Performance Assessment of Unstable Systems Subjected to Ramp Input Changes

The chapter presents a comprehensive analysis of performance assessment methods for unstable systems subjected to ramp input changes. It introduces an innovative IAE–TV index, which combines Total Variation (TV) and Integral Absolute Error (IAE) to evaluate the performance of PI controllers. The index is designed to measure the smoothness and accuracy of control outputs, ensuring that the controller meets desired performance targets. The chapter also discusses the theoretical derivation of the TV and IAE bounds, and provides a detailed evaluation procedure. Simulation results validate the effectiveness of the proposed IAE–TV index, demonstrating its potential to enhance control performance in unstable systems. The chapter concludes by highlighting the practical implications of the new index and its potential to improve control strategies in various industrial applications.