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Development of a novel mechatronic system for mechanical weed ...

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Materials and methods<br />

The drive contains a mathematical model <strong>of</strong> the whole <strong>system</strong> based on the<br />

<strong>mechanical</strong> inertia ratio <strong>of</strong> the <strong>system</strong>. The inertia ratio parameter is given as a<br />

percentage <strong>of</strong> the ratio between the inertia <strong>of</strong> the load and motor inertia. This<br />

parameter need to be properly set to optimise the speed gain.<br />

In the traditional approach, inertia ratio needs to be calculated, using the<br />

dimensions and densities <strong>of</strong> each component in the load, be<strong>for</strong>e the selection <strong>of</strong><br />

the servomotor as a decisive parameter <strong>for</strong> its sizing. The total inertia <strong>of</strong> the<br />

<strong>system</strong> is a sum <strong>of</strong> the coupling, the screw and the load inertias. However,<br />

specifications <strong>of</strong> all elements are <strong>of</strong>ten unreliable or unavailable and the<br />

complexity <strong>of</strong> the <strong>system</strong> can be a limiting factor <strong>for</strong> accurate calculation <strong>of</strong> the<br />

load inertia. The servo drive has an online auto-tuning algorithm but external<br />

factors can <strong>of</strong>ten limit its accuracy. A simple technique based on graphical<br />

analysis <strong>of</strong> the speed and torque values in the starting sequence, be<strong>for</strong>e the<br />

<strong>system</strong> reaches the steady state, can be applied. In this method the same<br />

equations are used as <strong>for</strong> motor sizing, but in reverse. The graphically<br />

determined torque and speed characteristics can be used to calculate the<br />

inertia <strong>of</strong> the load. The equation <strong>for</strong> accelerating torque calculation (Equation<br />

4.7) can be trans<strong>for</strong>med to solve it <strong>for</strong> JL (Equation 4.8)<br />

M = ( J + J ) * α<br />

(4.7)<br />

A M L<br />

MA<br />

JL = − JM<br />

(4.8)<br />

α<br />

where MA is the torque it takes to accelerate, JM is the inertia <strong>of</strong> the motor, JL is<br />

the inertia <strong>of</strong> the load and α is the actual acceleration <strong>of</strong> the motor.<br />

Typical change <strong>of</strong> the torque intensity which can cause a trapezoidal response<br />

<strong>of</strong> the speed (acceleration, constant speed and deceleration) is illustrated on<br />

the diagram in Figure 4.6.<br />

53

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