliary variable is used instead of the usual difference between system states. At the same time, the tracking error and the previewable future reference information are also considered in order to construct an augmented error system (AES). Then, the preview tracking problem is reduced to a robust control problem. Note that the AES is still an LPV system. Next, a state feedback controller is developed to ensure that the closed-loop system is asymptotically stable with H∞ guaranteed cost performance. Based on this, a preview controller for the original system is proposed. Finally, two numerical examples are provided to illustrate the effectiveness of the controller.

Design of a robust H∞ preview controller for a class of uncertain discrete-time systems

2017 ◽  
Vol 40 (8) ◽  
pp. 2639-2650 ◽  
Author(s):  
Li Li ◽  
Fucheng Liao
Keyword(s):  
Discrete Time ◽  
Reference Signal ◽  
Lyapunov Stability Theory ◽  
Interference Rejection ◽  
Discrete Time Systems ◽  
Controller Gain ◽  
Error System ◽  
The Difference ◽  
System States ◽  
Time Systems

The robust preview tracking control problem of uncertain discrete-time systems satisfying matching conditions is considered. First, we use the difference between a system state and its steady-state value, instead of the usual difference between system states, to derive an augmented error system that includes the future information on the reference signal and disturbance signal to transform the tracking problem into a regulator problem. Then, a robust preview controller of the augmented error system is proposed by integrating Lyapunov stability theory and LMI approach. Research shows that the preview controller gain matrix can be determined by solving a LMI. The proposed robust preview controller in this paper cannot only guarantee the asymptotic stability of the closed-loop system, but also enhance the interference rejection properties. An integrator is applied to make sure that the output tracks the reference signal with no static error. The numerical simulation example also illustrates the effectiveness of the results presented in the paper.

scholarly journals Optimal Preview Control for Linear Discrete-Time Periodic Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Fucheng Liao ◽  
Mengyuan Sun ◽  
Usman
Keyword(s):  
Discrete Time ◽  
Original Problem ◽  
Control Method ◽  
Original System ◽  
Periodic Systems ◽  
Invariant System ◽  
Preview Control ◽  
Time Invariant ◽  
Time Periodic ◽  
Time Invariant System

In this paper, the optimal preview tracking control problem for a class of linear discrete-time periodic systems is investigated and the method to design the optimal preview controller for such systems is given. Initially, by fully considering the characteristic that the coefficient matrices are periodic functions, the system can be converted into a time-invariant system through lifting method. Then, the original problem is also transformed into the scenario of time-invariant system. Later on, the augmented system is constructed and the preview controller of the original system is obtained with the help of existing preview control method. The controller comprises integrator, state feedback, and preview feedforward. Finally, the simulation example shows the effectiveness of the proposed preview controller in improving the tracking performance of the close-loop system.

Robust H2 perfomance of discrete-time periodic systems: LMIs with reduced dimensions

2008 ◽  
Vol 41 (2) ◽  
pp. 1348-1353 ◽  
Author(s):  
Dimitri Peaucelle ◽  
Yoshio Ebihara ◽  
Denis Arzelier
Keyword(s):  
Discrete Time ◽  
Periodic Systems ◽  
Reduced Dimensions ◽  
Time Periodic
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