The One Step Ahead Controllers represent a branch of the Minimum Prediction Error Adaptive Controllers. They combine the parameter estimation of the controlled system model with a particular control scheme; therefore, they are especially suitable for non-linear and time-varying systems. Since the estimated parameters are updated at each time step (by using the sampled data), these methods can be adopted for real-time applications. Consequently, the One Step Ahead Controllers do not require the knowledge of the dynamic characteristics of the controlled system (e.g. state space systems or transfer functions).
The One Step Ahead Adaptive (OSAA) algorithm combines the Least Square Algorithm (LSA) parameter estimator with a Deterministic Auto-Regressive Moving Average (DARMA) control scheme. The DARMA model can be characterized with a different number of time steps in the past (order of the estimated model) in relation to the dynamic feature of the controlled system.
Sometimes, an excessive control effort could arise, caused by sudden variations of the electric load. In order to reduce this control action, the OSAA control technique has been applied also in Weighted fashion. The Weighted One Step Ahead Adaptive (WOSAA) control algorithm considers a penalty associated with the control effort by use an appropriate cost function. In this way, the control variable does not assume too large values, even when the Gas Turbine undergoes sudden changes in the external load. As a consequence, the robustness and the stability features of the WOSAA control system are increased with respect to the OSAA algorithm.
The proposed techniques have been applied to a single shaft heavy-duty gas turbine (WOSAA) and to a double-shaft aero-derivative gas turbine (OSAA). They have been tested in Single-Input Single Output (SISO) mode. In the simulation tests, the plant is assumed to undergo sudden variations of the electric load. Second order schemes of the OSAA estimated model have been derived and applied to the double-shaft aero-derivative gas turbine.
The results show that the OSAA control technique, applied to the double-shaft aero-derivative gas turbine, effectively counteracts the load reduction with limited overshoot in the controlled variables and, introducing an integral correction, with a negligible static error. On the other hand, the WOSAA control algorithm is able to efficiently regulate the single shaft heavy-duty gas turbine, and to counteract the sudden variations of the electric load, with reduced control effort.
Design and Simulation of an LQR-PI Control Algorithm for Medium Wind Turbine
