Transient response analysis
This document discusses transient response and steady state response analysis for first and second order systems. For first order systems, the time constant tau determines how quickly the system response reaches steady state. Examples show calculating tau, steady state error, and plotting the system response. For second order systems, characteristics like peak time, maximum overshoot, and settling time are influenced by system parameters. Examples demonstrate plotting the response and calculating steady state error. In conclusion, first order system response depends on tau, while second order response depends on damping ratio and natural frequency. Faster response corresponds to smaller tau or higher damping ratio and natural frequency.
Transient response analysis
- 1. TRANSIENT- RESPONSE ANALYSIS FIRST ORDER SYSTEM SECOND ORDER SYSTEM TRANSIENT RESPONSE AND STEADY STATE RESPONSE
- 2. TRANSIENT RESPONSE AND STEADY STATE RESPONSE Transient Response Transient Response Steady-State Response Steady-State Response Figure 1 Figure 2
- 3. FIRST ORDER SYSTEM K 1 2s+1 R(s) C(s) Transfer function:
- 4. Plot of Response System t = 𝜏 (tau)
- 5. EXAMPLE 1 K 5 3s+9 R(s) C(s) ◦ Plot rensponse system control ◦ Constant time ◦ Steady state error (Ess)
- 6. Answer:
- 8. Error steady state Output (respon steady state) Constant time 𝜏 = constant time c(t)= input x 63% = 1 x 0.63 = 0.63
- 9. Error steady state is defined by Ess = Input-Output Ess = 1- 0.847 = 0.153
- 10. SECOND ORDER SYSTEM K 1 (𝑠 + 1)(𝑠 + 2) C(s)R(s) Transfer function: 𝐶(𝑠) 𝑅(𝑠) = 𝐾 𝑠2+3𝑠+(2+𝐾)
- 11. CHART OF RESPONSE SYSTEM tr tp ts 0.02 or 0.05 Steady state overshoot A B C D E F G H
- 12. EXAMPLE 2 Plot response control system Peak time (tp) Maximum overshoot Settling time (ts) Steady state error (Ess) K 9 (𝑠 + 3)(𝑠 + 5) C(s)R(s)
- 14. error steady state Output (respon steady state)
- 20. QUESTION ???
- 21. CONCLUSION On first order system the value of 𝜏 (tau) will decide accelerate of response system from start statecondition until steady state. The fewer the constant time, response will be better. While on second order system influenced by the value of and . The more the value of , response will be deeper.
- 22. THANK YOU