The mechanical system shown in Figure P5.52(a) is used as part of the unity feedback system shown in Figure P5.52(b). Find the values of M and D to yield 20% overshoot and 2 seconds settling time.
1. System Dynamic
where:
2. Laplace Transform
3. Motor&Load Transfer Function (θm(s)/Ea(s))
4. Direct Transfer Function
For the system:
The open-loop transfer function Ga(s) is:
5. Closed-loop transfer function
The closed-loop transfer function Gc(s) is:
That is to say:
6. Calculation of M and D
According to:
Besides:
In this way:
Meanwhile:
7. Matlab verification
We use Matlab to corroborate replacing all the values calculated in the original transfer function:
Find the values of M and D to yield 20% overshoot and 2 seconds settling time.
>> stepinfo (sys)
RiseTime: 0.3554
SettlingTime: 1.8989
SettlingMin: 0.9331
SettlingMax: 1.1999
Overshoot: 19.9890
Undershoot: 0
Peak: 1.1999
PeakTime: 0.8059
Written by Larry Francis Obando – Technical Specialist – Educational Content Writer
Mentoring Academic / Entrepreneur / Business
Copywriting, Content Marketing, White Papers (Spanish – English)
Escuela de Ingeniería Eléctrica de la Universidad Central de Venezuela, CCs.
Escuela de Ingeniería Electrónica de la Universidad Simón Bolívar, Valle de Sartenejas.
Escuela de Turismo de la Universidad Simón Bolívar, Núcleo Litoral.
Contact: Caracas, Quito, Guayaquil, Jaén, Villafranca de Ordizia- Telf. +34633129287
WhatsApp: +593981478463
email: dademuchconnection@gmail.com
3 comentarios sobre “Example 1 – Transient response of an electromechanical system.”