Modeling and implementation of a proportional derivative controller for electroviscous damper.
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This document summarizes a research article that models and implements a proportional-derivative (P-D) controller for an electroviscous damper. The researchers developed a mathematical model of the damper system and used MATLAB to simulate the open-loop and closed-loop step responses. The results showed that the P-D controller reduced overshoot and settling time compared to just proportional control, with little effect on rise time and steady-state error. The controller successfully controlled the performance of the electroviscous damper.
Modeling and implementation of a proportional derivative controller for electroviscous damper.
- 1. Control Theory and Informatics ISSN 2224-5774 (Paper) ISSN 2225-0492 (Online) Vol.3, No.6, 2013 www.iiste.org Modeling and Implementation of a Proportional-Derivative Controller for Electroviscous Damper. OMORODION Department of Materials and Production Engineering Ambrose Alli University, Ekpoma, Edo State, Nigeria S.O. AMIEBENOMO Department of Mechanical Engineering Ambrose Alli University, Ekpoma, Edo State, Nigeria C.I. OVIAWE Department of Mechanical Engineering Edo State Institute of Technology and Management Usen, Edo State, Nigeria ABSTRACT This paper is focus on the design, modeling and implementation of a proportional-derivative controller in the control of the performance characteristics of an electroviscous damper.The implementation shows that proportional derivative (P-D) controller reduce both the system overshoot and the settling time and had small effect on the rise time and steady state error. Keywords: proportional. Integral, controller, transfer function, electroviscousity. As early as 19th century (DUFF 1896, Quinke 1897), scientist began studying electroviscous fluid response to input electric field. The fluid gained prominent when winslow (1947, 1949) published results of his research work. Electro viscous fluids consist of fine polarizable particles dispersed in a nonconductive, low viscositiy fluid. Electro viscous fluids exhibit a rapid, yet reversible induced shear resistance when exposed to an applied electric field. Engineers and scientists have identified possible applications including vehicle suspensions, hydraulic values and soft clutches that would utilize the special properties of electro viscous fluid. Development of commercial applications of devices using electro viscous fluids has been hampered by inability to quickly and precisely control the electro viscous fluid state Clark, et.al., 1996). previous studies have focused on varying aspect as to the composition of fluid and particulate sizes varying the electric fluid strength and shearing rate has been investigated Strangroom (1978, 1980).The application of the fluid in mechanical devices also have been investigated Block and Kelly (1986). A simulation method was developed to describe structure formation in electro viscous suspensions (Klingen berg et al., 1989). Current devices such as electro viscous fluid bused valves, clutches or hydraulic mounts typically do not react quickly or precisely enough to meet needs of the applications (Duclos ,1987; Ushijima et al., 1988, Arguelles et al, 1973). The objective of this paper is to investigate the response of a typical electro viscous application in shock absorber to a step input signal using the proportional – derivative P-D controller. The proportional – derivative controller model e R(s) Controller U + Plant Y(s) Figure 1:P- D control model Plant is the system to be controlled. The controller provides the excitation for the plant designed to control the overall system behaviour. This controller is two – terms controller ; P-D controller and the system transfer function is given as; 25
