基于分数阶微积分的飞航式导弹控制系统设计方法研究
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摘要
PID控制器在飞行控制中一直占主导地位。因此，我们有必要进一步挖掘它的潜能，提高它的控制品质。
本文尝试利用分数阶微积分理论把传统的PID控制器的阶次推广到分数领域，设计一种新PID控制器—分数阶PI~λD~μ控制器，期望这种控制器能继承和发扬传统PID控制器的优点，同时能弥补其不足。相对传统PID而言，PI~λD~μ控制器主要有两个优点：一是增加了调节自由度；二是其微分项也具有积分的功能，这种记忆功能确保历史信息对现在和未来的影响。然后，利用分数阶控制器设计飞航导弹控制系统，以提高飞航导弹控制系统的品质。
本文首先介绍了分数阶微积分的历史、定义、性质及其数值方法；给出了分数阶系统的稳定性条件、可控性和可观性判断依据；分析了分数阶控制器PI~λD~μ的参数整定方法；结合飞航导弹的飞行特性，提出了自控段使用姿态自动驾驶仪+PI~λD，自导段使用过载自动驾驶仪+PD~μ的控制思想。
仿真结果表明：分数阶微积分理论在飞行控制系统设计中是一个有用的工具，由此而设计的分数阶控制器对其本身参数和被控对象参数的变化都不敏感，具有更灵活的结构和更强的鲁棒性；分数阶控制器提高了飞航导弹控制系统的性能，增强了导弹的抗干扰能力，提高了导弹的命中精度和机动性。
PID controllers belong to the dominating flight controllers and therefore there is a continuous effort to improve their quality.
Looking forward to developing the merit of the PID controllers and overcoming the flaw of the PID controllers, one of the possibilities to improve PID controllers is to use fractional order controllers based on the fractional calculus. The novelty of the proposed controllers consists in the extension of derivation and integration order from integer to non-integer order. The fractional order controllers mainly have two advantages relating to the integral-order controllers, the one is that it has more degrees of freedom in the model, the other is that it has a "memory" in model, the memory insures the history and its impact to present and future. At last, the fractional controllers are used to control the aerodynamic missile in order to improve the flight performance of the missile.
In this thesis, the elementary knowledge of fractional calculus, such as history, definitions, properties and digital method, are outlined. The stability, controllability and observability of fractional order system are investigated. The parameters tuning method of the fractional order controllers are determined according to the given requirements. Integrating flight characteristic of the aerodynamic missile, the PI~λD controllers are applied to attitude autopilot control of navigational stage and the PD~μ controllers are applied to overload autopilot control of homing stage.
The simulation results show that the fractional order controllers are not sensitive to the changes of control parameters and controlled object parameters. At the same time, it has more flexible structure and stronger robustness. The fractional calculus has been demonstrated to a useful tool for flight control and the designed fractional order controllers can be implemented to improve the missile performance. The missile can obtain a greater anti-jamming ability, a more excellent precision and an agile maneuverability.
本文尝试利用分数阶微积分理论把传统的PID控制器的阶次推广到分数领域，设计一种新PID控制器—分数阶PI~λD~μ控制器，期望这种控制器能继承和发扬传统PID控制器的优点，同时能弥补其不足。相对传统PID而言，PI~λD~μ控制器主要有两个优点：一是增加了调节自由度；二是其微分项也具有积分的功能，这种记忆功能确保历史信息对现在和未来的影响。然后，利用分数阶控制器设计飞航导弹控制系统，以提高飞航导弹控制系统的品质。
本文首先介绍了分数阶微积分的历史、定义、性质及其数值方法；给出了分数阶系统的稳定性条件、可控性和可观性判断依据；分析了分数阶控制器PI~λD~μ的参数整定方法；结合飞航导弹的飞行特性，提出了自控段使用姿态自动驾驶仪+PI~λD，自导段使用过载自动驾驶仪+PD~μ的控制思想。
仿真结果表明：分数阶微积分理论在飞行控制系统设计中是一个有用的工具，由此而设计的分数阶控制器对其本身参数和被控对象参数的变化都不敏感，具有更灵活的结构和更强的鲁棒性；分数阶控制器提高了飞航导弹控制系统的性能，增强了导弹的抗干扰能力，提高了导弹的命中精度和机动性。
PID controllers belong to the dominating flight controllers and therefore there is a continuous effort to improve their quality.
Looking forward to developing the merit of the PID controllers and overcoming the flaw of the PID controllers, one of the possibilities to improve PID controllers is to use fractional order controllers based on the fractional calculus. The novelty of the proposed controllers consists in the extension of derivation and integration order from integer to non-integer order. The fractional order controllers mainly have two advantages relating to the integral-order controllers, the one is that it has more degrees of freedom in the model, the other is that it has a "memory" in model, the memory insures the history and its impact to present and future. At last, the fractional controllers are used to control the aerodynamic missile in order to improve the flight performance of the missile.
In this thesis, the elementary knowledge of fractional calculus, such as history, definitions, properties and digital method, are outlined. The stability, controllability and observability of fractional order system are investigated. The parameters tuning method of the fractional order controllers are determined according to the given requirements. Integrating flight characteristic of the aerodynamic missile, the PI~λD controllers are applied to attitude autopilot control of navigational stage and the PD~μ controllers are applied to overload autopilot control of homing stage.
The simulation results show that the fractional order controllers are not sensitive to the changes of control parameters and controlled object parameters. At the same time, it has more flexible structure and stronger robustness. The fractional calculus has been demonstrated to a useful tool for flight control and the designed fractional order controllers can be implemented to improve the missile performance. The missile can obtain a greater anti-jamming ability, a more excellent precision and an agile maneuverability.
引文
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3 范金荣．21世纪前20年精确制导技术发展预测．现代防御技术．2003(1)：30-33
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