Closed-Loop Control System for Buck Converter To determine integral gain constants, the position of root locus for a buck converter is modified online as shown in Figure 4(a) to get Ki=36 at the minimum settling time=0.0852 s and rise time=0.0352 s as shown in Figure 4(b). Then mikroC software is used for programming the microcontroller that controls the MOSFET of the buck converter based on the previous Ki value. And so the programmed microcontroller controls constructed buck converter in Proteus software as indicated in Figure 5. The simulation result of the system of Figure 5 is recorded in Figure 6. As clearly shown in Figure 6, the following results are obtained for the buck converter controlled by the integral controller: C The output voltage (red) follows the reference voltage (green). C Rise time equals 0.05 s. C Steady state error equals (+/- 0.1) v. Figure 3. (a) The circuit of the buck converter during ton. (b) The circuit of the buck converter during toff. DESIGN OF BUCK CONVERTER USING INTEGRAL (I) CONTROLLER Integral (I) controller is a special case of PID controller, but with no use of the proportional (P) and the derivative (D) parts of the error. So control signal U for an integral controller is presented below U = K i Δ dt (2) where Ki is integral gain, Δ is the error or deviation of actual process value (PV) from the set point (SP). (3) Δ = SP − PV The integral (I) controller transfer function C(s) is given below C ( s ) = Ki / S (4) Fortunately, the basic approaches for optimal feedback compensator design could be accomplished quickly and easily in the MATLAB environment. MATLAB provides a graphical user interface (GUI) so that the closed-loop frequency response can be interactively changed by online modifying of the pole-zero pattern of the feedback controller as shown in Figure 4. When the desired frequency is obtained, users are also presented the corresponding transfer function of the feedback controller in the same interface. 32 Figure 4. (a) Root locus and open-loop bode plots of buck converter. (b) Step response of buck converter. IEEE A&E SYSTEMS MAGAZINE MARCH 2017