- 2. Control Theory and Informatics ISSN 2224-5774 (Paper) ISSN 2225-0492 (Online) Vol.3, No.6, 2013 www.iiste.org KP = proportional gain KdS = Derivative gain The tracking error is the difference between the desired input value (R) and actual output (Y). The error signal is sent to the P-D controller, and the controller compute the integral of this error signal. The signal (U) just past the controller is now equal to KP times the magnitude of the error plus the integral gain Kd times derivative gain error. ……………………………………………………………(2) This signal (U) will be sent to the plant, and the new output Y will be obtained. Table:Characteristics of P -D controller. System parameters Rise time overshoot settling Steady state error Kp Decrease Increase Small change Decrease Kd Small change Decrease Decrease Small change The focus of this paper is to show how each of Kp and Kd contributes to obtaining. Fast rise time , Minimum overshoot ,reduce steady – state error and Open – loop step response. THE MATHEMATICAL MODEL M (t) + (t) + kY (t) = u(t) ……………………………………………………………(3) Assume all initial conditions are zero using laplace transform ……………………………………………………………..(4) .............................................................................................. (5) Parameters used Stiffness K = 20N/m Mass M = 1kg Damping coefficient b = 15Ns/m Substituting the parameters in eqn. (5). The system transfer function is ……………………………………………………………..(6) Open loop step response employing matlab software is given as shown in the plot below; 26
- 3. Control Theory and Informatics ISSN 2224-5774 (Paper) ISSN 2225-0492 (Online) Vol.3, No.6, 2013 www.iiste.org PROPORTIONAL CONTROL IMPLEMENTATION Step Response 0.05 0.045 0.04 0.035 A p ue mlit d 0.03 0.025 0.02 0.015 0.01 0.005 0 0 0.5 1 1.5 2 2.5 3 3.5 4 Time (sec) Figure 2: Open step response graph From the Table 1 above , the proportional controller kp reduces the rise time, increases the overshoot, and reduces the steady state error. The closed loop transfer function of the proportional controller is given as; ……………………………………………………….(7) using matlab software, and taking proportional gain kp = 300 we have the plot below Step Response 1.4 1.2 A p d m litu e 1 0.8 0.6 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time (sec) Figure 3: Proportional controller graph This plot shows that the proportional controller reduced both the rise time and the steady-state error, increased the overshoot, and decreased the settling time. Proportional-integral control The transfer function is given as …………………………………………………………………..(8) 27
- 4. Control Theory and Informatics ISSN 2224-5774 (Paper) ISSN 2225-0492 (Online) Vol.3, No.6, 2013 www.iiste.org Step Response 1 0.9 0.8 0.7 Am plitude 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time (sec) Figure 4:P-D step response graph Conclusion The proportional-derivative controller has been successfully implemented in the control of electro viscous damper performance characteristics. Rise time, overshoot and the steady state error to step input responses has been implemented using the Mathlab software. REFERENCES Argulles, J., Martin, H. R., and Pick. J., 1973, “Some Experiments with Electrosensitive Fluids,” 3rd International Fluid Power Symposium, Paper F-pp. 25-35, May 9-11. Block, Hermann, and Kelly, Jeffrey Philip, 1986, “Electrorheological Fluids, “Eur. Pat. 0,191,585, Aug. 20. Contrad, H., Sprecher, A.F., Choi, Y., and Chen, Y., 1991, “The Temperature Dependence of the Electrical Properties and Strength of electrorheological Fluids, “The Society of Rheology, Inc., May, 1991, pp. 1393-1410. Duclos, Theodore G., 1987, “An Exponentially Tunable Hydraulic Mount which Uses Electro-Rheological Fluid,” proceedings of the 1987 Noise and vibration conference, pp. 131-137, April 28-30. Duclos, Theodore G., Acker, Debra N., and Carlson, J. David, 1988, “Fluids that Thicken Electrically,” Machine Design, Jan. 21, pp. 42-45. Klingenberg, D.J., van Awol, Frank, and Zukoski, C.F., 1989, “Dynamic Simulation of Electrorheological Suspensions,” Proceedings of the ACS Division of polymeric Materials Science and Engineering, Sept. 11-18, Vol. 61, pp. 154-155. Stangroom, James Edward, July 5, 1977, “Electric Field Responsive Fluids” U.S. Patent 4,033,892. Stangroom, James E., Devcember 12, 1978, “Electric Field Responsive Fluids,” U.S. Patent 4,129,513 Ushijima, T., Takano, K., and Noguchi, T., 1988, “Rheological Characteristics of ER Fluids and Their Application to Antivibration Devices with Control Mechanism for Automobiles,” Passenger Car Meeting & Exposition, Oct.31-Nov.3, 1988, Society of Automotive Engineers, Paper 881787, pp. 1-9. 28
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