Exploring LQI Control in Sampled-Data Systems: A Numerical Study for First-Order Systems

This work aims to numerically study the impact of implementing a discrete-time Linear Quadratic Integral (LQI) controller. The discrete-time controller is based on a previously designed continuous-time one. The precision of this implementation is assessed by comparing the cost function of the continuous-time controller with the results obtained from implementing a discrete-time controller in a sampled-data feedback loop. Our analysis explores the effects of discretisation using various integral approximations and different sampling times. Our simulations show a disparity between continuous and sampled-data system costs for insufficiently low sampling periods, along with how the performance of the integration methods depends on the chosen weighting matrices. This research highlights the challenges and considerations in transitioning from continuous-time to discrete-time control.