Mapúa Institute of Technology School of Electrical, Electronics and Computer Engineering Feedback and Control Systems Laboratory ECE!L"#$
C%&T'%L S(STEMS Module &o)* ! Time 'esponse of First %rder System
Submitted by* Sapalaran, Ma) Carmela +)
Submitted to* Engr) Ernesto ergara
Submitted on* -ugust !, $./
Interpretation of 'esults Module ! is about Time 'esponse of First %rder System) For the first part, the system is gi0en 1ith unit impulse as an input then it 1as plot in terms of time2domain using 3plot4 command based on the graph it 1as e5ponentially decaying, after that the gi0en system 1as generated to continuous2time transfer function then a graph 1as generated using the 3impulse4 command, based on the result both graphs are the same since they are the same function but 1ith different commands of generating the graph) The second part is about a system 1ith unit step as an input) 6i0en the same system 1ith the pre0ious item, it 1as plot 1ith a unit step input but then again it 1as plot it terms of time2domain using 3plot4 command based on the graph it 1as increasing e5ponentially, after that the gi0en system 1ith unit step input 1as generated to continuous2time transfer function then a graph 1as generated using the 3step4 command, based on the result both graphs are the same since they ha0e the same function but 1ith different methods of generating the graph 1hich is in terms of time2 domain and in terms of s2domain) The third part is about a system 1ith a ramp function as an input) #ased on the graph it is linear 1hich 1e can say it is a ramp function) For the fourth part it is a system 1ith a parabolic function as an input) #ased on the result, the graph really looks like a part of a parabolic cur0e)
The fifth part is about determining the time constant, rise time, and settling time of the step response gi0en the t1o system in the module) 7ith the use of the 3lti0ie14 command to kno1 the time on each point of the graph, based on the result if the pole is farther than the origin it makes the system to ha0e faster step response) System 8a9 1ith a pole s:2$ and system 8b9 1ith a pole s:2$., based on the gi0en, system 8b9 has a faster response) In the seat1ork 1e determine the transfer function by the graph gi0en, 1ith the time parameters and amplitude gi0en 1e deri0e the transfer function)
Conclusion* #ased on 1hat I;0e learned from this module 1e can generate plot 1ith t1o methods 1ith an input of unit impulse and unit step function) In terms of time2domain 1e can use plot command to generate a graph for both system 1ith unit impulse and unit step) Then in terms of s2domain 1e can generate plot using 3impulse4 command, for an input 1ith unit impulse 1hile 3step4 for an input 1ith unit step) a99 , to kno1 the rise time it is e?ual to $)$"a, and for settling time is e?ual to @"a)
