A Spectral Factorization Approach to the Discrete-Time Singular LQ Regulation Problem

2011 ◽  
Author(s):  
Wataru Kase ◽  
Yasuhiko Mutoh
Keyword(s):  
Discrete Time ◽  
Spectral Factorization ◽  
Phase Image ◽  
Minimum Phase ◽  
Factorization Approach ◽  
Lq Problem

In this paper, a solution to the discrete-time singular LQ problem for a non-square plant will be discussed. It will be shown that the solution is given by an inverted interactorizing gain for the minimum phase image of some squarizing systems. An interactor matrix plays an important role for deriving the minimum phase image.

Experimental Study of NMP Sample and Hold Input Using an Inverted Pendulum

2018 ◽  
Author(s):  
Yingxu Wang ◽  
Guoming G. Zhu ◽  
Ranjan Mukherjee
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Inverted Pendulum ◽  
Linear Quadratic Regulator ◽  
Sampling Period ◽  
Minimum Phase ◽  
Discrete Time System ◽  
Linear Quadratic ◽  
Sample And Hold ◽  
Control Configuration

Early research showed that a zero-order hold is able to convert a continuous-time non-minimum-phase (NMP) system to a discrete-time minimum-phase (MP) system with a sufficiently large sampling period. However the resulting sample period is often too large to adequately cover the original NMP system dynamics and hence not suitable for control application to take advantage of a discrete-time MP system. This problem was solved using different sample and hold inputs (SHI) to reduce the sampling period significantly for MP discrete-time system. Three SHIs were studied analytically and they are square pulse, forward triangle and backward triangle SHIs. To validate the finding experimentally, a dual-loop linear quadratic regulator (LQR) control configuration is designed for the Quanser single inverted pendulum (SIP) system, where the SIP system is stabilized using the Quanser continuous-time LQR (the first loop) and an additional discrete-time LQR (the second loop) with the proposed SHIs to reduce the cart oscillation. The experimental results show more than 75% reduction of the steady-state cart displacement variance over the single-loop Quanser controller and hence demonstrated the effectiveness of the proposed SHI.

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