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This paper presents the design and development of low cost archetype dual rotor helicopter (LCADRH) for academic research in an educational institution. The LCADRH is installed with optical pitch encoder and yaw encoder which measure elevation and side to side motion of helicopter. The objective of the project is to design and integrate the helicopter with data acquisition board and sensors to provide hardware features, software support capability for its rapid real time measurement and control. The low cost designed LCADRH facilitates the academic research for students in the institution and is able to provide hands on training to understand the concept of nonlinearity, system modelled and unmodelled dynamics and uncertainty, modelling, simulation and control by doing practical experiments. The mathematical model of the LCADRH is derived using grey box modelling method. The control of LCADRH is challenging due to its nonlinearity and effect of strong coupling between aerodynamic forces and torques generated by the both pitch and yaw actuators. In closed loop position control of LCADRH, pitch and yaw axis motion is regulated using linear quadratic controller (LQR). Encouraging results are obtained both in simulation and hardware.

Earlier some research was done on helicopter and its control in foreign countries [

In this paper, the mathematical model of LCADRH is identified using system identification. The main components of LCADRH is designed and integrated to get a helicopter prototype. The effect of nonlinearity and inherent coupling existence are observed in closed loop position control. Therefore, proposed LCADRH model can be used for providing hands-on training for undergraduate and postgraduate students in the area of modelling and control of nonlinear system. The block diagram of proposed system is shown in

There are many methods available for system identification of non-linear MIMO systems using measured input-output data such as black box modelling, grey box modelling etc. In this paper, we design an indigenous archetype dual rotor helicopter and its dynamics are modelled by grey box modelling. Using the system identification tool in MATLAB an idnlgrey object of this model is created and the unknown idnlgrey model parameters and initial states using measured data are estimated by prediction error method (PEM). The PEM is a parametric estimation method in which the system parameters are found out providing the initial set of values. Here the initial values are set by physical interpretation and presumption.

The objective of the PEM is to minimize the prediction error by the prediction parameter which minimizes the variation of prediction error,

where,

The PEM uses optimization to minimize the cost function. Initially the state space matrixes A, B contains the coefficients with initial value of fixed parameters and some fixed values. The estimating algorithm estimates the parameters in A and B matrix. The model is estimated using PEM with so far determined parameters as the initial values in MATLAB. To validate this method, a simulation model is used to generate the data for the system identification.

While designing controllers for complex systems with stringent performance requirements, LQR method is used. It is a powerful method to find the best controller that minimizes cost. It is mainly used where the system dynamics are given by a set of linear equations and the cost is given by a quadratic function. Here the weighting factors are supplied by a human. The settings of the controller are found by using a mathematical algorithm that minimizes the cost function. Q and R are the two matrices that parameterize the cost function. They weight the state vector and the system input respectively. LQR method tries to achieve optimal control by solving the algebraic riccatti equation.

The LQR controller is designed for linear state space model of LCADRH,

The states of LCADRH are,

where

and the input

where

satisfies the following cost function,

where Q and R are the weighting matrices that to be designed such that subject to the system dynamics.

The main components of LCADRH are 12V DC servo motor, 6V DC servo motor, optical pitch encoder, optical yaw encoder, hollow shaft slip ring and motor power circuit. The LCADRH shown in

side motions. Optical pitch encoder and optical yaw encoder provides the digital position feedback information. The hollow shaft slip ring is used to transfer power of two motors and optical pitch encoder signal without tangling of wires.

System Specification and Cost DetailsThe main components of LCADRH are shown in

The position control of LCADRH in open loop is tedious due to high nonlinearity and strong coupling effect. In open loop, LCADRH tend to change yaw position when pitch nose goes up and down and vice versa due to the existence of coupling effect between pitch and yaw actuators. The LQR closed loop position control of LCADRH is done under four cases to analyze the coupling effect that exists between the pitch and yaw actuators. In case I, the pitch angle is varied by giving step input of 10 degree whereas yaw angle is constant at 0 degree. In case II, yaw angle is varied by giving step input of 30 degree while the pitch angle is constant at 0 degree. In case III, the elevation of LCADRH is raised by setting pitch angle to square input with the amplitude of 5 degree and frequency of 0.05 Hz whereas the yaw angle is constant at 0 degree. In case IV, side to side motion is increased by setting the yaw angle to square input of 30 degree and frequency of 0.05 Hz and the pitch angle is constant at 0 degree. The objective of this closed-loop position control is to compare the measured closed-loop response with simulated response. The LQR controller gives encouraging results in reducing coupling effect, structural vibration and oscillation.

