In DC-DC converter circuit simulation, the current through the inductor reaches about three times the steady state value in the start-up. So, I would like to know if I have to add an inrush current control or not? Any circuit suggestions?
Because the output filter capacitor is at zero voltage initially, two things will happen. Firstly, the closed loop system will force the duty cycle to maximum so as to push maximum current to build up the output voltage as early as possible. Secondly, during on-time, the driving voltage for the inductor current will initially be the total input voltage, which is larger than the steady state value of input voltage minus the output voltage. Thus, the inductor current becomes large during start-up. Use a 'Soft-start' control circuit (using a RC circuit and diode) to over-ride the PI-controller during start-up. This permits the duty cycle to build up slowly (as the capacitor charges), reducing the inrush current, until the output voltage is close to the desired value, when the PI controller takes over. Several IC's have built-in soft start control.
As correctly observed, generally, the inductor limits this current a bit, but it's not always sufficient. You can try playing with a larger inductance or a higher switching frequency. Switching losses with MOSFETS are generally negligible up to about 100kHz.
I like to use micro controllers to drive my converters (I can fix some problems in software), so I generally program a soft start into the system. As long as one limits the maximum inrush to the capabilities of one's devices, you should be safe. Different types of capacitors can tolerate different levels of "abuse", e.g polypropylene types are generally better than electrolytic, but more expensive. The device data sheets are of help here.
You are probably aware that the switching devices have an pulsed rating which is higher than the DC rating. Take care with IGBT's, which latches up at about 2x continuous rating. MOSFETs can handle as much as 4x, does not latch up, but overheats and blows. (again, look at the device datasheet)
In fact I am doing an integrated design for the buck DC-DC converter, so on-chip, I would have the all components except the inductor and capacitor and the load resistance
If the inductor operates in a continuous mode this problem can be solved by keeping the duty cycle low initially. Thereafter normal operation may start. However, if therating of the MOSFET or IGBT is kept high enough, as suggested by David, then the circuit can be made simpler by avoiding extra PWM control.