The KBANN (Knowledge-Based Artificial Neural Networks) approach uses neural networks to refine knowledge that can be written in the form of simple propositional rules. We extend this idea further by presenting the MANNCON (Multivariable Artificial Neural Network Control) algorithm by which the mathematical equations governing a PID (Proportional-Integral-Derivative) controller determine the topology and initial weights of a network, which is further trained using backpropagation. We apply this method to the task of controlling the outflow and temperature of a water tank, producing statistically significant gains in accuracy over both a standard neural network approach and a nonlearning PID controller. Furthermore, using the PID knowledge to initialize the weights of the network produces statistically less variation in test set accuracy when compared to networks initialized with small random numbers.