This thesis is an ongoing project of Ericsson with collaboration of Blekinge Institute of Technology [BTH], and Linneaus University [LNU] to compare the functionality and performance of three controllers Polynomial Pole Placement, PID [Proportional Integral Derivative] and PD controller in third order. This paper presents the state space modeling approach of DC-DC Buck converter. The main aim of this thesis is, by considering the buck converter system of Ericsson BMR450 with the PID, POLYNOMIAL and PD controllers at feedback loop, thus running their Matlab file with their appropiate Simulink block diagram, and comparing the three controllers performance by verifying their appropiate output graphs. The third order controller design is complicated and response is slow. The second order design is easy and gives better responses than third order Polynomial, PID and PD controllers. / As per the results point of view, the polynomial performed well than PID and PD controllers. The simulations show that the polynomial controller reaches the reference voltage very well, were the PID and PD result does not differ very much while meeting with the required reference voltage. Thus we conclude that the Polynomial controller design and results were better than the PID and PD Controllers. If we compare both the second order [4] and third order controller methods, The second order controllers are easy in design and gives better responses than third order polynomial PID and PD controllers. / ERCS.MADHU KIRAN, D.NO: 1/1/131, B.C.COLONY, MUTHUKUR, NELLORE, ANDHRA PRADESH, INDIA. PIN - 524344. THOTA. Partha Saradhi, C/O CH SUVARNA RAJU D.NO: 4-5-47, VEGIVARI CHAVADI, KOTHA PETA, WARD NO:21, KOVVUR, WEST GODAVARI,ANDHRA PRADESH, INDIA PIN - 534350,