Optimal Control of Piece-Wise Linear Time-Invariant Periodic Control Systems

1979 ◽  
Vol 15 (1) ◽  
pp. 9-15
Author(s):  
Tadashi KITAMURA ◽  
Hajime AKASHI
Keyword(s):  
Optimal Control ◽  
Control Systems ◽  
Linear Time ◽  
Periodic Control ◽  
Linear Time Invariant ◽  
Time Invariant

Design and implementation of decoupled periodic control scheme for a laboratory-based quadruple-tank process

2021 ◽  
pp. 095965182110228
Author(s):  
Jatin K Pradhan ◽  
Arun Ghosh
Keyword(s):  
Real Time ◽  
High Frequency ◽  
Linear Time ◽  
Disturbance Attenuation ◽  
Minimum Phase ◽  
Periodic Control ◽  
Linear Time Invariant ◽  
Control Scheme ◽  
Gain Margin ◽  
Time Invariant

It is well known that linear time-invariant controllers fail to provide desired robustness margins (e.g. gain margin, phase margin) for plants with non-minimum phase zeros. Attempts have been made in literature to alleviate this problem using high-frequency periodic controllers. But because of high frequency in nature, real-time implementation of these controllers is very challenging. In fact, no practical applications of such controllers for multivariable plants have been reported in literature till date. This article considers a laboratory-based, two-input–two-output, quadruple-tank process with a non-minimum phase zero for real-time implementation of the above periodic controller. To design the controller, first, a minimal pre-compensator is used to decouple the plant in open loop. Then the resulting single-input–single-output units are compensated using periodic controllers. It is shown through simulations and real-time experiments that owing to arbitrary loop-zero placement capability of periodic controllers, the above decoupled periodic control scheme provides much improved robustness against multi-channel output gain variations as compared to its linear time-invariant counterpart. It is also shown that in spite of this improved robustness, the nominal performances such as tracking and disturbance attenuation remain almost the same. A comparison with [Formula: see text]-linear time-invariant controllers is also carried out to show superiority of the proposed scheme.

scholarly journals Data-Driven Optimal Control of Linear Time-Invariant Systems

2020 ◽  
Vol 53 (2) ◽  
pp. 7191-7196
Author(s):  
Dzmitry Kastsiukevich ◽  
Natalia Dmitruk
Keyword(s):  
Optimal Control ◽  
Linear Time ◽  
Data Driven ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Time Invariant

Near Energy Optimal Control Allocation for Dual-Input Over-Actuated Systems

2016 ◽  
Author(s):  
Molong Duan ◽  
Chinedum Okwudire
Keyword(s):  
Optimal Control ◽  
Optimal Allocation ◽  
Linear Time ◽  
Control Allocation ◽  
Static System ◽  
Time Step ◽  
Control Effort ◽  
Linear Time Invariant ◽  
Time Invariant ◽  
Feed Drive System

This paper proposes a method for near energy optimal allocation of control effort in dual-input over-actuated systems using a linear time-invariant (LTI) controller. The method assumes a quadratic energy cost functional, and the non-causal energy optimal control ratio within the redundant actuation space is defined. Near energy optimal control allocation is addressed by using a LTI controller to align the control inputs with a causal approximation of the energy optimal control ratio. The use of a LTI controller for control allocation leads to low computation burden compared to techniques in the literature which require optimization at each time step. Moreover, the proposed method achieves broadband, near optimal control allocation, as opposed to traditional allocation methods which make use of a static system model for control allocation. The proposed method is validated through simulations and experiments on an over-actuated hybrid feed drive system. Significant improvements in energy efficiency without sacrificing positioning performance are demonstrated.

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