where , and are vectors of length N, where N is the number of links.
In this case, the functions f and g are not in a closed form since the error and the velocity are calculated iteratively using the dynamic and the feedback control modules. Therefore, the simulation program will be used to determine the optimal values for the required parameters. Also here, we can form one objective function as in the first example. Notice here that we can consider that a critically damped behavior is preferred, so we can use the relation between and that produces this behavior, which is:
This will reduce the number of optimization variables from three to two.