Coulomb Friction Limit Cycles in Elastic Positioning Systems

1999 ◽  
Vol 121 (2) ◽  
pp. 298-301 ◽  
Author(s):  
A. Bonsignore ◽  
G. Ferretti ◽  
G. Magnani
Keyword(s):  
Coulomb Friction ◽  
Closed Loop ◽  
Tracking Error ◽  
Pole Placement ◽  
Stick Slip ◽  
Positioning Systems ◽  
Relay Control ◽  
Pure Coulomb ◽  
Pole Placement Controller ◽  
Motor Velocity

The state space control of a positioning system affected by torsional elasticity at the gearbox is considered, using a motor position transducer only. An output feedback, pole placement controller is used, with an additional integral action on the tracking error to cancel it at steady state. Both experiments and simulations point out that large oscillations may appear for some sets of closed-loop poles which yields, in contrast to stick-slip cycles, instantaneous motor velocity reversals. It is shown that such oscillations are induced by “pure” Coulomb friction. The period of the oscillations is predicted precisely following the Tsypkin’s relay control theory and also by the approximate describing function method. The latter also allows understanding of how oscillations depend on observer and feedback control design and on plant parameters; thus we are able to derive guidelines for the design of an oscillation free closed-loop system.

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.

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.

Improved Pole-placement Control with Feed-forward Dead Zone Compensation for Position Tracking of Electro-Pneumatic Actuator System Improved Pole-placement Control with Feed-forward Dead Zone Compensation for Position Tracking of Electro-Pneumatic Actuato

2021 ◽  
Vol 20 (2) ◽  
pp. 25-32
Author(s):  
Noorhazirah Sunar ◽  
Mohd Fua’ad Rahmat ◽  
Ahmad ‘Athif Mohd Fauzi ◽  
Zool Hilmi Ismail ◽  
Siti Marhanis Osman ◽  
...  
Keyword(s):  
Dead Zone ◽  
Pneumatic Actuator ◽  
Pole Placement ◽  
Position Tracking ◽  
Zone Model ◽  
Feed Forward ◽  
The Dead ◽  
Chattering Effect ◽  
Pole Placement Controller ◽  
Pole Placement Control

Dead-zone in the valve degraded the performances of the Electro-Pneumatic Actuator (EPA) system.  It makes the system difficult to control, become unstable and leads to chattering effect nearest desired position.  In order to cater this issue, the EPA system transfer function and the dead-zone model is identified by MATLAB SI toolbox and the Particle Swarm Optimization (PSO) algorithm respectively.  Then a parametric control is designed based on pole-placement approach and combine with feed-forward inverse dead-zone compensation.  To reduce chattering effect, a smooth parameter is added to the controller output.  The advantages of using these techniques are the chattering effect and the dead-zone of the EPA system is reduced.  Moreover, the feed-forward system improves the transient performance.  The results are compared with the pole-placement control (1) without compensator and (2) with conventional dead-zone compensator.  Based on the experimental results, the proposed controller reduced the chattering effect due to the controller output of conventional dead-zone compensation, 90% of the pole-placement controller steady-state error and 30% and 40% of the pole-placement controller with conventional dead-zone compensation settling time and rise time.

Comparison of Controllers for a UAV with Integral Effect and Kalman Estimator: By Bessel Polynomials and LQR

2013 ◽  
Vol 436 ◽  
pp. 54-60 ◽  
Author(s):  
Wenceslao Eduardo Rodríguez ◽  
Ramiro Ibarra ◽  
Gerardo Romero ◽  
David Lara ◽  
Jaime Arredondo ◽  
...  
Keyword(s):  
Steady State ◽  
Pole Placement ◽  
Control Technique ◽  
State Estimator ◽  
Control Laws ◽  
State Response ◽  
Integral Effect ◽  
Aerial Vehicle ◽  
Pole Placement Controller ◽  
Selection Of

This paper presents the development of two different control techniques as an approach having to remove steady-state error present in the response of attitude of a mini unmanned aerial vehicle. A problem that arises when performing pole placement controller is the selection of the poles, the Bessel approximation allows the selection of the eigenvalues in function to a specified response time for a feedback pole placement controller and state estimator (observer). On the other hand presents an optimal control technique combined with Kalman filter to estimate the state affected by perturbations in the system, both cases using the integral effect to eliminate the steady state error.These two control laws has the property of responding to a desired response according to a time or state response desired.

scholarly journals On the Robust Multiple Objective Control with Simultaneous Pole Placement in LMI Regions

2021 ◽  
Vol 20 ◽  
pp. 272-280
Author(s):  
Antonis Vouzikas ◽  
Alexandros Gazis
Keyword(s):  
Robust Control ◽  
Complex Plane ◽  
Uncertain Systems ◽  
Closed Loop ◽  
Pole Placement ◽  
Multiple Objective ◽  
Control Laws ◽  
Control Approach ◽  
Guaranteed Cost ◽  
Objective Control

This article studies the problem of designing robust control laws to achieve multiple performance objectives for linear uncertain systems. Specifically, in this study we have selected one of the control objectives to be a closed-loop pole placement in specific regions of the left-half complex plane. As such, a guaranteed cost based multi-objective control approach is proposed and compared with the H_2/H_∞control by means of an application example

scholarly journals The usage of Lambert W function for identification and speed control of a DC motor

2019 ◽  
Vol 32 (4) ◽  
pp. 581-600
Author(s):  
Radmila Gerov ◽  
Zoran Jovanovic
Keyword(s):  
Closed Loop ◽  
Dc Motor ◽  
Pole Placement ◽  
Step Response ◽  
Lambert W Function ◽  
Placement Method ◽  
Speed Regulation ◽  
Measured Speed ◽  
Proportional Controller ◽  
Integral Gain

The paper proposes a new method of identifying the linear model of a DC motor. The parameter estimation is based on the closed-loop step response of the DC motor under a proportional controller. For the application of the method, a deliberate delay of the measured speed was introduced. The paper considers the speed regulation of the direct current motor with negligible inductance by applying 1-DOF and 2-DOF, proportional integral retarded controllers. The proportional and integral gain of the PI retarded controllers was received by using a pole placement method on the identified model. The Lambert W function was applied for the identification and in designing the controller with the purpose of finding the rightmost poles of the closed-loop as well as the boundary conditions for selecting the gain of the PI controller. The robustness of the calculated controllers was considered under the effect of an disturbance, uncertainty in each of the DC motor parameters as well as perturbations in time delay.

Asperity Spring Friction Model With Application to Belt-Drives

2003 ◽  
Author(s):  
Tamer M. Wasfy
Keyword(s):  
Finite Element ◽  
Coulomb Friction ◽  
Friction Model ◽  
Belt Drive ◽  
Finite Element Code ◽  
Time Step ◽  
Stick Slip ◽  
Normal Contact ◽  
Belt Drives ◽  
Coulomb Friction Model

An asperity spring friction model that uses a variable anchor point spring along with a velocity dependent force is presented. The model is incorporated in an explicit timeintegration finite element code. The friction model is used along with a penalty-based normal contact model to simulate the dynamic response of a two-pulley belt-drive system. It is shown that the present friction model accurately captures the stick-slip behavior between the belt and the pulleys using a much larger time-step than a pure velocity-dependent approximate Coulomb friction model.

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