PiD ContRol in gReAteR DetAil

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Let s take a closer look at the PID control algorithm definitions. After that, we will write some programs that implement more of the ideas discussed.

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PID Control in Greater Detail

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Before we go any further, let s get an understanding of what we are talking about when we say that the motor is controlled by a PID loop or equation. The PID loop defines how much energy is to be fed to the motor at any one time during the move. There are four parts to the equation that determines this load. The four parts are referred to as the P, I, D, and K components. The K component is the system friction factor and is sometimes ignored.

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The P part is a proportional component. The I part is an integrative component. The D part is a derivative component. The K part is the overall system friction component

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The code controlling the motor power is executed in a loop and the factors are modified each time through the loop as dictated by instantaneous motor performance. If these four components are described properly within the control algorithm, much improved control of the motor will be achieved. Let s look at each component, one at a time, to see what its function is and what it accomplishes. The control scheme we develop does not have to be mathematically perfect to give us good performance. In fact, with Spin and its limited math, a mathematically perfect system cannot be achieved. However, we can get close enough to have a very acceptable operation. The friction component K represents the power that has to be applied to the system to overcome the friction in the system and get the motor turning. Anything less than this, and nothing happens. K can be considered to be a constant though it usually increases with motor speed. The proportion component P tells us that the power to be supplied to the motor is proportional to the speed at which we want to run the motor. This is the largest part of the equation and therefore has to be picked carefully. It will also, of course, depend on the load on (and inertia of) the motor. The faster we want the motor to run, the larger the P component, and the larger the load, the larger the P component. In mathematical terms, the energy provided can be expressed as follows: E=P*X

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note X can be 1 or greater than or less than 1.

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If there are no load changes and the system response is linear (meaning that twice the speed requires twice the power), that is all we need to run the motor. If, however, the load is changing, we have to add to and subtract from the power to keep the motor at the same speed, and we have to keep adding to or subtracting from the power until the motor gets up to proper speed. This is the I (integrative) component in the equation. Because it is

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needed only when there s an error in where the motor should be, I is based on this error. The higher the error, the more we have to add to the power setting to make the motor speed up or slow down to get it to where we need it to be. Needless to say, this is done a bit at a time every time we go through the control loop. In mathematical terms, the energy provided can be expressed as follows: I = (desired position actual position) * (a constant or variable of some kind)

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note The constant is selected to provide as rapid a correction as possible (while keeping the motor under control).

The derivative component D is a measure of the difference in how far the motor moves each time through the cycle with respect to time. (Think about this one for a while.) We are looking to see if the motor is where it is supposed to be with regard to time. To determine this, we need to know where the motor is at any one time, and we need to know where we expect it to be at that time. We therefore need to know precisely (in encoder counts) where the motor is at all times. In mathematical terms, the energy provided can be expressed as follows: D = (expected position present position) * (a constant or variable of some kind)