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important trigonometric equations

Control Systems - Steady State Errors

The deviation of the output of control system from desired response during steady state is known as  steady state error . It is represented as  e s s . We can find steady state error using the final value theorem as follows. e s s = lim t → ∞ e ( t ) = lim s → 0 E ( s ) Where, E(s) is the Laplace transform of the error signal,  e ( t ) e ( t ) Let us discuss how to find steady state errors for unity feedback and non-unity feedback control systems one by one. Steady State Errors for Unity Feedback Systems Consider the following block diagram of closed loop control system, which is having unity negative feedback. Where, R(s) is the Laplace transform of the reference Input signal  r ( t ) r ( t ) C(s) is the Laplace transform of the output signal  c ( t ) c ( t ) We know the transfer function of the unity negative feedback closed loop control system as C ( s ) R ( s ) = G ( s ) 1 + G ( s ) ⇒ C ( s ) = R ( s ) G ( s ) 1 + G ( s ) The output of the sum