Essentials of Control Techniques and Theory by John Billingsley
By John Billingsley
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Extra resources for Essentials of Control Techniques and Theory
By switching B and D on while A and C are off, braking can be applied to stop the motor. ” There are four windings that can be thought of as North, South, East, and West. Each has one end connected to the supply, so that it can be energized by pulling the other pin to ground. Just like a compass, when the North winding is energized, the rotor will move to a North position. The sequence N, NE, E, SE, S, SW, W, NW, and back to North will move the rotor along to the next North position. Yes, it is the “next” North because there are many poles in the motor and it will typically take 50 of these cycles to move the rotor through one revolution.
Indb 35 10/12/09 1:41:15 PM 36 ◾ Essentials of Control Techniques and Theory The system in this case represents a ball, falling under gravity while at the same time traveling horizontally. In each interval dt, the vertical velocity vy will change by g*dt, while the horizontal vx velocity stays the same. The vertical position will change by vy*dt and the horizontal position by vx*dt. If the vertical position falls below zero and the velocity is downwards, the ball must bounce. We have a system that is non-linear in the extreme!
We can define state variables to be the position and velocity, x and v. 4 Position controller. The first state equation is very simple. It simply states that rate-of-change of position is equal to the velocity! dx = v. dt The second one expresses the acceleration in terms of the input and the velocity, dv = bu − av dt since a typical motor has inbuilt damping. For now we will ignore this and set a to zero. So now we need to set up a believable simulation that will show us the result of any feedback that we may apply.