In addition to what @timethereaper has said, I think that your equation here is misleading. This is not necessarily the acceleration, it is the control feedback signal. So if you want to control something, you need to know where it is (displacement) and how it is moving (velocity). Then your control feedback signal will be some weighted (gain1, gain2) combination of those two. Other than that simple thinking, I don't think there is any derivation. It is just an idea of how to control something and applies to anything you want to control. It often will end up in some way affecting acceleration. It is usually just a starting point and the final working controller is much more complicated.G Man said:acceleration = (gain1 x displacement) + (gain2 x velocity)
A Control Theorem is a mathematical principle used in control engineering to analyze and design control systems. It involves using mathematical models to describe the behavior of a system and then using control theory to determine the best way to manipulate the inputs of the system to achieve a desired output.
A PD controller is a type of feedback controller that uses proportional and derivative control to regulate the output of a system. It calculates the error between the desired output and the actual output, and then uses that error to adjust the input to the system. The proportional term is based on the current error, while the derivative term is based on the rate of change of the error.
A PD controller controls acceleration by adjusting the input to the system based on the error between the desired acceleration and the actual acceleration. The controller calculates the error and uses the proportional and derivative terms to determine the appropriate input to achieve the desired acceleration.
The gains in a PD controller refer to the values assigned to the proportional and derivative terms. These gains determine how much the controller will respond to changes in the error and its rate of change. Choosing the right gains is crucial in designing an effective PD controller.
The effectiveness of a PD controller can be measured by its ability to reduce the error between the desired output and the actual output. This is typically done by analyzing the controller's response to different input signals and evaluating its performance based on criteria such as settling time, overshoot, and steady-state error.