The rotary inverted pendulum is an interesting example of an underactuated unstable nonlinear system. It is widely used as a benchmark example for nonlinear control design. In this work, we examine some adaptive estimation and classical control techniques for the rotary inverted pendulum system, with hardware implementation on the Quanser QUBE-SERVO. Starting with the system model, derived using the Euler-Lagrange formulation, we validate the model on experimental data, using standard estimation techniques, such as gradient descent with integral cost, pure least squares (PLS), and recursive least squares (RLS) with covariance resetting. The standard control design for the rotary inverted pendulum has two parts: (i) swing-up control, where energy-based ideas are used to move the pendulum from the downward rest position towards the upward position, and (ii) balance control, which uses feedback to render the equilibrium point stable. We compare several designs for both swing-up as well as balance control, including pole placement using classical performance measures (such as the ITAE criterion), and LQR (linear quadratic regulator) design. The efficacies of the designs are compared and validated using simulations and hardware implementations on the QUBE-SERVO.
