[moved] How to charge a power capacitor bank properly?

I designed of a high voltage power supply to charge a capacitor bank by constant current with the phase shift full bridge converter. In the circuit, I can only measure the peak value of the inductor current by using a CT and estimate the average current. The circuit worked well with the resistor load, but it has a serious problem with the power capacitor bank. The controller did not work properly, the charge current varied with a large scale leading to the broken phenomenon of the Mosfets. How can I solve that problem?
P/S: The average value of the inductor current can not be sensed directly from the circuit. It was estimate from the peak current value. There is a necessity to get the average value directly, but I still do not know how to do it in a simple way.

What inductor are you talking about? The primary of the transformer or the output choke inductor? A CT cannot measure DC current, so for sensing the output current of the converter you will need something else, like a resistive shunt or hall effect sensor. A CT can measure the peak primary current, but this is not directly related to the output current, since duty cycle will be changing rapidly.

Too many circuit details taken as granted. Please describe completely, start with a schematic!

The CT is placed at the secondary side of the transformer to measure the secondary winding current as shown in the attached figure. The peak current of the output inductor will be taken from the secondary current of the transformer. After that the average current of the output inductor will be estimated by using the peak current, output voltage, and effective duty cycle values. All the calculations are done by a digital signal processor. While the circuit is working to charge the capacitor bank as shown in the attach figure, the controller is unstable. Since the dynamic of the capacitor load is really fast and sensitive, the controller looses easily with a small change at the output. If the charge current at the output is measured directly and accurately, the performance of the circuit could be better. Could you tell me how to get the average current at the output directly and accurately in order to make a stable controller?

Is it correct to say you want to drive the mosfets with regulated PWM at the gates, so that there is no current overload?

Short duty cycle at first, because the capacitor gobbles all charging juice quickly.

Then gradually make the duty cycle longer, as the capacitor nears maximum charge?

I would start with measuring a set characteristic curves output current versus duty cycle for different output voltages. This can be also used to calibrate the CT measurement in a multi-dimensional table.

Then setup the controller according to the determined control process characteristic. Or - if feasible - define a duty cycle versus output voltage curve to achieve the intended charging profile, without current feedback. The CT may be still used as an overcurrent protection.