A Criticism of Position Control of the Inverted Pendulum with Biased Angle Measurements Using Double-Loop PID

Using imperfect measuring tools increases inaccuracies which then leads to a weak performance or in worst-case scenario, causing instability. On the other hand, utilizing more reliable instruments hire charges. Biased measurements is one of the problems caused by inaccuracies. Even a poor calibration may create the same effects. Eventually finding methods that help stabilizing systems asymptotically, using more affordable sensors and having easier calibrations is essential. Inverted pendulum is one of the benchmark devices in control theory because of its strong nonlinearity coupling. To control both angle and position of an inverted pendulum with classical control theory, a double-loop PID controller is required. This controller can be castoff in parallel or series arrangements. In this work, both methods utilized considering the effect of biased angle measurement. Simulation results obtained, considering nonlinearities such as quantized measurements, the dead zone of DC motor, and saturation. Analytical calculations demonstrate the effects of measurement bias on the closed-loop system. Besides, both simulation and experimental results confirm this assertion.