Enhancing Boiler-Turbine Trajectory Tracking with LQR-Optimized PID Control Strategy

The goal of this research is to stabilize and track the trajectory for electrical power produced by a boiler turbine system utilizing a Proportional-Integral-Derivative (PID) controller. The controller gains are computed using a linear quadratic regulator (LQR). Initially, the system's nonlinear mathematical model is derived from the first principle model. The nonlinear system is subsequently linearized around the equilibrium point by using the Taylor series to create the stabilizing controller. Finally, the LQR theory is used to calculate the gains of the PID controller to obtain the required response for the electrical power. In this paper, a criteria for choosing the weighting matrices of LQR for tracking electrical power is provided, based on the damping ratio and natural frequency of the closed loop system. The performance of the boiler turbine system is analyzed on the generated electrical power output generated. The results show that the suggested control approach is successful in rejecting disturbances present in the system as well as stabilizing the electrical power of the boiler turbine system. The analysis of the controller’s performance is conducted through the calculation of Integral absolute error (IAE), Integral square error (ISE), and Integral time absolute error (ITAE) which gives insights into the controller’s effectiveness in regulating the system behavior.