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.

scholarly journals Vibration-Attenuation Controller Design for Uncertain Mechanical Systems with Input Time Delay

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Yuanchun Ding ◽  
Falu Weng ◽  
Xiaohua Jiang ◽  
Minkang Tang
Keyword(s):  
Closed Loop ◽  
Controller Design ◽  
State Space Model ◽  
Mechanical Systems ◽  
Sufficient Conditions ◽  
Uncertain System ◽  
Disturbance Attenuation ◽  
System Model ◽  
Closed Loop System ◽  
Vibration Attenuation

The problems of vibration-attenuation controller design for uncertain mechanical systems with time-varying input delay are of concern in this paper. Firstly, based on matrix transformation, the mechanical system is described as a state-space model. Then, in terms of introducing the linear varying parameters, the uncertain system model is established. Secondly, the LMI-based sufficient conditions for the system to be stabilizable are deduced by utilizing the LMI technique. By solving the obtained LMIs, the controllers are achieved for the closed-loop system to be stable with a prescribed level of disturbance attenuation. Finally, numerical examples are given to show the effectiveness of the proposed theorems.

Delayed-Acceleration Feedback for Active-Multimode Vibration Control of Cantilever Beams

2007 ◽  
Author(s):  
Khaled A. Alhazza ◽  
Ali H. Nayfeh ◽  
Mohammed F. Daqaq
Keyword(s):  
Cantilever Beam ◽  
Controller Design ◽  
Equations Of Motion ◽  
Time Integration ◽  
Free Vibrations ◽  
Delayed Feedback Control ◽  
Vibration Modes ◽  
Stability Boundaries ◽  
Single Input Single Output ◽  
The Stability

We present a single-input single-output multimode delayed-feedback control methodology to mitigate the free vibrations of a flexible cantilever beam. For the purpose of controller design and stability analysis, we consider a reduced-order model consisting of the first n vibration modes. The temporal variation of these modes is represented by a set of nonlinearly-coupled ordinary-differential equations that capture the evolving dynamics of the beam. Considering a linearized version of these equations, we derive a set of analytical conditions that are solved numerically to assess the stability of the closed-loop system. To verify these conditions, we characterize the stability boundaries using the first two vibration modes and compare them to damping contours obtained by long-time integration of the full nonlinear equations of motion. Simulations show excellent agreement between both approaches. We analyze the effect of the size and location of the piezoelectric patch and the location of the sensor on the stability of the response. We show that the stability boundaries are highly dependent on these parameters. Finally, we implement the controller on a cantilever beam for different controller gain-delay combinations and assess the performance using time histories of the beam response. Numerical simulations clearly demonstrate the controller ability to mitigate vibrations emanating from multiple modes simultaneously.

scholarly journals Online Validation of Relay based Identification and Controller Design with an Anti-Reset Windup for a Binary Distillation Column

2018 ◽  
Vol 7 (4.30) ◽  
pp. 516
Author(s):  
Eadala Sarath Yadav ◽  
Thirunavukkarasu Indiran ◽  
Shanmuga Priya Selvanathan ◽  
Ganesh UG
Keyword(s):  
Control Algorithm ◽  
Distillation Column ◽  
Closed Loop ◽  
Controller Design ◽  
Model Identification ◽  
Parameters Estimation ◽  
Model Parameters ◽  
Trial And Error ◽  
Sustained Oscillations ◽  
Conventional Methods

Sequential auto-tuning based model identification is a closed loop approach, which has an extensive benefit compared to conventional methods because of user defined manipulated gain to the process within the verge of instability. Model parameters estimation of multi input multi output process is challenging because of existence of multivariable interaction among the variables. In this paper ideal relay is used as a sequential basis for binary distillation column in real time. Obtaining sustained oscillations in conventional methods is based on trial and error, benefit of relay is that oscillations can be generated as scaling of user defined gains. Predictive PI control algorithm is implemented. Results depicts the efficiency of methodology and importance of anti-reset term in the algorithm. 

Passivity-Based Stabilization of Underactuated Mechanical Systems

2013 ◽  
Vol 421 ◽  
pp. 16-22
Author(s):  
Shan Shan Wu ◽  
Wei Huo
Keyword(s):  
Closed Loop ◽  
Control Method ◽  
Controller Design ◽  
Design Method ◽  
Mechanical Systems ◽  
Matching Condition ◽  
Loop System ◽  
Closed Loop System ◽  
Underactuated Mechanical Systems ◽  
Stabilization Control

A new stabilization control method for underactuated linear mechanical systems is presented in this paper. By proper setting the desired closed-loop system, the matching condition for controller design is reduced to one equation and an adjustable parameter (damping coefficient) is introduced to the controller. Stability of the closed-loop system is proved based on passivity. As an application example, stabilization control of 2-DOF Pendubot is studied. The system is linearized at its equilibrium point and the proposed controller design method is applied to the linearized system. The procedure of solving matching condition and design controller for the Pendubot is provided. The simulation results verify feasibility of the proposed method.

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 Online Validation of Relay based Identification and Controller Design with an Anti-Reset Windup for a Binary Distillation Column

2018 ◽  
Vol 7 (4.19) ◽  
pp. 983
Author(s):  
Eadala Sarath Yadav ◽  
Thirunavukkarasu Indiran ◽  
Shanmuga Priya Selvanathan ◽  
Ganesh UG
Keyword(s):  
Control Algorithm ◽  
Distillation Column ◽  
Closed Loop ◽  
Controller Design ◽  
Model Identification ◽  
Parameters Estimation ◽  
Model Parameters ◽  
Trial And Error ◽  
Sustained Oscillations ◽  
Conventional Methods

Sequential auto-tuning based model identification is a closed loop approach, which has an extensive benefit compared to conventional methods because of user defined manipulated gain to the process within the verge of instability. Model parameters estimation of multi input multi output process is challenging because of existence of multivariable interaction among the variables. In this paper ideal relay is used as a sequential basis for binary distillation column in real time. Obtaining sustained oscillations in conventional methods is based on trial and error, benefit of relay is that oscillations can be generated as scaling of user defined gains. Predictive PI control algorithm is implemented. Results depicts the efficiency of methodology and importance of anti-reset term in the algorithm.  

