Abstract
In this article, by using Lagrange energy method, we establish the dynamical model of a two degrees-of-freedom helicopter, which is subject to holonomic constraints. A control method based on Udwadia–Kalaba theory is proposed to achieve the trajectory tracking control of the 2-degrees-of-freedom helicopter. Different from traditional methods, this method could solve the constraint force of the mechanical system without adding additional parameters such as Lagrange multipliers. When initial conditions are compatible, we can use the nominal control which is based on Udwadia–Kalaba equation to control 2-degrees-of-freedom helicopter in real time. But when initial conditions have incompatibility, the simulation result could produce divergence phenomenon. To solve the trajectory tracking control problem of 2-degrees-of-freedom helicopter under incompatible initial conditions, a modified controller is proposed. We also make simulation contrast by different control methods to validate the effectiveness and superiority of the modified controller. Simulation results show that the modified controller can drive the 2-degrees-of-freedom helicopter to perfectly track the desired trajectory with less control cost and high control accuracy.
Highlights
At present, there are many methods that focus on the trajectory-tracking control of 2-degrees-of-freedom unmanned helicopters
The control methods are mainly divided into two types: the methods based on model (such as linear–quadratic–regulator (LQR), linear– quadratic–Gaussian (LQG), and sliding mode control)[1,2] and the methods based on experience (such as proportional–integral–derivative (PID), neural network control and fuzzy control).[3,4]
According to the above view, this article establishes the dynamical model of the 2DOF helicopter with constraints by using Lagrange approach and designs a new kind of 2DOF helicopter flight control method to realize a small unmanned helicopter’s yaw and pitch movement
Summary
There are many methods that focus on the trajectory-tracking control of 2-degrees-of-freedom unmanned helicopters. Udwadia and Kalaba[5,6,7] at university of Southern California have carried on the long-term research in this domain and obtained many useful results, which are summarized to Udwadia–Kalaba equation By using this method, we can establish motion equations of mechanical systems which are subject to holonomic constraints. The nominal control method based on Udwadia–Kalaba equation can accomplish the trajectory tracking control task of 2-DOF helicopter. The other one is to obtain linear or nonlinear dynamic differential equations by theoretical calculation.[25] Some scholars consider the specificity of small helicopter and modify the existing model of large helicopters. The kinetic energy of the system includes three parts: the vertical support rod l1, the cross bar l2, and the main rotor with motor
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