Time Domain 
   System Dynamic Response
             Time domain dynamic response (1)
        •  Because  time  is  used  as  an  independent  variable  in  most  control 
           systems,  it  is  usually  of  interest  to  evaluate  the  state  and  output 
           responses with respect to time or, simply, the time response. 
        •  In the analysis problem, a reference input signal is applied to a system, 
           and the performance of the system is evaluated by studying the system 
           response in the time domain.
        •  Time response: is the response given by the system which is function 
           of the time to applied excitation.
     Time domain dynamic response (2)
     The time response of a control system is usually divided into 
     two  parts:  the  transient  response  and  the  steady-state 
     response. 
    
   (t): transient response is defined as the part of the time response that goes 
   to zero as time becomes very large.
    
   (t):The steady-state response is simply the part of the total response that 
   remains after the transient has died out. (final accuracy of the system)
           All real, stable control systems exhibit 
           transient phenomena to some extent before 
           the steady state is reached 
   Time domain dynamic response (3)
  • Steady state error: it is the difference 
   between the desired output and actual output 
   (reference input) at infinite time or at steady 
   state. 
       ess=lim t→∞  (r(t)-c(t)) 
      Where : r(t) desired output
                    c(t) Actual output
           Time domain dynamic response (4)
          Advantages of studying time dynamic response: 
          -  Classifying  the  response  of  some  standard  systems  to 
             standard  inputs  can  provide  an  insight  into  more 
             complicated systems.
               oEx system: first order – second order
               oEx inputs: unit-  ramp- sinusoid
          - Time  domain  standard  Characteristics  of  a  standard 
             dynamic  response  can  be  used  for  inferring  system 
             specifications.
          -   Response  to  simple  inputs  can  be  used  for  system 
             identification, i.e. for black box modeling.