Let the desired closed-loop poles for level 2 controller be located at p1, p2, p3.

(i) Using Equation 9.45 for the Jacobian matrix of Example 9.5 find the gain matrix that will provide equal poles p1¼p2¼p3¼0.3. Use the MATLAB pole-placement algorithm from Ref. [12]. Find the gain matrix using both methods for poles at p1¼0.3; p2¼0.3; p3¼0.7. What do you see?

(ii) Calculate the step responses for case (i). Compare the results.