Controlling Current Density in Electrowinning Cell
The system is complicated by many nonlinear processes. 

As the topic is electrode focused, the primary controlled parameter should be the electrode surface current density $\sigma$, especially on the depositing electrode.

the total coltage applied on the electrolytic cell is devided on several potential differences:

$$U_\mathrm{applied} = U_{td}(\sigma) + U_\mathrm{kin}(\sigma) + U_\mathrm{diff}(\sigma) + U_\mathrm{cond}(\sigma)$$

where the particular terms are


electrode potential difference given by reaction thermodynamics
electrode potential difference given by reaction kinetics
electrode potential difference given by near electrode diffusion gradient.
free solution potential difference controlling ion migration.


For practical reasons, I advice using empiric approach :


either constant current power source, if applicable
either manual voltage control, using visual ampermeter feedback. 




For further reading, I recommend:


For starters, Electrochemistry on hyperphysics
Wikipedia articles,  following internal and external links, also searching for mentioned topics. 
for more advanced matters, textbooks for Physical chemistry.