How feedback chooses motor effort

Our intake needs a simple decision: collect until a detector changes. An arm needs something more: move toward an angle, slow down, and stay near it. Both use feedback, but a boolean possession rule cannot tell us how strongly to drive an arm motor.

Before the final project, let’s connect the control overview to that more general problem. This is a paper-and-pencil lesson. You should leave able to explain a feedback loop and reason about its measurements, without having to implement a tuned arm controller yet.

Choose a quantity you can measure¶

Position tells us where something is, such as an arm angle in degrees. Velocity tells us how quickly position changes, such as degrees per second. Holding an angle and maintaining a speed are different goals.

Suppose an arm is at 20 degrees and we want 50 degrees. The desired value is the setpoint; their difference is the error:

Here $r$ is the requested angle and $y$ is the measured angle. In this example, 50° minus 20° gives an error of 30°. Positive error means we need to move in the direction of increasing angle. Before using this rule, agree on where zero is, which direction is positive, and which units the sensor provides. Subtracting degrees from encoder rotations gives a meaningless answer even if Python accepts both numbers.

The controller repeats this calculation using a new measurement each update. The arrow back from the sensor closes the loop. The mechanism still takes time to move; calling a calculation does not instantly place it at the target.

Proportional control: respond to the current error¶

A proportional controller chooses effort by multiplying error by a gain:

For this thought experiment, $u$ is voltage and $k_P$ is 0.1 volts per degree. These are invented arithmetic examples, not settings for a real arm.

As error shrinks, the correction shrinks. If we pass the target, the sign reverses. Increasing the gain gives a stronger correction for the same error, but does not guarantee a better response. Motion has momentum, measurements arrive at intervals, and output is limited.

For example, if the allowed output were -4 to 4 V and the calculation requested 7 V, only 4 V could be applied. This is saturation. A controller cannot produce effort beyond the mechanism’s permitted range.

The I and D terms¶

PID combines proportional, integral, and derivative contributions. You can understand their purposes before learning the full equation:

Integral can keep accumulating while output is saturated, leading to excessive correction later; this is windup. Derivative reacts to changes, including measurement noise. Adding all three terms is not automatically an improvement. WPILib recommends feedforward rather than integral for many FRC applications. Its PID introduction includes equations and response plots when you’re ready for more detail.

Anticipate a load, then correct what remains¶

At the target, our proportional calculation asks for zero volts. A real arm may still need effort to oppose gravity. Feedforward estimates the effort needed from a model of the mechanism; feedback corrects the remaining error. They can be added together before applying limits. An arm’s gravity term depends on its angle; it is not one universal number to copy between mechanisms. WPILib’s feedforward introduction explains how gravity, friction, and motion enter those estimates.

Read a response before changing a gain¶

Imagine recording these angles at equal time intervals after changing the target to 50 degrees. These are illustrative readings, not simulated or measured results:

Overshoot means going beyond the target. Settling means staying within an agreed band around it. A few samples suggest behavior but don’t prove what happened between them. Log the target, measurement, and applied effort together so you can relate cause to effect. A timeout alone cannot establish that a target was reached, and crossing it once cannot establish that the mechanism settled.

Where does this belong in robot code?¶

For a future arm, a command could request an angle while the subsystem repeatedly updates a position controller. The command decides when to finish; the subsystem owns measurement conversion, limits, and the agreed holding behavior. Decide explicitly what happens after interruption and disabling. Holding position may require continuing control while enabled; “command finished” and “motor off” are not always the same requirement.

Some device controllers run a feedback loop themselves. In that arrangement the subsystem sends a setpoint and reads status instead of independently issuing a second competing effort command. The ownership principle stays the same.

Our course intake needs neither an angle setpoint nor PID. Its possession rule already fits its goal. Learning control means choosing a suitable method and measurement, not adding PID to every motor.

Check your reasoning¶

1. With a 50° target and a 30° measurement, calculate the requested voltage using the example gain. What changes if you double the gain?

2. Which trace would make you check direction conventions before any gain changes?

3. Why can zero position error still require a nonzero holding effort?

4. What would you need to measure to regulate intake roller speed?

Next: demonstrate and extend your mechanism subsystem.