Places the pole at s = −αs, i.e., αs becomes the bandwidth of Gc(s).
Note that Gc(s) has unity static gain (owing to the integrator characteristic of the mechanical dynamics), whereas a constant Δτl will result in a steady-state control error e(∞) = −Gl(0)Δτl = Δτl/(αsJ). The latter is the (well-known) reason why P control is inadequate. With (13), the closed-loop system will have time constant 1/αs and a 10%-to-90%-of-thestep rise time trc = ln9/αs. Starting with a specification for trc, the bandwidth should thus be selected as