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

Abstract

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.

An analytical adaptive optimal control approach without solving HJB equation for nonlinear systems with input constraints

“…In recent years, among the mentioned methods, the regularization method and the approach based on a discriminant equation are almost not used, and literatures have focused more on Galerkin methods [32], inverse optimal control [33], SDRE approaches [34,35], and RL-based methods [36]. The control approach in [32] for boiler-turbine units combines a high-order sliding mode disturbance observer and a receding Galerkin optimal controller to compensate for disturbances. However, effective implementation of this approach requires complete knowledge of the system.…”

“…In order to adjust the weights of the NN, let (32) and (33) give the adaptation laws. Despite actuator constraints and uncertainty in drift dynamics, applying the obtained control input (26) results in the tracking errors and the estimated weights being ultimately bounded.…”

“…Therefore, choosing them is a trade-off between not to make the hyperbolic tangent in ( 26) too small to keep the value of u close to zero and not too large so that the hyperbolic tangent function quickly reaches its saturation value. According to (39), it is recommended to choose small values for 𝜂 1 in the adaptation law (32). Moreover, Γ 1 has a direct impact on the adaptation speed, where a larger value of Γ 1 results in a faster adaptation.…”

“…□ Remark 6. In a comparison between the proposed method and the methods used in recent literature mentioned in Section 1.1.1, it can be said that unlike [32,36], the proposed method does not require a prior knowledge of system dynamics. Furthermore, the proposed method does not require the approximation of the HJB equation.…”