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This paper presents a biologically inspired control system developed for maintaining balance in a simulated human atop an oscillating platform. This work advances our previous research by adapting a human balance controller to an inverted pendulum and controlled by linear-Hill muscle models. To expedite neuron/synapse parameter value selection, we employ a novel two-stage process that pairs a previously developed analytic method with particle swarm optimization. Using the parameter values found analytically as inputs for particle swarm optimization (PSO), we take advantage of the benefits of each method while avoiding their pitfalls. Our results show that PSO optimization allowed improved balance control from modest (<10%) changes to the synaptic parameters. The improved performance was accompanied by muscle coactivations, however, and further refinement is needed to better align overall behavior of the neural controller with biological systems.