A Linear Quadratic Regulator Problem for Descriptor Lumped and Distributed Systems with Discrete Time

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.

Download Full-text

Linear quadratic regulator problem governed by granular neutrosophic fractional differential equations

ISA Transactions ◽

10.1016/j.isatra.2019.08.006 ◽

2020 ◽

Vol 97 ◽

pp. 296-316 ◽

Cited By ~ 11

Author(s):

Nguyen Thi Kim Son ◽

Nguyen Phuong Dong ◽

Hoang Viet Long ◽

Le Hoang Son ◽

Alireza Khastan

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Linear Quadratic Regulator ◽

Linear Quadratic ◽

Regulator Problem ◽

Fractional Differential

Download Full-text

Calculation of Optimized Movement Trajectories for the Human Forearm

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.401-403.1347 ◽

2013 ◽

Vol 401-403 ◽

pp. 1347-1352

Author(s):

Li Li Yang

Keyword(s):

Discrete Time ◽

Linear Quadratic Regulator ◽

Minimum Variance ◽

Movement Trajectory ◽

Linear Quadratic ◽

Variance Model ◽

Movement Trajectories ◽

Human Forearm ◽

Optimal Movement ◽

Time Linear

Using the minimum variance model, optimal human forearm trajectories formation was investigated using a discrete time linear quadratic regulator. First, the continuous dynamics of the human forearm were established on the basis of the relation between muscle torque and neural control signal, and then we transferred the continuous system dynamics to discrete time notation. Finally we expressed the objective function of minimum variance model using a discrete time linear quadratic regulator and employed Riccati recursion to obtain the optimal movement trajectories of the human forearm. The results of example simulation show that the optimal movement trajectory of the forearm follows a smooth curve, and the speed curve of the hand is single peaked and bell shaped. These are in good agreement with the inherent kinematic properties of optimal movement, and therefore the method is effective for calculating the optimal movement trajectory of the human forearm.

Download Full-text