A Comparative Study on N-Dot Acceleration Technique

Abstract

For aero-engines, the throttle command is often changed dramatically, which will perturb the control error (defined as actual rotor speed minus desired rotor speed) of the primary set-point controller. When the perturbation is amplified by the gain, the controller will output unreasonable values of control variables, i.e. the mass of fuel flow, and cause abnormal engine operation. For this reason, limit protection controllers are applied to constrain the controlled variables at a safe level. Besides, the transient control modes are required to provide smooth, stall free operation of the engine. The schedule-based approach, which is the traditional transient control mode, is easy to implement but the performance of acceleration and deceleration will suffer from degradation or manufacturing errors. With the development of digital control system, N-dot control mode has been adopted in some modern aero-engines, which focuses on rotor acceleration rather than rotor speed. To some extent, this method can overcome the obstacles of the schedule-based approach. In terms of N-dot control mode, there are two main methods: direct control and indirect control. The former one suggests using a differentiator to get the actual N-dot value, then minus it by the desired N-dot value to get the error of N-dot. When the error is reduced to zero by a controller, the actual N-dot value follows the desired N-dot value. The latter one suggests inputting the desired N-dot value to an integrator for a rotor speed value, which essentially transforms the N-dot command to the speed command. With this transformation, the familiar set-point controller can be used to control the engine following the N-dot command indirectly. This paper presents implementation schemes of the two types of N-dot control, and focuses on a comparative study of them. To avoid integral windup issue when the indirect method switches controllers, such as from N-dot controller to set-point controller, we have introduced a logic to determine whether the integrator is operational. This design allows flexible switchings. After frequency domain analysis, we find out that the essential difference between the two schemes lies in the magnitude of crossing frequency. The direct N-dot control, with a higher crossing frequency, has faster responses but is sensitive to noise. While the indirect N-dot control, with a lower crossing frequency, has slower responses but can suppress noise. When the dynamic nature of sensor and actuator is considered, the direct N-dot control with a higher crossing frequency may cause the close-loop system unstable. Using a reliable aero-engine mathematical model, we designed a set of simulations to test the two N-dot schemes. The simulation results showed that the direct N-dot control performed better than the indirect one under ideal situation. When noise or dynamic nature of sensor and actuator was taken into consideration, however, the indirect N-dot control was more robust, which confirmed the analysis above.