Control System Design for a Mobile Inverted Pendulum via Sliding Mode Technique

Nonlinear control of mobile inverted pendulum

“…The controllers proposed for MIP in [1], [8], [9] can perform autonomous navigation whereas in [3] it can track driver's input. As an application of MIP, a baggage transportation system is proposed in [16] by configuring the system into two co-operative subsystems namely, balancing and traveling control subsystem and navigation control subsystem.…”

“…The system can not be fully feedback linearizable and the internal dynamics are nonlinear [5], [6]. Many control strategies are developed for MIP in the literatures based on the stabilization principle of inverted pendulum [7] and control techniques such as pole placement [3], [8], sliding mode [9], [10], backstepping [11], Lyapunov redesign [12], adaptive control, fuzzy control [13], [14] and neural control [15] have been proposed.…”

Constrained H∞/LTR control design for a mobile inverted pendulum

“…Therefore, the Equation (10) cannot be true. However, it is not necessary to have the exact equality as in Equation (10). It is just necessary to have the equity over the band of frequencies relevant to our concern.…”

“…According to [10], a continuous-time nonlinear model of a mobile inverted pendulum ( Fig. 1) can be written as follows,…”

“…Then the constrained input is given as By using the method in [6], the state feedback gain can be obtained as follows, ] 0.8290 5469 . 10 [ K The LMIs in [6] are solved with γ=0.5 and α=1. The norm of the resulting state feedback gain is not large, it is only 10.5794.…”