A comparison of linear discrete-time design methods for servosystem control

1997 ◽  
Vol 211 (4) ◽  
pp. 281-300 ◽  
Author(s):  
A R Plummer
Keyword(s):  
Discrete Time ◽  
Closed Loop ◽  
Solution Method ◽  
Controller Design ◽  
Pole Placement ◽  
Closed Loop System ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Time Model ◽  
Sensitivity Functions

Three linear discrete-time model-based controller design techniques are compared: pole placement, linear quadratic Gaussian (LQG) and H∞ control. It is shown that design choices can be made for all three controllers by considering the effect on the sensitivity functions of the closed-loop system. Also all three controllers can be implemented using an identical controller structure. A comparative study of the application of the techniques to an electromechanical servosystem is made. The controllers are designed from a discrete-time plant model estimated from experimental data, and a polynomial-based solution method is used in each case. It is concluded that acceptable performance can be achieved using any of the controllers if informed design choices are made.

scholarly journals LMI Pole Regions for a Robust Discrete-Time Pole Placement Controller Design

Algorithms ◽  
2019 ◽  
Vol 12 (8) ◽  
pp. 167
Author(s):  
Danica Rosinová ◽  
Mária Hypiusová
Keyword(s):  
Discrete Time ◽  
Closed Loop ◽  
Controller Design ◽  
Loop System ◽  
Pole Placement ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Robust Controller ◽  
Pole Placement Controller ◽  
Robust Controller Design

Herein, robust pole placement controller design for linear uncertain discrete time dynamic systems is addressed. The adopted approach uses the so called “D regions” where the closed loop system poles are determined to lie. The discrete time pole regions corresponding to the prescribed damping of the resulting closed loop system are studied. The key issue is to determine the appropriate convex approximation to the originally non-convex discrete-time system pole region, so that numerically efficient robust controller design algorithms based on Linear Matrix Inequalities (LMI) can be used. Several alternatives for relatively simple inner approximations and their corresponding LMI descriptions are presented. The developed LMI region for the prescribed damping can be arbitrarily combined with other LMI pole limitations (e.g., stability degree). Simple algorithms to calculate the matrices for LMI representation of the proposed convex pole regions are provided in a concise way. The results and their use in a robust controller design are illustrated on a case study of a laboratory magnetic levitation system.

Application of LQR Techniques to the Anti-Sway Controller of Overhead Crane

2010 ◽  
Vol 139-141 ◽  
pp. 1933-1936 ◽  
Author(s):  
Bin Yang ◽  
Bin Xiong
Keyword(s):  
Closed Loop ◽  
Controller Design ◽  
Lagrange Equation ◽  
Linear Quadratic Regulator ◽  
Analytical Mechanics ◽  
Overhead Crane ◽  
Closed Loop System ◽  
Linear Quadratic ◽  
Weighting Matrix ◽  
Motion System

This paper explains and demonstrates how to design an anti-sway controller of overhead crane for eliminating pendulum of hook-headed. In this paper, we use Lagrange Equation in analytical mechanics to obtain a mathematical model of crane crab motion system. Then the paper comes up with a piece of new idea, i.e. applies linear quadratic regulator techniques to the anti-sway controller’ design of overhead crane. In order to make the designed linear optimal system meet the practical production requirements better, we use a parametric formula’s method of solutions to LQ inverse problems to obtain the weighting matrix Q. In fact, the method is simple and practical, and ensures the performance of closed-loop system is optimized. The paper will introduce the design steps of anti-sway controller of overhead crane and realization of anti-sway controller, which are new and original in this paper.

scholarly journals Transformation of LQR Weights for Discretization Invariant Performance of PI/PID Dominant Pole Placement Controllers

Robotica ◽  
2019 ◽  
Vol 38 (2) ◽  
pp. 271-298 ◽  
Author(s):  
Kaushik Halder ◽  
Saptarshi Das ◽  
Amitava Gupta
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Pid Controller ◽  
Closed Loop ◽  
Weighting Factor ◽  
Pole Placement ◽  
Algebraic Riccati Equation ◽  
Linear Quadratic ◽  
Similar Time ◽  
Dominant Pole

