A Sampled-Data Formulation for Boundary Control of a Longitudinal Elastic Bar

2000 ◽  
Vol 123 (2) ◽  
pp. 245-249 ◽  
Author(s):  
Wu-Chung Su ◽  
Sergey V. Drakunov ◽  
U¨mit O¨zgu¨ner
Keyword(s):  
Control Problem ◽  
Boundary Control ◽  
Discrete Time ◽  
Inequality Constraints ◽  
Sampling Period ◽  
Sampled Data ◽  
Discrete Time System ◽  
Time Control ◽  
Finite Dimensional Approximation ◽  
Dimensional Approximation

The sampled-data boundary control problem for a longitudinal flexible bar is formulated as a linear discrete-time control problem in an infinite-dimensional state space. With zero-order-hold applied to the control channel, the system is lifted into an infinite sequence of constant control problems. The finite-dimensional approximation of the discrete-time system is controllable-observable if the sampling period satisfies some inequality constraints, which are related to the associated eigenvalues.

Modified Bilinear Integration Algorithm Based on the Modulated Sine Function

2005 ◽  
Vol 219 (8) ◽  
pp. 609-616 ◽  
Author(s):  
Fu-Hwa Liu ◽  
Cheun-Ming Chen
Keyword(s):  
Discrete Time ◽  
Sampling Period ◽  
Sampled Data ◽  
Discrete Time System ◽  
Integration Algorithm ◽  
Controlled System ◽  
Sample Data ◽  
Z Domain ◽  
Natural Response ◽  
Bilinear Integration

This study presents a novel discretization method for converting an analogue controller into its corresponding counterpart for a discrete-time system. The proposed method is appropriate for the natural response curve and, thus, is more effective for certain digitally redesigned systems. Based on the mapping region of the transformation using the proposed method from the s-domain to the z-domain, a transformation involving a modulated parameter n is used to generate a corresponding stable discrete-time controller for a stable continuous-time controller. As a suitable modulated parameter in the proposed transformation is selected to digitalize an analogue-controlled system, the new sampled-data-controlled system achieves a precise discrete-time response, and can also tolerate a large sampling period for sample-data implementation. A simulated example is used to demonstrate the results.

Minimum Time Control of Second Order Pulse-Width-Modulated Sampled-Data Systems

1962 ◽  
Vol 84 (1) ◽  
pp. 101-109 ◽  
Author(s):  
E. Polak
Keyword(s):  
Pulse Width ◽  
Phase Plane ◽  
Sampling Period ◽  
Second Order ◽  
Data Systems ◽  
Sampled Data ◽  
Relay System ◽  
Pulse Width Modulated ◽  
Minimal Time ◽  
Time Control

This paper treats the minimal time control problem for two second order pulse-width-modulated sampled-data systems, one with a double integrator type plant and one with a plant described by an integral and a time constant. Such plants are encountered in systems with hydraulic components. It is shown rigorously that for minimal time control the phase plane can be divided into two regions: a striplike region around the optimal switching trajectory for a continuous relay system with the same plants, in which the pulse width must be adjusted for optimal action; and the rest of the phase plane in which an optimal p.w.m. system of the type described behaves like a continuous optimal relay system, the pulse duration being equal to the sampling period. A brief description of an electromechanical computer capable of implementing minimal time control for these systems is also given.

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.

Finite-Time H∞ Control of one Family of Fuzzy Discrete-Time System with Norm-Bounded Disturbance

2011 ◽  
Vol 225-226 ◽  
pp. 428-432 ◽  
Author(s):  
Cai Xia Liu ◽  
Ying Qi Zhang
Keyword(s):  
Discrete Time ◽  
Finite Time ◽  
Function Theory ◽  
Matrix Inequalities ◽  
Time Stability ◽  
Discrete Time System ◽  
Time System ◽  
Finite Time Stability ◽  
Time Control ◽  
Bounded Disturbance

This paper deals with finite-time control problem of a class of fuzzy discrete-time system with time-varying norm-bounded disturbance. Applying the Lyapunov function theory and matrix inequalities, a sufficient condition is obtained for robust finite-time stability and the fuzzy system satisfies a prescribed level for the effect of the disturbance input on the controlled output.

Optimal Mini Segway Control Using Non-Minimum Phase Sample and Hold Input

2019 ◽  
Author(s):  
Yingxu Wang ◽  
Guoming G. Zhu
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
System Performance ◽  
Low Cost ◽  
Sampling Period ◽  
High Gain ◽  
Minimum Phase ◽  
Discrete Time System ◽  
Loop Control ◽  
Sample And Hold

Abstract Our early work shows the reduction of feasible sampling period when sample and hold inputs (SHI) are used to convert a continuous-time non-minimum phase (NMP) system to a discrete-time minimum phase (MP) system, comparing to conventional zero-order hold. Consequently, high-gain discrete-time controllers can be designed and used to improve continuous-time NMP system performance since the resulting discrete-time system is MP. This paper demonstrates the performance improvements of a mini Segway robot through experiments utilizing a dual-loop control architecture. An inner-loop continuous-time controller stabilizes the mini Segway robot and the outer-loop discrete-time controller, designed based on the discrete-time MP system, is used to improve the overall system performance. Experimental results show that the mini Segway cart oscillation magnitudes are significantly reduced and its stability is also improved. This study also confirms the feasibility of implementing the SHI into a low cost microcontroller such as Arduino. That is, the additional computational load of SHIs is minimal.

scholarly journals Stability Results of a Class of Hybrid Systems under Switched Continuous-Time and Discrete-Time Control

2009 ◽  
Vol 2009 ◽  
pp. 1-28 ◽  
Author(s):  
M. De la Sen ◽  
A. Ibeas
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Linear Time ◽  
Sampling Period ◽  
Switched System ◽  
Time Interval ◽  
Stabilizing Controller ◽  
Switching Law ◽  
Discrete Dynamic System ◽  
Time Control

This paper investigates the stability properties of a class of switched systems possessing several linear time-invariant parameterizations (or configurations) which are governed by a switching law. It is assumed that the parameterizations are stabilized individually via an appropriate linear state or output feedback stabilizing controller whose existence is first discussed. A main novelty with respect to previous research is that the various individual parameterizations might be continuous-time, discrete-time, or mixed so that the whole switched system is a hybrid continuous/discrete dynamic system. The switching rule governs the choice of the parameterization which is active at each time interval in the switched system. Global asymptotic stability of the switched system is guaranteed for the case when a common Lyapunov function exists for all the individual parameterizations and the sampling period of the eventual discretized parameterizations taking part of the switched system is small enough. Some extensions are also investigated for controlled systems under decentralized or mixed centralized/decentralized control laws which stabilize each individual active parameterization.

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