Dynamic Models for predicting the concentration profiles of the reactants and product in a Continuous Stirred Tank Reactor for the transesterification of used cooking oil (triglyceride) to biodiesel has been developed using the principle of conservation of mass. The developed system of differential equations were integrated numerically using fourth order Runge-Kutta algorithm embedded in ode 45 solver of 7.5 Mathlab program. The models were validated by solving the model equations with kinetic data and other relevant data from literatures. The results and trends were similar and in agreement with those from these literatures. Simulations of the reactor to (±) step changes in the inlet flowrates of the reactants (used cooking oil and methanol) showed great effect on biodiesel production, (instability-oscillations and reduction in output concentration of biodiesel). A feedback control strategy was developed with a Proportional-Integral (PI) Controller and a close loop model was developed for control studies. The closed loop response of the reactor output (biodiesel concentration) showed continuous oscillatory response with offset. Hence the controller parameters (proportional gain C K and integral time I τ) were tuned using the "On-Line Trial and Error Method" implemented using MathLab Simulink to obtain optimum values that ensured quick stability of the closed-loop system, reduced or no oscillatory response and no offset. The optimum controller parameters were: proportional gain 8.306 C K = and integral time I τ = 17.157 minutes.