小型无人直升机的模型预测控制算法研究

Model predictive control for small-scale unmanned helicopte

针对无人直升机在阵风干扰环境中的姿态控制精度低的问题.本文将非线性刚体动力学模型在悬停点应用小扰动理论得到了线性化数学模型.考虑系统输入输出和控制量约束,采用模型预测控制将控制器的设计问题转化为每个采样时刻求解一个带不等式和等式约束的凸二次规划问题.通过设计终端状态约束解决了有限时域模型预测控制(model predictive control, MPC)算法的稳定性问题,并通过引入松弛变量使得约束优化问题更容易求解.随机和常值阵风干扰下无人机悬停仿真验证了本文MPC预测控制器具有幅度不超过0.25 m/s的良好干扰抑制能力,性能明显优于线性二次型调节器(linear-quadratic regulator, LQR).

In this paper, the problem of low accuracy of attitude stability control of hovering of small-scale unmanned helicopter under the environment of wind disturbance has been investigated. We developed the rigid body dynamic nonlinear model for the unmanned helicopter and then derived the linear model based on the small disturbance theory at the hovering point. Considering the constraints on states and control, the design problem of the model predictive controller （MPC） is converted into solving a quadratic programming （QP） with inequalities and equalities constraint at each sampling period. The stability of finite horizon MPC algorithm can be guaranteed by setting terminal state constraint. Furthermore, the infeasible problem of QP under strict constraints can be handled by using slack variables. Simulations of unmanned helicopter under random and constant wind disturbance have been carried out to demonstrate the effectiveness and practicability. The MPC controller achieved good disturbance attenuation with maximum 0.25 m/s which is better than LQR controller.