Lim 1 s sg e e s ramp lim 1 2 s g s e e s parabola

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= ( ) ( ) ) ( lim 1 0 s sG e e s ramp = = ( ) ( ) ) ( lim 1 2 0 s G s e e s parabola = = Table 3-1: Type of input and steady-state error DR CHONG Static Error Constant § The three (3) terms in the denominator that are taken to the limit determine the steady-state error. § The limits are called static error constants . 14 Static error constants Equation Steady-state error Position constant, K p Velocity constant, K v Acceleration constant, K a 0 lim ( ) ( ) p s K G s H s = 0 lim ( ) ( ) v s K sG s H s = 2 0 lim ( ) ( ) a s K s G s H s = ( ) p K e + = 1 1 ( ) v K e 1 = ( ) a K e 1 = Table 3-2: Static Error Constants DR CHONG System Type § By using the static error constant, the e ss , for the system can be obtained based on the system type . § The system type is defined as: § The value of n in the denominator, or § The number of pure integrations in the forward path. § Number of poles at origin of s –plane. 15 If n = 0, it is Type 0 system. If n = 1, it is Type 1 system. If n = 2, it is Type 2 system DR CHONG Static Error Constant 16 Example 3-4 For each system of figures below, evaluate the static error constants and find the expected error for the standard step, ramp, and parabolic inputs. DR CHONG
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5 Static Error Constant 17 Example 3-5 A unity feedback system has the following forward transfer function: a. Evaluate the system, K p , K v , K a . b. Use your answers to (a) to find the e ss for the standard step, ramp, and parabolic inputs. ( ) ( )( ) 9 7 8 1000 ) ( + + + = s s s s G DR CHONG Static Error Constant 18 System Type Static error constant K p K v K a Type 0 Type 1 Type 2 ( ) p K e + = 1 1 ( ) v K e 1 = ( ) a K e 1 = ( ) 0 =
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  • Spring '19
  • Dr.Saifulza
  • Dr Chong

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