Dynamic Modeling and Controller Design of a Planar Parallel 3-RRR Compliant Micromanipulator

2005 ◽  
Author(s):  
Jingjun Yu ◽  
Dong Zhao ◽  
Shusheng Bi ◽  
Guanghua Zong
Keyword(s):  
Design Methodology ◽  
Closed Loop ◽  
Controller Design ◽  
Equations Of Motion ◽  
Control Plant ◽  
Ccd Camera ◽  
Step Response ◽  
Matlab Simulink ◽  
Compliant Joints ◽  
Bode Plots

This paper presents control system formulations of a planar parallel 3-RRR parallel compliant micromanipulator. The design methodology is illustrated with one of such designs constructed at Beijing University of Aeronautics and Astronautics, China. Compliant joints and motion-amplifying mechanism allow rapid and accurate response as well as larger workspace. The three PZT actuators attached on the linkages produce the bending moments. The sensor is a CCD camera feeding back the tool point position. The plant is the equations of motion which can be formulated using the Lagrangian method and dynamics software. The system dynamic model was developed with ADAMS which can export the nonlinear and linearized control plant to Matlab Simulink. Overall dynamic behavior of the manipulator will be illustrated through simulations with Matlab Simulink Toolbox. After comparison of two different control plans, the controller obtained from LQR method was chosen to achieve the control objectives. Closed-loop performance in response to a step reference was plotted. Bode plots of the sensitivity and complementary sensitivity showed their relation to the step response. Gain and phase margins was computed.

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.

Synthesis of Controllers for MIMO Systems with Time Response Specifications

2014 ◽  
Vol 3 (3) ◽  
pp. 25-52 ◽  
Author(s):  
Maher Ben Hariz ◽  
Wassila Chagra ◽  
Faouzi Bouani
Keyword(s):  
Global Optimization ◽  
Optimization Problem ◽  
Closed Loop ◽  
Controller Design ◽  
Mimo Systems ◽  
Optimal Solution ◽  
Optimization Method ◽  
Time Response ◽  
Step Response ◽  
Global Optimization Method

This paper proposes the design of fixed low order controllers for Multi Input Multi Output (MIMO) decoupled systems. The simplified decoupling is used as a decoupling system technique due to its advantages compared to other decoupling methods. The main objective of the proposed controllers is to satisfy some desired closed loop step response performances such as the settling time and the overshoot. The controller design is formulated as an optimization problem which is non convex and it takes in account the desired closed loop performances. Therefore, classical methods used to solve the non convex optimization problem can generate a local solution and the resulting control law is not optimal. Thus, the thought is to use a global optimization method in order to obtain an optimal solution which will guarantee the desired time response specifications. In this work the Generalized Geometric Programming (GGP) is exploited as a global optimization method. The key idea of this method consists in transforming an optimization problem, initially, non convex to a convex one by some mathematical transformations. Simulation results and a comparison study between the presented approach and a Proportional Integral (PI) controller are given in order to shed light the efficiency of the proposed controllers.

Integrated Design and Control for a Programmable Four-Bar Linkage

1999 ◽  
Author(s):  
Q. Li ◽  
W. J. Zhang ◽  
L. S. Guo
Keyword(s):  
High Speed ◽  
Control Algorithm ◽  
Design Methodology ◽  
Motion Tracking ◽  
Closed Loop ◽  
Controller Design ◽  
Integrated Design ◽  
Dynamic Performances ◽  
And Control ◽  
Four Bar Linkage

Abstract As the demand increases for machines of high accuracy, high speed and high stiffness, programmable closed-loop linkages emerge in the development of modern machinery. A mechatronic design methodology is proposed in this paper for the integrated design of mechanical structure and control algorithm for a programmable closed-loop mechanism system. This design methodology suggests a negative mass redistribution scheme, which follows the principle of a shaking force/shaking moment balancing scheme, for the modification of an existing four-bar mechanism, with the aim to obtain a simple system dynamic model and thus to facilitate controller design. In consequence, motion tracking performance and vibration behavior of the linkage system are significantly improved by simply applying a conventional PD control algorithm. The dynamic performances are further improved by using a model-based controller. The effectiveness of the proposed methodology has been verified by simulation studies.

