77__all__ = ['step' , 'stepinfo' , 'impulse' , 'initial' , 'lsim' ]
88
99def step (sys , T = None , X0 = 0. , input = 0 , output = None , return_x = False ):
10- '''
11- Step response of a linear system
10+ '''Step response of a linear system
1211
1312 If the system has multiple inputs or outputs (MIMO), one input has
1413 to be selected for the simulation. Optionally, one output may be
@@ -20,35 +19,27 @@ def step(sys, T=None, X0=0., input=0, output=None, return_x=False):
2019 ----------
2120 sys: StateSpace, or TransferFunction
2221 LTI system to simulate
23-
2422 T: array-like or number, optional
2523 Time vector, or simulation time duration if a number (time vector is
2624 autocomputed if not given)
27-
2825 X0: array-like or number, optional
2926 Initial condition (default = 0)
30-
3127 Numbers are converted to constant arrays with the correct shape.
32-
3328 input: int
3429 Index of the input that will be used in this simulation.
35-
3630 output: int
3731 If given, index of the output that is returned by this simulation.
3832
3933 Returns
4034 -------
4135 yout: array
4236 Response of the system
43-
4437 T: array
4538 Time values of the output
46-
4739 xout: array (if selected)
4840 Individual response of each x variable
4941
5042
51-
5243 See Also
5344 --------
5445 lsim, initial, impulse
@@ -67,8 +58,7 @@ def step(sys, T=None, X0=0., input=0, output=None, return_x=False):
6758
6859def stepinfo (sysdata , T = None , yfinal = None , SettlingTimeThreshold = 0.02 ,
6960 RiseTimeLimits = (0.1 , 0.9 )):
70- """
71- Step response characteristics (Rise time, Settling Time, Peak and others).
61+ """Step response characteristics (Rise time, Settling Time, Peak and others)
7262
7363 Parameters
7464 ----------
@@ -137,8 +127,7 @@ def stepinfo(sysdata, T=None, yfinal=None, SettlingTimeThreshold=0.02,
137127 return S
138128
139129def impulse (sys , T = None , X0 = 0. , input = 0 , output = None , return_x = False ):
140- '''
141- Impulse response of a linear system
130+ '''Impulse response of a linear system
142131
143132 If the system has multiple inputs or outputs (MIMO), one input has
144133 to be selected for the simulation. Optionally, one output may be
@@ -150,30 +139,24 @@ def impulse(sys, T=None, X0=0., input=0, output=None, return_x=False):
150139 ----------
151140 sys: StateSpace, TransferFunction
152141 LTI system to simulate
153-
154142 T: array-like or number, optional
155143 Time vector, or simulation time duration if a number (time vector is
156144 autocomputed if not given)
157-
158145 X0: array-like or number, optional
159146 Initial condition (default = 0)
160147
161148 Numbers are converted to constant arrays with the correct shape.
162-
163149 input: int
164150 Index of the input that will be used in this simulation.
165-
166151 output: int
167152 Index of the output that will be used in this simulation.
168153
169154 Returns
170155 -------
171156 yout: array
172157 Response of the system
173-
174158 T: array
175159 Time values of the output
176-
177160 xout: array (if selected)
178161 Individual response of each x variable
179162
@@ -193,8 +176,7 @@ def impulse(sys, T=None, X0=0., input=0, output=None, return_x=False):
193176 return (out [1 ], out [0 ], out [2 ]) if return_x else (out [1 ], out [0 ])
194177
195178def initial (sys , T = None , X0 = 0. , input = None , output = None , return_x = False ):
196- '''
197- Initial condition response of a linear system
179+ '''Initial condition response of a linear system
198180
199181 If the system has multiple outputs (?IMO), optionally, one output
200182 may be selected. If no selection is made for the output, all
@@ -204,31 +186,25 @@ def initial(sys, T=None, X0=0., input=None, output=None, return_x=False):
204186 ----------
205187 sys: StateSpace, or TransferFunction
206188 LTI system to simulate
207-
208189 T: array-like or number, optional
209190 Time vector, or simulation time duration if a number (time vector is
210191 autocomputed if not given)
211-
212192 X0: array-like object or number, optional
213193 Initial condition (default = 0)
214194
215195 Numbers are converted to constant arrays with the correct shape.
216-
217196 input: int
218197 This input is ignored, but present for compatibility with step
219198 and impulse.
220-
221199 output: int
222200 If given, index of the output that is returned by this simulation.
223201
224202 Returns
225203 -------
226204 yout: array
227205 Response of the system
228-
229206 T: array
230207 Time values of the output
231-
232208 xout: array (if selected)
233209 Individual response of each x variable
234210
@@ -250,8 +226,7 @@ def initial(sys, T=None, X0=0., input=None, output=None, return_x=False):
250226
251227
252228def lsim (sys , U = 0. , T = None , X0 = 0. ):
253- '''
254- Simulate the output of a linear system.
229+ '''Simulate the output of a linear system
255230
256231 As a convenience for parameters `U`, `X0`:
257232 Numbers (scalars) are converted to constant arrays with the correct shape.
@@ -261,16 +236,13 @@ def lsim(sys, U=0., T=None, X0=0.):
261236 ----------
262237 sys: LTI (StateSpace, or TransferFunction)
263238 LTI system to simulate
264-
265239 U: array-like or number, optional
266240 Input array giving input at each time `T` (default = 0).
267241
268242 If `U` is ``None`` or ``0``, a special algorithm is used. This special
269243 algorithm is faster than the general algorithm, which is used otherwise.
270-
271244 T: array-like, optional for discrete LTI `sys`
272245 Time steps at which the input is defined; values must be evenly spaced.
273-
274246 X0: array-like or number, optional
275247 Initial condition (default = 0).
276248
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