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摘要:
为了提升航空发动机非线性模型预测控制（MPC）的实时性，将交替方向乘子法（ADMM）应用于模型预测控制的滚动优化中。基于状态空间模型构造预测方程，通过引入辅助变量和对偶变量，将二次型性能指标和发动机约束改写为适合ADMM算法求解的形式。在航空发动机部件级模型上开展的仿真结果表明，基于ADMM算法的单变量模型预测能够实现对指令信号的高性能跟踪和约束的有效管理。相比于内点法（IPM），ADMM算法在滚动优化过程中，在不同控制指令下，均具有更高的实时性，且在预测时域增加的情况下，计算耗时增加更少，验证了其在模型预测控制中应用的有效性。
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关键词:
- 航空发动机 /
- 模型预测控制 /
- 交替方向乘子法(ADMM) /
- 二次规划(QP) /
- 实时性
Abstract:In order to improve the real time performance of the nonlinear model predictive control (MPC) for aero-engine, an alternating direction method of multipliers (ADMM) was applied to the receding horizon optimization of MPC. The predictive equation was constructed based on the state space model. The auxiliary variables and dual variables were introduced to rewrite the quadratic control performance index and engine constraints into a new form which could be solved by ADMM. Simulations on a component level model show that the single input variable model predictive control based on ADMM achieves both high-quality reference tracking performance and efficient limit management of aero-engine. Compared with interior point method (IPM), the real time performance of ADMM is much better than that of IPM at different magnitude control commands, and the increment of time consumption is much less than that of IPM with the increase of the predictive horizon. The effectiveness of the ADMM in MPC is valid.
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图 4 控制序列优化所需平均时间与预测时域的关系
Figure 4. Average time consumption for control sequence optimization vs predictive horizon
表 1 仿真参数
Table 1. Simulation parameters
编号 ΔNh np 1 0.03 2 2 0.08 2 3 0.15 2 4 0.18 2 5 0.18 4 6 0.18 6 7 0.18 8 8 0.18 10 9 0.18 12 10 0.18 14 
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表 2 两种算法完成一次控制序列优化所需时间对比
Table 2. Time consumption comparison of two methods in finishing one-time control sequence optimization
编号 所需时间/ms IPM ADMM 1 10.67 3.67 2 10.57 3.80 3 10.10 3.60 4 11.97 3.50 5 25.87 5.00 6 41.33 6.80 7 76.50 8.20 8 108.83 10.53 9 167.00 14.13 10 224.60 15.53
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