Linear-Quadratic Model Predictive Control for Continuous-time Systems with Time Delays and Piecewise Constant Inputs

Exact discretization of continuous linear time-delay systems with quadratic objective functions, under piecewise constant manipulated variables, is used to design and implement a novel linear model predictive controller, termed the continuous-time linear-quadratic model predictive controller (CT-LMPC). The key novelty in the paper is the exact numerical discretization of CT time-delay linear-quadratic systems. The control model of the CT-LMPC is parameterized using transfer functions with delays. We formulate linear-quadratic optimal control problems (LQ-OCPs) with time delays for the CT-LMPC and derive their discretization under the assumption of piecewise constant inputs. Time-delay systems are ubiquitous in process industries, such as the cement industry, where conveyor belts introduce delays, making continuous-time modeling advantageous. We illustrate the CT-LMPC with both SISO and MIMO examples inspired by the cement industry. The results demonstrate that, for fixed parameters, the CT-LMPC outperforms the conventional discrete-time LMPC as the sampling time increases.