SummaryLinear quadratic regulator (LQR), a popular technique for designing optimal state feedback controller, is used to derive a mapping between continuous and discrete time inverse optimal equivalence of proportional integral derivative (PID) control problem via dominant pole placement. The aim is to derive transformation of the LQR weighting matrix for fixed weighting factor, using the discrete algebraic Riccati equation (DARE) to design a discrete time optimal PID controller producing similar time response to its continuous time counterpart. Continuous time LQR-based PID controller can be transformed to discrete time by establishing a relation between the respective LQR weighting matrices that will produce similar closed loop response, independent of the chosen sampling time. Simulation examples of first/second order and first-order integrating processes exhibiting stable/unstable and marginally stable open loop dynamics are provided, using the transformation of LQR weights. Time responses for set-point and disturbance inputs are compared for different sampling times as fraction of the desired closed loop time constant.

scholarly journals Robust H∞ Loop Shaping Controller Synthesis for SISO Systems by Complex Modular Functions

2021 ◽  
Vol 26 (1) ◽  
pp. 21
Author(s):  
Ahmad Taher Azar ◽  
Fernando E. Serrano ◽  
Nashwa Ahmad Kamal
Keyword(s):  
Design Methodology ◽  
Closed Loop ◽  
Complex Analysis ◽  
Controller Design ◽  
Filter Design ◽  
Design Procedure ◽  
Elliptic Functions ◽  
Loop System ◽  
Closed Loop System ◽  
Loop Shaping

In this paper, a loop shaping controller design methodology for single input and a single output (SISO) system is proposed. The theoretical background for this approach is based on complex elliptic functions which allow a flexible design of a SISO controller considering that elliptic functions have a double periodicity. The gain and phase margins of the closed-loop system can be selected appropriately with this new loop shaping design procedure. The loop shaping design methodology consists of implementing suitable filters to obtain a desired frequency response of the closed-loop system by selecting appropriate poles and zeros by the Abel theorem that are fundamental in the theory of the elliptic functions. The elliptic function properties are implemented to facilitate the loop shaping controller design along with their fundamental background and contributions from the complex analysis that are very useful in the automatic control field. Finally, apart from the filter design, a PID controller loop shaping synthesis is proposed implementing a similar design procedure as the first part of this study.

A Note on Pole Placement of Mechanical Systems

1991 ◽  
Vol 113 (3) ◽  
pp. 420-421 ◽  
Author(s):  
C. Minas ◽  
D. J. Inman
Keyword(s):  
Least Squares ◽  
Canonical Form ◽  
Output Feedback ◽  
Closed Loop ◽  
Weighted Least Squares ◽  
Mechanical Systems ◽  
Pole Placement ◽  
Feedback Gain ◽  
Closed Loop System ◽  
Feedback Method

An output feedback method is developed, that systematically places a desired number of poles of a closed-loop system at or near desired locations. The system is transformed to its equivalent controllable canonical form, where the output feedback gain matrix is calculated in a weighted least squares scheme, that minimizes the change of the remaining modes of the system. The advantage of this method over other pole placement routines is the fact that the influence on the remaining unplaced modes of the system is minimum, which is particularly important in preserving closed-loop stability.

