Introducing integral compensation into controller synthesis based on noncausal LPTV scaling and control experiments with cart inverted pendulum

This paper aims at improving control performance of control systems designed through discrete-time non-causal linear periodically time-varying (LPTV) scaling by introducing integral compensation. A controller designed with noncausal LPTV scaling generally becomes LPTV rather than linear time-invariant. This situation may cause a new issue when we introduce integral compensation. Hence, we study in detail how to introduce integral compensation to construct an augmented system for which a controller is designed through noncausal LPTV scaling. Effectiveness of the introduced integral compensation is also demonstrated by control experiments with a cart inverted pendulum whose pendulum length can be set from three different choices.