A New Approach on Stabilization Control of an Inverted Pendulum, Using PID Controller

Abstract:

Inverted Pendulum is a standard problem in control systems and is appropriate for depicting linear control principles. In this system there is an inverted pendulum connected to a cart that moves along a horizontal track with the help of a motor. We can determine the cart’s position and velocity from the motor and the rail track limits the cart’s movement in a bidirectional path. The pendulum’s angle of deviation and the position of the cart are determined by two sensors mounted on the system. Essential measurements and motor control signals are generated by a medium control board linking the computer and the system. Analysis of the results and yielding the control commands are done with the help of a MATLAB program. This is indeed a single input- dual output system because we must be able to control two parameters (pendulum’s angle and cart’s position) with just one control signal to the motor. Since the PID (Proportional Integral Derivative) controller is usually proper for SISO (Single Input Single Output) systems, we are eager to propose a procedure to control one of these parameters underneath the other. In this paper two tactics are described: 1. controlling the cart’s position beneath the pendulum’s angle, and 2. controlling the pendulum’s angle beneath the cart’s position. Regarding the results, one method is proven to be superior. We also mention some practical considerations in this paper.

• Periodical: Advanced Materials Research (Volumes 403-408)
• Pages: 4674-4680
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.403-408.4674
• Online since: November 2011
• Authors: Kaveh Razzaghi, Ali Akbar Jalali
• Keywords: Inverted Pendulum, Linearization, MIMO, PID

References

[1] S. Mirsaeed Ghazi, Ali A. Jalali, "Low frequencies optimal control of an Inverted Pendulum.", International Conference on E-Learning and Industrial Electronics (IEEE-ICELIE), pp.85-90, 2006.

DOI: 10.1109/icelie.2006.347190

[2] Q.R. Li, W.H. Tao, S. Na, C,Y Zhang, L.H Yao, " Stabilization control of Double Inverted Pendulum System." , 3rd International Conference on Innovative Computing Information and Control (ICICIC), pp.417-423, 2008.

DOI: 10.1109/icicic.2008.662

[3] J. Aracil, J.A. Acosta, F. Gordillo, "Kinetic energy shaping in the Inverted Pendulum.", 6th IFAC Symposium on nonlinear Control Systems (NOLCOS), 2004.

DOI: 10.1016/s1474-6670(17)31367-8

[4] G.D Franklin and J.D Powel. "Digital control of dynamic systems", Menlo Park, CA: Adison Wesley Longman, 1998.

[5] J.J Slotin and W. Li, Applied nonlinear control, Prentice Hall, USA, pp.105-122, 1998.

[6] J. Xie, X. Xu, K. Xie, "Modeling and simulation of the Inverted Pendulum based on granular hybrid system.", Chinese Control and Decision Conference (CCDC), pp.3795-3799, 2008.

DOI: 10.1109/ccdc.2008.4598041

[7] Regents of the University of Michigan. (1996), "Control tutorials for MATLAB and simulink", [Online]. Available http://www.engin.umich.edu/class/ctms/examples/pend/invpid.htm.