Balancing Double Inverted Pendulum on a cart by Linearization Technique
Mandar R. Nalavade1, Mangesh J. Bhagat2, Vinay V. Patil3
1Mandar R. Nalavade, Department of Electrical, Control System, Veermata Jeejabai Technical Institute, Mumbai (Maharashtra), India.
2Mangesh J. Bhagat, Department of Electrical, Control System, Veermata Jeejabai Technical Institute, Mumbai (Maharashtra), India.
3Vinay V. Patil, Department of Electrical, Control System, Veermata Jeejabai Technical Institute, Mumbai (Maharashtra), India.
Manuscript received on 20 March 2014 | Revised Manuscript received on 25 March 2014 | Manuscript published on 30 March 2014 | PP: 153-157 | Volume-3 Issue-1, March 2014 | Retrieval Number: A1031033114/2014©BEIESP
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Abstract: Double Inverted Pendulum on a cart (DIPC) is a classic problem in dynamics and control theory and is widely used in control laboratories to demonstrate the effectiveness of control systems as well as a benchmark for testing control algorithms. It is suitable to investigate and verify different control methods for dynamic systems with higher order nonlinearities. A controller is proposed to swing a double inverted pendulum to an unstable upright inverted position and stabilize around the point by using Linear Quadratic Regulator (LQR) technique. Linearization form of nonlinear system is obtained by Jacobian with proper cost function and the modeling of it is accomplished with the help of Euler – Lagrangian equation derived by specifying Lagrangian, difference between kinetic and potential energy of DIPC. Simulation results are retrieved by MATLAB.
Keywords: Double Inverted Pendulum on a Cart, Jacobian, Lagrangian, LQR.
Scope of the Article: Data Mining Methods, Techniques, and Tools