Based on the example below

How to get the correct range for my transfer function which is

My Kcr is 5604.68 and Pcr is 0.8075

s EXAMPLE 8-2 Consider the PID-controlled system shown in Figure 819. The PID controller is given by (s + a)2 G.(s) - K It is desired to find a combination of K and a such that the closed-loop system will have 10% (or less) maximum overshoot in the unit-step response. (We will not include any other condition in this problem. But other conditions can easily be included, such as that the settling time be less than a specified value. See, for example, Example 8-3.) There may be more than one set of parameters that satisfy the specifications. In this example, we shall obtain all sets of parameters that satisfy the given specifications. To solve this problem with MATLAB, we first specify the region to search for appropriate K and a. We then write a MATLAB program that, in the unit-step response, will find a combination of K and a which will satisfy the criterion that the maximum overshoot is 10% or less. Note that the gain K should not be too large, so as to avoid the possibility that the system re- quire an unnecessarily large power unit. Assume that the region to search for K and a is 25Ks3 and 0.5 s I s 1.5 If a solution does not exist in this region, then we need to expand it. In some problems, however, there is no solution, no matter what the search region might be. In the computational approach, we need to determine the step size for each of K and a. In the actual design process, we need to choose step sizes small enough. However, in this example, to avoid an overly large number of computations, we choose the step sizes to be reasonablesay, 0.2 for both K and a. To solve this problem it is possible to write many different MATLAB programs. We present here one such program, MATLAB Program 8-6. In this program, notice that we use two "for loops. We start the program with the outer loop to vary the "K" values. Then we vary the "a" values in the inner loop. We proceed by writing the MATLAB program such that the nested loops in the pro- gram begin with the lowest values of K and a and step toward the highest. Note that, depend- ing on the system and the ranges of search for "K" and "a" and the step sizes chosen, it may take from several seconds to a few minutes for MATLAB to compute the desired sets of the values. In this program the statement solution(k, :) = [K(i) ali m] will produce a table of K, a, m values. (In the present system there are 15 sets of K and a that will exhibit m