Steady- state error is an important parameter in control systems that indicates thee difference between the desired output and thee actual output after thee system has settled. Calculating thi error helps in designing systems that meet specific close requirements. Thi article provides a step approvach h to determinale steady steady-state error in various control system configurations.

Understanding Steady- State Error

Steady- state error is the residual error resideng after transient effects have dissipated. It is influenced d by the system type, input signal, and the system 's transfer function. Common input signals include step, ramp, and parabolt inputs, each affecting the steady- state error differently.

Etap - by- Stopień obliczenia method

Follow these steps to calculate thee steady-state error:

  • Identyfikator tego input signal type (step, ramp, etc.).
  • Określić te systemy transfer function, G (s).
  • Oblicz te error constant based on thee system type: indi1; FLT: 0 predis3; indis3; indis1; FLT: 1 predis3; indis3; Pozytion error constant (Kp) for step input.
  • Velocity error constant (Kv) for ramp input.
  • Acceleration error constant (Ka) for parabolt input.
  • Use thee appropriate formula: indi1; indi1; FLT: 0 indi3; endi3; endi1; FLT: 1 indi3; FLT: 1 indiput: indi1; endi1; FLT: 2 indisat; endisa3; e endi1; endisation: 3 indisation; endisa3; endisa3; s endi1; FLT: 4 indisat: indisat: indisat: indisat: endisat; FLT: 1; endisat; endisabet; endisabelt; endisatisat; endisatisatil; FLT: 1; FLT: 1; FLT: 1; entisatisatisatisat;
  • For ramp input: XXX1; XXX1; FLT: 0 XXX3; XXX3; e XXX1; FLT: 1 XXX3; XXX3; SIS; VII1; FLT: 2 XX3; XXX3; = 1 / Kv XXX1; XXX1; FLT: 3 XXX3; XXX3; EFX3;
  • For parabolt input: behav1; behav1; FLT: 0 behav3; behav3; e behav1; FLT: 1 behav3; behav3; ss behav1; behav3; FLT: 2 behav3; behav3; = 1 / Ka behav1; behav1; FLT: 3 behav3; Behav3; FLT: 3 behav3; Behav3;
  • Oblicz te error constant using thee system transfer function and input type.
  • Complute the steady-state error using the formulas above.

    • Badanie Calculation

    Consider a unity beedback control system with the transfer function G (s) = 10 / (s + 2). For a step input, the position error constant Kp is calculated as:

    Xi1; Xi1; FLT: 0 Xi3; Xi3; Kp = lim Xi1; Xi1; FLT: 1 Xi3; s → 0 Xi1; Xi1; FLT: 2 Xi3; Xi3; G (s) = 10 / 2 = 5 Xi1; Xi1; FLT: 3 Xi3; Xi3; Xi3;

    Te stałe stany error is then:

    (1); (1); (1); (1 + Kp) = 1 / 6; (1 + 5) = (1 + 5) = (1); (1); (1); (1 + 5) = 1 / 6; (1 + 5); (1); (1); (1); (1 + 5); (1 + 3; (1 + 3); (1 + 3; (1 + 5); (1 + 3); (1 + 5); (1 + 5); (1 + 3); (1 + 3); (1 + 3) (1 + 5); (1 + 5); (1 + 5); (1 + 3); (1 + 3) + (1) + 1 (1); (1) + (1) + 3); (1 (1) + (1 (1) + 1) + 1 (1) + 1 (1); (1 (1) + 1); (1 (1) + 1); (1); (1); (1); (1) (1); (1); (1