Receding Galerkin Optimal Control with High-Order Sliding Mode Disturbance Observer for a Boiler-Turbine Unit

The control of the boiler-turbine unit is important for its sustainable and robust operation in power plants, which faces great challenges due to the control unit's serious nonlinearity, unmeasurable states, variable constraints, and unknown time-varying lumped disturbances. To address the above issues, this paper proposes a receding Galerkin optimal controller with a high-order sliding mode disturbance observer in a composite scheme, in which a high-order sliding mode disturbance observer is first employed to estimate the lumped disturbances based on a deviation form of the mathematical model of the boiler-turbine unit. Subsequently, under the hypothesis of state constraint, a receding Galerkin optimal controller is designed to compensate the lumped disturbances by embedding their estimates into the mathematically based predictive model at each sampling time instant. With the help of an interpolation polynomial, Gauss integration, and nonlinear solvers, an optimal control law is then obtained based on a Galerkin optimization algorithm. Consequently, disturbance rejection, target tracking, and constraint handling performance of a controlled closed-loop system are improved. Some simulation cases are conducted on a mathematical boiler-turbine unit model to demonstrate the effectiveness of the proposed method, which is supported by the quantitative result analysis, such as tracking and disturbance rejection performance indexes.