Application Area 6: Optimize Dynamic Response
Often the task of optimization is to find the values of some design variables so that the dynamic response is optimized in some way.
![](../../../images/solvers/optimization_dyn_response.png)
Figure 1.
The figure above shows a simple representation of a stabilizer. The stabilizer is basically a PID controller that prevent the mass from deviating from its initial point. The disturbing force is a time variant function.
- Objective
- Minimize the integral of displacement magnitude, velocity magnitude and acceleration magnitude over time. Keep the value of gains under a certain number. (This is done by adding constraints).
- Design Variables
- Three gains of PID controller
. Note: For this example, finite differencing is used to compute the sensitivities. The code with detailed explanation is provided in the PID Controller Example section.