This research work emphasizes on design of a robust control for a 3DOF robotic manipulator under uncertainties. The plant model was achieved using the independent joint method and the uncertainty problem was addressed by designing a robust controller using H-Infinity synthesis which was compared with PID. This was achieved with algorithms implemented in MATLAB. The H-Infinity controller recorded 0dB, while PID controller recorded 0.117dB and 0.061dB for joints I and II respectively in Complementary Sensitivity (T) graph at low frequencies. H-Infinity controller achieved better disturbance rejection characteristics with sensitivity (S) graph recording peak sensitivity of 0.817dB and 1.79dB at joints I and II respectively than PID controller which achieved 3dB and 1.86dB at joints I and II respectively. H-Infinity controller achieved better noise rejection characteristics with T graph recording lower gains at joints I and II respectively at high frequencies than PID controller which recorded higher gains at joints I and II respectively. Thus, it was concluded that the H-Infinity controller achieved better performance and stability robustness characteristics for the joint torque control than the PID.

This work centers on robust compensating function scheme for adequate electrical power system stabilization. There has been high level of disturbances in the power line and lack of adequate compensation technique to cancel the effects of the resultant instability which has caused power failures. The problem was addressed by the consideration of disturbances in the power line during the design of the compensating function for the improvement of the power system performance and stability. H-Infinity synthesis robust compensating function design method was used to design an adequate compensator that can improve the performance and stability of the power system.  From the results, the H-infinity Synthesis Controlled Generating Plant (HCGP) recorded an overshoot of 0%, settling time of 1.04 seconds, tracking error of 0dB, gain margin of 21.7dB and phase margin of 79.6 degrees. The simulation was repeated by varying the value to k to -0.3, and the generating plant produced same results. This shows that the system can maintain performance and stability equilibrium even when there is change in its parameters. Since the HCGP satisfied the performance and stability robustness, therefore it was concluded that power system robust compensating function scheme for improved performance and stability robustness was achieved using H-Infinity synthesis method.

The heat exchanger is a device that helps to circulate calculated amount of heat in a system. It can be applied in order to reduce the number of heat sources while maintaining a precise level of heat. Heat exchanger is expected to be part of the solution to CO2 emission and climate issues since its application reduces the sources of heat and cost of production such as in electrical power plant. Due to the critical need for the solution to the enormous emission of CO2 and the need to reduce cost of running power plants, the study and improvement of the heat exchanger has become very important.  The heat exchanger suffers from disturbances due to its harsh environment. In order to maintain desired performance the heat exchanger requires an adequate control measure. Many types of controllers have been designed, however from the review it was observed that most of the controllers produced marginal stability which will not maintain good performance of the system in the presence of significant disturbance. The major objectives of this work are to reduce the tracking error for performance improvement, to reduce the peak sensitivity for better disturbance rejection and to improve the stability margins for stability robustness. In this work, an optimal robust control was developed for the heat exchanger using H2 synthesis technique. From the results, the controlled system trajectory tracking error and overshoot were reduced to zero and the peak sensitivity to disturbance was reduced to 0.189 dB. Gain and phase margins satisfied the robust stability characteristics; gain margin was greater than 20 dB and phase margin was greater 60 dB. This means that the designed optimal controller will guarantee robust performance and stability of the system even in the presence of large disturbance.