Inverted Pendulum Lab Report Pdf

Design a Robust Control for Inverted Pendulum

Dr. ARUNESH KUMAR SINGH Dr. D.K.CHATURVEDI NITIN KUMAR PAL Assistant Professor Professor Ph.D. Student

Abstract: In this paper, robust controller is developed by using H∞ controller to improve the performance of the Invert Pendulum. In this study, a design methodology is introduced that combines the classical PID, the fuzzy controllers and H∞ controller in an intelligent way and thus a new controller has been achieved. The simulations done on inverted pendulum using the new H∞ fuzzy PID controller provides ‘better’ system responses

The greatest singular value is also denoted by When A is a square n-by-n matrix , then the nth singular value (i.e., the least singular value) is denoted by .

VI. SIMULATION AND RESULTS In this paper, the mathematical model and equations using the transfer function of the inverted pendulum have been determined. By implementing all these equations into MATLAB M-file command, and simulate it in MATLAB SIMULATION. The following Open Loop and closed loop SIMULATION of system are shown in Fig (4) and Fig (5). Fig.4 Open- Loop Inverted Pendulum System Fig.5 Closed Loop Inverted Pendulum System The Open and closed loop response of Inverted Pendulum is shown in following Figure (6) to Figure (9), it can be noticed that the inverted pendulum system is not stable without controller. The curve of the pendulum’s angle was approached infinity as the time increases. Fig. 6 Impulse Response of Open loop Inverted Pendulum

Fig. 7 Step Response of Open loop Inverted Pendulum Fig.8 Impulse Response of Closed loop Inverted Pendulum Fig.9 Step Response of Closed loop Inverted Pendulum
A. PID Control

Paz “The Design of the PID Controller” Klipsch School of Electrical and Computer Engineering June 12, 2001.
[9] Katsuhiko Ogata “Modern control Engineering” university of Minnesota, prentice hall, Upper Saddle River. New Jersey 07458
[10] F.Greg Shinskey “PID Control” copyright 2000 CRC Press LLC. “www.engnetbase.com”.
[11] Theory of Robust Control by Carsten Scherer Mechanical Engineering Systems and Control Group Delft University of Technology the Netherlands
.
[12] Lotfi A. Zadeh Berkeley, CA “Fuzzy Logic Toolbox for use with MATLAB” copyright 1995-2002 by The Math Works, Inc.
[13] Yasunobu Seiji and Yamasaki Hiroaki, “Evolutionary Control Method and Swing Up and Stabilization Control of Inverted Pendulum”, Joint 9th IFSA World Congress and [14] Stonier R.J. and Young N., “Co-evolutionary learning and hierarchical fuzzy control for the inverted pendulum”, The Congress on Evolutionary Computation, CEC, 2003, volume 1, Page 467-473
[15] Ben M. Chen, Robust and H∞ Control, Springer-Verlag, 2000.
[16] Sunjie Zhang, Zidong Wang, Derui Ding, and Huisheng Shu “H∞ Fuzzy Control With Randomly Occurring Infinite Distributed Delays and Channel Fadings” IEEE Transactions On Fuzzy Systems, Vol. 22, No. 1, February