1. A welding system, comprising: a power source with an output configured to provide a welding signal as a series of waveforms during a welding process; a feedback system operatively coupled with said power source and configured to sense at least one feedback parameter associated with said welding process, said at least one feedback parameter having a non-linear relationship with at least one waveform parameter of said welding signal, said non-linear relationship providing a larger adaptive range of control defined at least in part by a minimum feedback parameter value associated with a minimum waveform parameter value and a maximum feedback parameter value associated with a maximum waveform parameter value; and a controller operatively coupled with said feedback system and with said power source, said controller configured to: compare said feedback parameter to a setpoint value to derive an error value, determine a parameter scaling factor for said at least one controlled waveform parameter based on a current workpoint value and said error value, said parameter scaling factor varying as a function of said error value over said larger adaptive range of control, and modify values of said at least one waveform parameter in response to values of said feedback parameter in accordance with said non-linear relationship, said error value, and said parameter scaling factor such that said larger adaptive range of control has a greater magnitude than a narrower range of adaptive control which can be achieved by a linear relationship between said at least one feedback parameter and said at least one waveform parameter.