涡轴发动机时延鲁棒串级PI控制器设计

针对涡轴发动机分布式控制系统中存在时延导致系统性能退化的问题，利用线性矩阵不等式（LMI）方法设计了时延鲁棒串级PI控制器。先利用内模控制（IMC）方法得到涡轴发动机串级控制器内、外环的PI控制器结构；再利用频域回路成形的方法给出保证系统具有期望性能的LMI形式约束条件；利用梯度近似的方法通过劳斯-赫尔维茨判据得到保证系统稳定的控制器参数约束条件；最后，在基于TrueTime的涡轴发动机分布式非线性仿真平台上进行数字仿真。仿真结果表明：在0.04 s时延条件下，当功率需求下降5%时，系统的调节时间小于5 s，功率涡轮转速超调不超过0.5%，且其最大燃油变化率只有传统串级PI控制系统的67%；设计的控制器能有效应对涡轴发动机分布式控制系统中存在的时延问题，同时能够以更小的代价保证系统具有期望的性能。

Design of time-delay robust cascade PI controller for turboshaft engine

To address the problem of system performance degradation caused by time delay in the distributed control system of turboshaft engines, this study proposes a method for designing a time-delay robust cascade PI controller based on linear matrix inequalities (LMIs) method. Firstly, the PI controller structure of the inner and outer loops of the cascade controller of the turboshaft engine is obtained according to the internal model control (IMC) method. The constraints in the form of LMI are given by the frequency loop shaping method, which ensures that the system has the desired performance. Then, gradient approximation method is used to derive stability constraints of the system based on the Routh-Hurwitz criterion. Finally, the digital simulation is carried out on the distributed nonlinear simulation platform for the turboshaft engine. The simulation results show that when the power demand drops by 5% with 0.04 s time delay, the adjustment time of the system is less than 5 s, and the power turbine speed overshoot does not exceed 0.5%, with the maximum fuel rate being 67% of the legacy control loop. This shows that the proposed method can effectively deal with the time delay in the turboshaft engine with distributed control system, and ensure the desired system performance at a lower cost .