Backstepping Based Adaptive Control of Magnetic Levitation System

2013 ◽  
Vol 341-342 ◽  
pp. 945-948 ◽  
Author(s):  
Wei Zhou ◽  
Bao Bin Liu
Keyword(s):  
Parameter Uncertainty ◽  
Closed Loop ◽  
Controller Design ◽  
Magnetic Levitation ◽  
Adaptive Controller ◽  
Closed Loop System ◽  
Actual System ◽  
Levitation System ◽  
Magnetic Levitation System ◽  
Control Accuracy

In view of parameter uncertainty in the magnetic levitation system, the adaptive controller design problem is investigated for the system. Nonlinear adaptive controller based on backstepping is proposed for the design of the actual system with parameter uncertainty. The controller can estimate the uncertainty parameter online so as to improve control accuracy. Theoretical analysis shows that the closed-loop system is stable regardless of parameter uncertainty. Simulation results demonstrate the effectiveness of the presented method.

scholarly journals The discrete-time tracking problem with H∞ model matching approach plus integral control

2019 ◽  
Vol 292 ◽  
pp. 01018
Author(s):  
Murat Akın ◽  
Tankut Acarman
Keyword(s):  
Discrete Time ◽  
Closed Loop ◽  
Controller Design ◽  
Model Matching ◽  
Matching Problem ◽  
Design Algorithm ◽  
Integral Control ◽  
Loop Transfer Function ◽  
Model Transfer ◽  
Static Output

In this study, the discrete-time H∞ model matching problem with integral control by using 2 DOF static output feedback is presented. First, the motivation and the problem is stated. After presenting the notation, the two lemmas toward the discrete-time H∞ model matching problem with integral control are proven. The controller synthesis theorem and the controller design algorithm is elaborated in order to minimize the H∞ norm of the closed-loop transfer function and to maximize the closed-loop performance by introducing the model transfer matrix. In following, the discrete-time H∞ MMP via LMI approach is derived as the main result. The controller construction procedure is implemented by using a well-known toolbox to improve the usability of the presented results. Finally, some conclusions are given.

Finite-time dissipative control for networked control systems with hybrid-triggered scheme

2020 ◽  
pp. 014233122094650
Author(s):  
Qian Zhang ◽  
Huaicheng Yan ◽  
Shiming Chen ◽  
Xisheng Zhan ◽  
Xiaowei Jiang
Keyword(s):  
Control Systems ◽  
Finite Time ◽  
Closed Loop ◽  
Controller Design ◽  
Networked Control Systems ◽  
Sufficient Conditions ◽  
Networked Control ◽  
Closed Loop System ◽  
Network Resources ◽  
Dissipative Control

This paper is concerned with the problem of finite-time dissipative control for networked control systems by hybrid triggered scheme. In order to save network resources, a hybrid triggered scheme is proposed, which consists of time-triggered scheme and event-triggered scheme simultaneously. Firstly, sufficient conditions are derived to guarantee that the closed-loop system is finite-time bounded (FTBD) and [Formula: see text] dissipative. Secondly, the corresponding controller design approach is presented based on the derived conditions. Finally, a numerical example is presented to show the effectiveness of the proposed approach.

scholarly journals Damage Detection and Vibration Control of a Delaminated Smart Composite Plate

2000 ◽  
Vol 9 (1) ◽  
pp. 096369350000900 ◽  
Author(s):  
Aditi Chattopadhyay ◽  
Changho Nam ◽  
Youdan Kim
Keyword(s):  
Composite Plate ◽  
Closed Loop ◽  
Order Theory ◽  
Pole Placement ◽  
Transverse Shear Deformation ◽  
Mean Square ◽  
Smart Composite ◽  
Closed Loop System ◽  
Higher Order Theory ◽  
Placement Technique

In this paper, the effects of delamination on the dynamic characteristics of a composite plate are investigated. The refined higher order theory is used to model the smart composite plate in the presence of delaminations. The theory accurately captures the transverse shear deformation through the thickness, which is important in anisotropic composites, particularly in the presence of discrete actuators and sensors and delaminations. Next, the detection of delamination is investigated using the Root Mean Square (RMS) values of the response of the composite plate subject to disturbances. An active control system is designed to minimise the effect of delamination. The pole placement technique is applied to design the closed loop system by utilising piezoelectric actuators. Numerical results show that the RMS information can be used to estimate the location of the delamination. The controller designed makes the delaminated plate behave like a healthy plate model. The controller also reduces the magnitudes of RMS responses due to disturbance.

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