To analyze the coupling impact of LCADRH MIMO system in LQR closed loop position control, the first control variable

Component/Parameter | Specification |
---|---|

Pitch motor | ±12 V |

Yaw motor | ±6 V |

Pitch angle | 0 to 45 degree |

Yaw angle | 0 to 360 degree |

Optical pitch encoder | 128 to 5000 pulses per revolution |

Optical yaw encoder | 256 to 10,000 pulses per revolution |

Hollow shaft slip ring | 2 A |

Pitch propeller thurst force constant | 1.037 N/V |

Yaw propeller thurst force constant | 0.428 N/V |

Main component of LCADRH | Cost (in USD) |
---|---|

Pitch 12V DC servo motor | 107.19 |

Yaw 6V DC servo motor | 252.00 |

Optical pitch encoder | 62.32 |

Optical yaw encoder | 73.00 |

Hollow shaft slip ring | 316.00 |

Other Accessories (Pitch propeller, yaw propeller, Helicopter body, motor circuit, spindle, propeller shield, cables, connecting wires, bearing, yoke, screws, nuts etc.) | 84.00 |

Total cost | 894.51 (in USD) |

shown in

LCADRH rotates about the yaw axis by 3.56 degree at t = 0.622 s due to the rise of elevation about pitch axis by 10 degree. This is due to the generation of rotary force by pitch motor about the yaw axis. From t = 10 s to t = 50 s, the measured yaw angle is constant at 3.516 degree. It is observed from the results that the implementation of LQR controller for the closed loop position control of LCADRH gives better result in tracking the desired pitch angle. From the experimental result of pitch and yaw angle, it is observed that structural vibration is purged. Therefore LCADRH is designed well at low cost.

The

In this case, coupling existence between the pitch and yaw actuators of LCADRH is observed by giving step input of 30 degree about yaw axis. The simulated pitch and yaw angle possess consistent tracking of desired pitch and yaw angle as shown in

The

This shows the absence of coupling effect of yaw actuator on pitch axis in LQR closed loop position control of LCADRH.

In case III, square input of 5 degree with a periodicity of 20 seconds is given as desired set point for pitch to analyze the forward and backward movement of LCADRH and its corresponding coupling impact on yaw. The simulated result of pitch angle and yaw angle follows the desired set point of pitch and yaw angle. As shown in

In case IV, square input of 30 degree with a periodicity of 20 seconds is given as desired set point for yaw to analyze the side to side motions of LCADRH and its corresponding coupling impact on pitch actuator.

The LCADRH is designed and developed for the academic research on control system experiments in educational institution. The real time measurement and control of helicopter is provided by integrating with data

acquisition board and sensors to provide hardware features, software support capability. The mathematical modelling of LCADRH is identified from its real input output data using grey box modelling. LQR controller is designed for LCADRH for the pitch and yaw position control. The coupling effect, nonlinearity and system dynamics of LCADRH is analyzed using experimental setup by giving step and square wave input. The simulation results of pitch and yaw angle follows the desired angle with less steady state error. The experimental results of pitch and yaw position shows the absence of structural vibration, oscillation and measurement noise. The designed LQR position controller controls elevation and side to side motion with consistent tracking of desired pitch and yaw angle and it reduces the existence of coupling effect between pitch actuator and yaw actuator.

Because of its cost effective nature, the proposed LCADRH model can be developed in third world countries giving the under graduate and post graduate students an affordable opportunity to learn modelling, simulation, and control oriented experiments in a non linear coupled MIMO system.

The authors gratefully acknowledge Dr. S. Baskar, Professor, EEE, Thiagarajar College of Engineering, Madurai, for his meticulous guidance, encouragement and his valuable discussions. One of the authors of this paper (P.S. Manoharan) acknowledges Science and Engineering Research Board, Department of Science and Technology (DST), India for sanctioning the funding under Fast Track Young Scientist Scheme, vide sanction number SERB/F/2056/11-12 dated 15.02.2012.

A. P. S. Ramalakshmi,P. S. Manoharan, (2016) Design, Control and Analysis of Low Cost Archetype Dual Rotor Helicopter for Educational Institution. Circuits and Systems,07,3329-3342. doi: 10.4236/cs.2016.710284