Development of Virtual Environment for Swing-Up Control of Rotary Double Inverted Pendulum for Engineering Education

The swing-up control of rotary double inverted pendulum is a benchmark problem discussed during advanced control systems engineering. It is a single input underactuated system which consists 4th order nonlinear kinematics. Coriolis forces of the pendulum links coupled with the gravitational forces makes it a challenging task to stabilize the total system. The fabrication of such a system under an acceptable level of accuracy requires precision machining and high-quality electronic components such as encoders and motors. Under the current economical fluctuations, affording a full product directly from the market is a financially challenging task for the Sri Lankan state universities. Considering current number of student enrolments, one product per an institute would not serve enough. In this study, an offline virtual model similar to the real-world conditions with encoder behaviour with sensor noise and actuator dead zone has been developed for the swing-up control of rotary double inverted pendulum. The mathematical model was developed using the Euler-Lagrangian method. The swing-up controller was designed as a muti-stage energy controller with a vertical stabilizing controller. The computer aided design shows the real time motion. Collectively, this virtual environment could be used by multiple users at once to engage in the teaching and learning process of advanced control systems engineering without depending on physical resources or the internet.