Rotational Inverted Pendulum:

The rotational inverted pendulum is a nonlinear plant that is commonly found in university control laboratories (often, however, it is of the cart-pole variety on a track). The inverted pendulum consists of two joints: the rotating base, and the actual "pendulum''. Note that this system is an "underactuated'' system, as there is only a single input (actuator) to control two outputs. The inverted pendulum system utilizes two optical encoders to measure the angular position of both joints at each sampling instant. The optical encoder outputs are passed through a signal conditioning circuit before being acquired by the computer. The signal conditioning circuit outputs pulses which are counted by four separate counter/timers on a data acquisition board installed in the computer. The signal conditioning circuit is used to double the encoder's effective resolution, as well as to determine the direction of rotation. The system is actuated by a DC motor which applies a variable torque to the rotating base. A servo-amplifier is used to control the DC motor; this amplifier accepts control inputs from the DAS20's D/A converter in the range [-5,5] Volts. The inverted pendulum system allows the user to change the system parameters, or add disturbances, by attaching containers of various size and contents to the end of the pendulum (e.g., in labs on adaptive control a container of bolts or water is added to the end of the pendulum as a disturbance). The mass of the container and its contents significantly changes the system parameters, while the motion of the contents within the container acts as a disturbance to the system. For more details on the rotational inverted pendulum system see:

S. Yurkovich and M. Widjaja, "Fuzzy Controller Synthesis for an Inverted Pendulum System," to appear in IFAC Control Engineering Practice, Vol. 4, 1996.

M. Widjaja and S. Yurkovich, "Intelligent Control for Swing Up and Balancing of an Inverted Pendulum Systems," Proceedings of the IEEE International Conference on Control Applications, Albany, NY (September 1995)