Vibration Control of a Rotating Shaft: An Analytical Solution

1999 ◽  
Vol 66 (1) ◽  
pp. 254-259 ◽  
Author(s):  
S. M. Yang ◽  
G. J. Sheu
Keyword(s):  
Closed Loop ◽  
Controller Design ◽  
Feedback Gain ◽  
Beam Model ◽  
Vibration Modes ◽  
Rotating Shaft ◽  
Rotating Speed ◽  
Rayleigh Beam ◽  
Sensor Actuator ◽  
Whirl Speed

It has been shown that a rotating shaft in the Rayleigh beam model has only a finite number of whirl speeds and vibration modes when the rotating speed is higher than half of the whirl speed. The system’s unbalanced response can therefore be written analytically by the vibration modes and the generalized coordinates. This paper presents an analytical controller design of optimal sensor/actuator location and feedback gain for minimizing the steady-state unbalanced response. Because all of the critical speeds and vibration modes are included in the controller design, there will be no residual mode, hence no spillover. An example is used to illustrate that the controller design in collocated or noncollocated configuration not only guarantees the closed-loop stability but also effectively suppresses the unbalanced response.

Perfectly matched closed-loop dynamics based on IP controller for bi-axial contour following

2017 ◽  
Vol 231 (1) ◽  
pp. 52-62
Author(s):  
Jianhua Wu ◽  
Zhenhua Xiong ◽  
Han Ding
Keyword(s):  
Closed Loop ◽  
Transfer Functions ◽  
Controller Design ◽  
The Other ◽  
Coupling Mechanism ◽  
Tuning Method ◽  
Parameters Tuning ◽  
Loop Dynamics ◽  
Contour Following ◽  
The Individual

This article aims to achieve high contour following performance for bi-axial systems. First, the effects of closed-loop dynamics on the contour following performance are analyzed and it is determined that perfectly matched closed-loop dynamics is preferable. Next, the Integral-Proportional (IP) controller is utilized to control each axis and the parameters tuning method is proposed to achieve perfect matching. The tuning method contains two main parts. One primary part is to establish the relations between the two controller parameters by setting both axes to have the same closed-loop transfer functions. The other primary part is to determine the individual IP controller parameters loop by loop according to the bandwidth index. The design process is correspondingly implemented in two steps. First, the smaller bandwidth axis controller parameters are tuned, and then the other axis is tuned according to the above relations. In applications, feedforward controllers are usually added to enhance the motion performance, whose parameters depend on the individual closed-loop dynamics and can be directly determined. The novelty of this article is that no coupling mechanism is required to perfectly match the closed-loop dynamics and the contour following performance is improved via individual controller design alone. Both the controller and the tuning method are simple and easy to implement, which are of interest to control engineers. Experiments are carried out on an X-Y motion stage, which is commanded to follow diamond and circle contours. Results show that the proposed method can match closed-loop dynamics perfectly and significantly improve the contour following performance.

Passivity-Based Tracking Control Design for Underactuated Mechanical Systems

2012 ◽  
Vol 591-593 ◽  
pp. 1225-1230 ◽  
Author(s):  
Shan Shan Wu ◽  
Wei Huo
Keyword(s):  
Tracking Control ◽  
Closed Loop ◽  
Controller Design ◽  
Design Method ◽  
Mechanical Systems ◽  
Matching Condition ◽  
Loop System ◽  
Closed Loop System ◽  
Underactuated Mechanical Systems ◽  
Design Procedures

Passivity-based tracking control of the underactuated linear mechanical systems is investigated in this paper. As our main contribution, the matching condition is decreased into two equations and an adjustable gain (damping gain) is introduced into the controller by setting the desired closed-loop system properly. Stability of the closed-loop system is proved based on passivity of the system. Furthermore, as examples, tracking control of 2-DOF Acrobot and 2-DOF Pendubot are studied. The systems are linearized at their equilibriums and the passivity-based controller design method is applied to the linearized systems. Matching conditions are solved and the design procedures of associate controllers for the two robots are provided. The simulation results show that the designed controllers can realize asymptotical tracking for the given desired trajectories.

scholarly journals Root locus approach in design of PID controller for cruise control application

2021 ◽  
Vol 2115 (1) ◽  
pp. 012023
Author(s):  
M Manju Prasad ◽  
M A Inayathullah
Keyword(s):  
Control System ◽  
Pid Controller ◽  
Closed Loop ◽  
Controller Design ◽  
Closed Loop Control ◽  
Cruise Control ◽  
Root Locus ◽  
Loop Control ◽  
Cruise Control System ◽  
Loop Control System

Abstract The Proportional Integral Derivative (PID) controller is an effective and common feedback control design used in closed loop control systems. One such best consideration of closed loop control system would be cruise control system. This is a system that automatically controls the speed of an electric vehicle despite external disturbances. In this paper, the goal is to design a PID controller using root locus technique for a closed loop cruise control system. By root locus approach, the controller constants and controller design is finalized. Simulation results through MATLAB environment validate the effectiveness of controller design.

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