In conventional linear parameter-varying (LPV) modelling and gain scheduling control design for turbojet engines, the linearisation is performed at a set of equilibrium points, and the validity of such LPV models is ensured near the equilibria. However, the linear model can only provide an approximate description of the engine’s state when the system operates away from equilibrium. In this paper, it is suggested that such linearisation should be carried out not only at equilibrium states but also in transient (off-equilibrium) operating regimes. This will result in a global approximation to the system states whether equilibrium or off-equilibrium. Theoretically, the transient control performance can be improved by introducing such an off-equilibrium linearisation-based control procedure. Subsequently, a gain scheduling control procedure based on off-equilibrium linearisation models is proposed by using sum-of-squares (SOS) programming, which, compared with many convex programming methods, can provide less conservative results. The resulting off-equilibrium linearisation-based nonlinear control procedure with SOS programming can capture a wide range of transient engine dynamics with better accuracy, and further achieve better control performance.

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基于非平衡线性化的涡轮喷气发动机非线性控制与平方和规划

在涡轮喷气发动机的传统线性参数变化（LPV）建模和增益调度控制设计中，线性化是在一组平衡点处执行的，并且这种LPV模型的有效性在平衡附近得到保证。然而，线性模型只能提供系统运行偏离平衡时发动机状态的近似描述。在本文中，建议这种线性化不仅应在平衡状态下进行，而且应在瞬态（非平衡）运行状态下进行。这将导致系统状态的全局近似，无论是平衡状态还是非平衡状态。理论上，可以通过引入这种基于非平衡线性化的控制程序来改善瞬态控制性能。随后，提出了一种基于非平衡线性化模型的增益调度控制程序，采用平方和（SOS）规划，与许多凸规划方法相比，可以提供较少保守的结果。由此产生的基于非平衡线性化的非线性控制程序与 SOS 编程可以更准确地捕获广泛的瞬态发动机动力学，并进一步实现更好的控制性能。