Tracking-protection-recovery switching control for aero-engines☆
Introduction
Since engines are one of the most essential components of aircraft, research on engine control has attracted much attention in recent years [1], [2], [3]. Modeling and control of the aero-engine has become more and more important research field. Advanced control methods have been applied to the aero-engine control, such as adaptive control [4], distributed control [5], fuzzy control [6], gain scheduling control [7], linear parameter-varying (LPV) control [8], model predictive control (MPC) [9], sliding mode control (SMC) [10], and so on. The strong couplings among flight dynamics, aerodynamics, propulsion and control [1], [2], [3] result in various engine safety boundaries during the working process of the aero-craft. Safety boundaries usually include the combustion stabilization boundary, the combustor wall temperature limitation, the inlet channel un-start boundary, and so on. Disastrous accidents may happen once the system trajectory exceeds any one of the safety boundaries. Therefore, protection measures must be taken. On the other hand, to pursue desirable flight performance, the aero-engines are usually required to work close to the safety boundaries. For example, in work [23] and [24] controllers are designed to pursue performance such as fast response, handling quality and robust stability. The traditional safety protection measures usually sacrifice the rapidity performance to guarantee safety. One of the effective strategies to deal with the contradiction between the rapidity performance and safety requirements is to apply the switching control scheme [11], [12] to the multi-objective control problem.
Applying the switching multi-objective control scheme, the design procedure is with larger degree of freedom and less conservatism. The tracking controller and protection controllers can be designed separately. That reduces the complexity and enlarges the degree of freedom of design. Otherwise, it is more complicated if we consider the safety constraints simultaneously when designing the thrust tracking controller for an aero-engine. The properly designed switching law can select the intervals when protection controllers are necessary, leaving more intervals for the system to pursue tracking performance. The multi-objective switching control strategy is expected to bring improvement on both thrust tracking performance and safety.
Several results on multi-objective switching control are available in the literature [13], [14], [15], [16], [17], [18], [19], [20], [38]. The widely used min/max control switching law is studied in work [13] and [14]. However, the safety performance, finite number of switching and stability are all not guaranteed theoretically. The min/max control switching scheme is combined with sliding mode control to ensure safety in [10]. The result in [10] is extended to the multi-input case to make full use of the control inputs [39]. However, a properly designed switch-off condition may bring more freedom to pursue tracking performance. Moreover, an associated sliding mode surface is designed for the fan speed set-point objective, which may also limit the system to pursue tracking performance.
To solve the multi-objective control problem using switching strategy, we must guarantee transient performance as much as possible in the safety region. An expected switching law, including switch-on condition and switch-off condition for the protection controller, should be properly designed to guarantee both thrust control performance and safety. A safety-margin-dependent switching law was proposed [15], [16], [17], [18]. The protection controller is activated at precisely necessary moments. It is reasonable that more information than only the control input must be used. But the switching designed only according to the safety margin may bring unexpected control discontinuity and thus deteriorate the performance. The work [19] designs a bumpless switching controller to reduce this control discontinuity. A coordinated switching strategy is presented to take advantage of the two switching methods above in [20]. But no stability analysis is included.
However, how to conduct the dual design of the controller and the switching law to improve both thrust performance and safety margin is an essential problem. The well-developed switched system theory [25], [26], [27], [28], [29], [30], [31], [32], [37] provides no methods to solve this problem. This motivates our research work.
In this work, a novel tracking-protection-recovery switching strategy will be proposed to solve the thrust tracking and safety protection multi-objective control problem for the aero-engines. The contradiction between the tracking performance and the safety requirement will be largely overcome by the proposed strategy, the one with larger design degree of freedom and less conservatism. The switching controller can be designed in three steps. For the tracking stage, the tracking controller will be designed to make the fan speed track the command as quickly as possible. For the protection stage, the protection controller will be activated as the system trajectory reaches the safety boundary to ensure safety. For the recovery stage, the recovery controller and the resetting law will be properly designed to ensure invariance and stability. Finally, a case study for a two-spool turbofan engine model will be performed to verify the effectiveness of the given method.
Section snippets
Multi-objective control problem arising from aero-engine control
For an aircraft, an aero-engine control system with high performance is required to achieve high performance flight. But there are many limitations during the working process. High performance is usually achieved very near the safety limitations. Control design must make a compromise between performance and in Fig. 1, the safe working region is shown. The fan speed, as an important representation of thrust, is usually selected as the controlled output. During an acceleration procedure, for
Main results
In this section, we will propose a tracking-protection-recovery multi-objective switching control strategy. An asymptotic tracking condition for the closed-loop switched system will be given.
Case study
We will verify the effectiveness of the proposed tracking-protection-recovery switching strategy through the two-spool turbofan engine model in work [10]. The considered simplified model can approximate the aero-engine well under the step command with small amplitude such as the step signal yr1(t) we consider here. The parameters are the same as in the motivating example. Obviously, the given parameters satisfy the Assumption1 to Assumption3.
For the tracking stage, the tracking PI control
Conclusion
A novel tracking-protection-recovery multi-objective switching strategy has been proposed in this paper. As a solution to the thrust tracking and safety protection control problem for the aero-engines, the proposed strategy overcomes the contradiction between the tracking performance and the safety requirement, with larger design degree of freedom and less conservatism. The proposed switching controller can be designed in three steps.
For the tracking stage, we take advantage of the
References (40)
A multi-regulator sliding mode control strategy for output-constrained systems
Automatica
(2011)- et al.
Switching control of thrust regulation and inlet buzz protection for ducted rocket
Acta Astronaut.
(2010) - et al.
Multi-objective flight controller for an airplane with multiple operating points
- et al.
Hysteresis-based switching algorithms for supervisory control of uncertain systems
Automatica
(2003) - et al.
Stability and L2 gain analysis for switched delay systems: a delay-dependent method
Automatica
(2006) - et al.
Global finite-time stabilization of a class of switched nonlinear systems with the powers of positive odd rational numbers
Automatica
(2015) - A. Rodriguez, J. Dickeson, O. Cifdaloz, A. Kelkar, J. Vogel, D. Soloway, R. Mc Cullen, J. Benavides, S. Sridharan,...
- et al.
The X-51A scramjet engine flight demonstration program
- et al.
Modelling for couplings of an airframe - propulsion integrated hypersonic vehicle with engine safety boundaries
Proc. IMechE, Part G: J. Aerosp. Eng.
(2010) - M. Pakmehr, Towards verifiable adaptive control of gas turbine engines, Ph.D. dissertion, Georgia Institute of...