Electric train speed control using linear quadratic Gaussian control under measurement noise and operating uncertainties
This paper presents an estimator-based linear quadratic Gaussian (LQG) control framework for electric-train speed regulation under noisy measurements and uncertain operating conditions. A control-oriented nonlinear longitudinal model is developed by considering traction and braking forces, aerodynamic drag, rolling resistance, grade resistance, wheel-slip effect, actuator saturation, and speed-dependent power limitation. The model is linearized around a nominal operating point, and an integral error state is added to improve reference-speed tracking. An LQR feedback controller is then combined with an extended Kalman filter to estimate train speed and sensor bias from noisy measurements. The proposed controller is evaluated through numerical simulations under constant-speed and variable-speed references with passenger-load variation, track-slope disturbance, aerodynamic uncertainty, wheel slip, sensor bias, measurement noise, process noise, and combined disturbances. Additional simulation-based sensitivity analysis is also performed using an extended practical-dynamics plant that includes reduced-order traction motor dynamics, actuator delay, adhesion limitation, and track-curvature resistance. Direct LQR feedback and conventional sliding mode control (SMC) are used as comparison baselines. The results show that direct LQR is highly sensitive to noisy measurements, while SMC gives lower tracking-error indices but produces larger overshoot, actuator saturation, and higher traction-energy demand. In contrast, the proposed LQG controller provides smoother and more actuator-feasible control while maintaining acceptable tracking accuracy. The extended practical-dynamics results further show that the controller remains stable and feasible under the added simulation-based railway effects. Therefore, the proposed LQG framework offers a practical balance between speed tracking, noise rejection, control smoothness, and actuator feasibility for simulation-based electric-train speed regulation.