###### Dynamic control

Dynamic control is an automaton branch, then a robotics field. Given the desired values of the kinematic control, it computes the motor wanted force to reach the desired position.  #### Think of the dynamic control as a black box with some input and outputs. In input, we have the referring trajectory and the sensor’s state. The output has the actuator’s desired force. Most of the time, the motors have an electric drive to convert the desired force to the desired current.

There are many types of dynamic control. During my research activity, I worked on adaptive control. Before discussing adaptive control, I want to introduce the PID, the most common dynamic control.

The PID control comprises three parts: proportional, integrative and derivative.

Taking into account the dynamic control inputs, we compute the position error, subtracting the actual position from the desired one. We multiply the positional error to the positional gain, the derivative of the positional error to the derivative gain and the error integration to the integrative gain. Adding the three components, we have the  PID control output.

The controller has to pick the gains. Due to instability, the derivative gain is close to zero. We choose a significant proportional gain and a little integrative gain to bring the error to zero. The gains must be computed by control techniques, like the zero-pole technique.

The PID controller has been introduced to evidence an essential aspect of adaptive control. The PID controller computes the desired force by a generic second-order system. Instead, the adaptive controller takes the system model into account, and then we have a faster controller, which increases the computational complexity.

The adaptive controller is model-based, and we must compute the system’s mathematical model. We consider that every mathematical model has some approximation due to reasonable assumptions during the model construction.

The adaptive controller idea is that the control “corrects” the model parameters to zero position error. Take the advice that only the trajectory-stressed parameters are “corrected”.

Another critical point is that the corrected parameters are not valid for updating the mathematical model. The estimated and real parameters error differs from zero, without prejudice, the control effectiveness.

In this post, I introduced dynamic control. For a more thorough description, I suggest visiting my research page, or you can see my Google Scholar profile.

It is a pleasure to see you here at this article end, and I’m delighted if you need don’t hesitate to contact me, for any motivation at the following mail.

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Elisabetta Cataldi