Derivations of Steady State Error Coefficients and Steady State Error according to Type of System
Computation steady state error constants for input signals according to Type of System
Type of System:
The number of poles at origin of open loop transfer function G(s)H(s) of the system.
Type of system is increased by adding one pole at origin.
Eg: Type 0, Type 1, Type 2, etc.
Disadvantages of Static Error Coefficient Method:
It cannot give error if the input is other than standard test signals.
It doesn't provide precise value of error.
It doesn’t provide variation of error w.r.t time.
Error constant only defined for O.L.T.F G(s)H(s) of system.
Before applying this method the system must be checked for stability.
This method is applicable only to stable system and not to unstable systems.
Dynamic Error coefficient Method(Error series method) is used
Conclusion:
For type 0 system only step input is accepted (as ess= ( "A" )/"1+Kp" , ess = ꚙ, ess = ꚙ ).
For type 1 system step and ramp inputs are accepted (as ess = 0 , ess = A/K, ess = ꚙ ).
For type 2 system all inputs are accepted (as ess = 0 , ess = 0 , ess = A/K ).
All steady state errors are positional in nature.
Finite steady state error is inversely proportional to forward path gain K.