1. A proportional-integral-derivative controller apparatus, the apparatus comprising: one or more processors configured to execute computer program modules, the computer program modules being executable to effectuate an encoder block comprising an expansion kernel, the expansion kernel comprising: a plurality of spiking neurons, individual ones of the plurality of spiking neurons being associated with a plurality of receptive fields, the encoder block being configured to encode an input into a spiking output using the expansion kernel; wherein the plurality of receptive fields comprises: an integrating operator associated with an integrating gain, the integrating operator being configured to produce a first output based on a time integral of the input; a differentiating operator associated with a differentiating gain, the differentiating operator being configured to produce a second output based on a time derivative of the input; and a proportional operator associated with a proportional gain, the proportional operator being configured to produce a third output, the third output being proportional to the input; and wherein the spiking output comprises a weighted sum of the first output, the second output, and the third output.