Sampled-Data Control for Optimal Gain Margin of Cart Inverted Pendulum System: Comparison with Continuous-Time Control

Seeking to robustly stabilize the cart-inverted-pendulum (CIP) system in the discrete domain, this paper first obtains, via an iterative approach for a sampling rate $T$, the controller that achieves a multiloop gain margin optimization that is analogous to what has been achieved via continuous-domain in [13]. Unlike what may be expected, however, the optimal gain margins obtained are not found to improve monotonically with reduction in $T$. Consequently the optimal $T$ and the corresponding discrete-domain controller that maximizes the gain margin is obtained. The same, moreover, is found to be superior to what the optimal continuous-domain design yields. An explanation for this counter intuitive observation is provided. This has also been verified using physical implementation.