scholarly journals Modelling and robust control of an unmanned coaxial rotor helicopter with unstructured uncertainties

2017 ◽  
Vol 9 (1) ◽  
pp. 168781401668796 ◽  
Author(s):  
Zhi-Yan Dong ◽  
Shun-An Liu ◽  
Chao Liu ◽  
Jin-Lin Liu ◽  
Lei Feng
Keyword(s):  
Robust Control ◽  
Closed Loop ◽  
Controller Design ◽  
General Rule ◽  
Step Response ◽  
Integrative Approach ◽  
Actuator Dynamics ◽  
Coaxial Rotor ◽  
Uncertainty Model ◽  
Empirical Coefficients

A complete methodology for an unmanned coaxial rotor helicopter with unstructured uncertainties was proposed to achieve high-accuracy tracking performance from modelling to robust control. An integrative approach was introduced to systematically construct a whole dynamic model. The key parameters were selected carefully after iteratively being checked by empirical coefficients to decrease the budget and risk of programme. Moreover, a new control scheme is proposed to simultaneously incorporate six inputs to control six states based on the investment of singularity value responses and the general rule of relative gain array. Coprime factor uncertainty model is considered to represent a class of unstructured uncertainties, such as unmolded actuator dynamics and unpredicted interferences between two rotors. Furthermore, the [Formula: see text] loop-shaping control was proposed to apply the control design of the coaxial rotor helicopter to manage complicated uncertainties and multivariable coupling. Finally, simulation results show the effectiveness of the proposed controller design in the step response of the closed loop. The stable closed-loop plant is achieved and the tolerant size of unstructured uncertainty is up to 36.09%. Good step responses and satisfied decoupling were also investigated in detail.

Modal Controllability and Observability of General Mechanical Systems

1995 ◽  
Vol 117 (4) ◽  
pp. 510-515 ◽  
Author(s):  
B. Yang
Keyword(s):  
Closed Loop ◽  
Linear Independence ◽  
Transfer Functions ◽  
Controller Design ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Vibration Modes ◽  
Trial And Error ◽  
Root Locus ◽  
Controllability And Observability

Controllability and observability are studied for general mechanical systems with combined effects of damping, gyroscopic and circulatory forces. A new modal analysis is proposed to represent the system transfer functions by the nonorthogonal eigenvectors that are associated with the original equations of motion. Investigation of linear independence of the rows and columns of the transfer functions yields the modal controllability and observability conditions. Because of their explicit relationships with the vibration modes, the controllability and observability tests require less computation than the conventional criteria, avoid trial and error in selection and positioning of actuators and sensors, and can be applied to systems with unidentified parameters. Moreover, the closed-loop root locus sensitivity coefficients are examined to give insights into modal controllability and observability, and to provide useful guidance for active controller design.

Data-driven I-PD Gain Tuning using Closed-loop Step Response Data

2019 ◽  
Vol 139 (8) ◽  
pp. 882-888
Author(s):  
Shiro Masuda ◽  
Jongho Park ◽  
Yoshihiro Matsui
Keyword(s):  
Closed Loop ◽  
Data Driven ◽  
Step Response ◽  
Response Data

Mode-Based Controller Design for Hammerstein Models Using Closed-Loop Tranjent Response Data

2016 ◽  
Vol 136 (5) ◽  
pp. 625-632
Author(s):  
Yoshihiro Matsui ◽  
Hideki Ayano ◽  
Shiro Masuda ◽  
Kazushi Nakano
Keyword(s):  
Closed Loop ◽  
Controller Design ◽  
Response Data ◽  
Hammerstein Models
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