fixed bug in calculation of percent overshoot

[sawyerbfuller]

Now it gives the correct result even if the transfer function is not strictly proper.

Other changes:

• step_info now calculates overshoot with respect to dcgain rather than the final (edit: numeric) value of the (computed) step response.
• adjusted the length of the step response to go for a little longer, to within 0.1% rather than 1% of steady-state, to improve precision of step_info (and updated unit tests)

a remark: sys.dcgain() now always returns a complex number because it evaluates at a frequency of zero (1 for DT systems) (as a result of #542?). This returns a real-valued complex number. I think there is a reasonable argument that it should be cast to a float because currently we assume system parameters are real-valued.

[coveralls]

Coverage remained the same at 88.861% when pulling b36d053 on sawyerbfuller:fix-stepinfo into 66d4a53 on python-control:master.

[murrayrm]

Is #337 also addressed, by chance?

[sawyerbfuller]

sorry, didn't have a chance to get to that one on this PR

[bnavigator]

LGTM

[juanodecc]

Dear @sawyerbfuller, the solution could have problem with systems with initial condition different of zero. I want to contribute , but at the moment, I don't now how test the last version.

I maked this example, to explain:

import numpy as np
import control as ctrl
import matplotlib.pyplot as plt

A = [[0,1,0],[0,0,1],[-1,-2,-3]]
B = [[0],[0],[1]]
C = [1,0,0]
D = 0

sys=ctrl.ss(A,B,C,D)

t= np.linspace(0,20,1000)
t1,y1 =ctrl.step_response(sys,t,[-1,0,2])

plt.plot(t1,y1)
ctrl.step_info(sys)

new_overshoot = 100. * (y1.max() - sys.dcgain()) / sys.dcgain()
print('new_overshoot =', new_overshoot)

{'RiseTime': 2.616832783582626,
'SettlingTime': 9.555404558233526,
'SettlingMin': 0.8926922608222024,
'SettlingMax': 1.1446150537879327,
'Overshoot': 15.77739060863902,
'Undershoot': 0.0,
'Peak': 1.1446150537879327,
'PeakTime': 6.06629418012336,
'SteadyStateValue': 0.9886343506022361}

new_overshoot = 38.34913836051592

[bnavigator]

But ctrl.step_info(sys) does not have any initial conditions. It does know nothing of the step_response() call.