# Close Loop Operation of Converters

Mar 17, 2022So far we have been studying open-

### loop

## converters

. We study the boost converter. The boost converter. The boost converter. described but the ultimate goal is to see that the output voltage is well regulated in the sense that if there is a variation in the input voltage temperature variation or even load variation the output voltage V nothing has to be regulated to a more or a less constant value, this would be the objective that we would like to set ourselves for any type of power supply. accordingly change the duty cycle which is actually the control input for most controllers most DC DC## converters

so to do this regulation V is not fed back. and is compared to the reference and passed to a controller which could be a type of proportional or integral proportional or derivative integral proportional PID controller and whose output goes to a pulse width modulator pwm modulator and finally to the gate controller and to switch the switch controllable switch we have now used in almost all of your open circuit dc dc converters so this would be the plan when closing the circuit so in this section of the video lecture I will try to focus on the## close

d-### loop

converters, so I'll take examples.I'll take examples like the buck converter, boost converter and try to

## close

the loop negatively and then I'll see how the controller works and then we can probably look at some simulation examples so you get some. practical on how to step up or do closed loop#### operation

of dc dc converters and the same concept similar concept can be applied even to isolated converters and other dc loo open p converters that you may encounter in the future let's discuss the#### operation

of buck converter closed loop the process is similar even if for any other type of converter so let's draw the circular path of the BAA converter so we have an input and say it comes from the battery for now it could come from the output of the rectifier and let's say I have a switch now the switch I'm showing as a BJT can also be an IGBT or even a MOSFET and I have this diode followed by the output filters heal which is the combination of the inductor and the capacitor , you are now very familiar with the buck converter circuit, now this is the buck converter circuit, this is R zero and the voltage is e through that is V zero and let's say we're giving the gate pulse to the base of the transistor and we'll feel like we need to sense the output voltage so this is what you call the sense variable and this is the control variable , even the control input, so the control input here is goes variation in a variation of the duty cycle, so let us detect the output, pass it through the appropriate sark tree, so let's say we perceive it appropriately amplified or attenuated, and take it to a comparator, a difference amplifier, so here let's set the V not a reference this is what is wanted we don't reference what is wanted and we need to compare the feedback we don't value the feedback value with the value reference V zero and the difference gives the error E and the error is fed to the controller now this is the controller which can be P P IR a PID and in many cases can be an integral controller l proportional and the output of this P AI controller is compared to a triangle now this is a triangle carrier which actually determines which defines the switching frequency of the converter and this what we see is the compare compare signal let's say this is the VC control voltage which is the comparator signal for the delta and which will produce the PWM modulation modulation so it is actually your V mm uitry circuit which will pass through a gate drive circuit gate or a base unit and you will be given to get our power semiconductor switch base so in block schematic this is what the closed loop system looks like so the blue part of the system here in this page all this blue part is the open circuit system and to write in the blue part who saw that just gave VC control as a constant voltage compounded with Iraq and that was the PW model compared and the correct PWM generation gate and giving it as an on-off condition for the power semiconductor switch and all the rest of the blue portion was the power circuit portion so we see constant and all this portion together with the components power supply form the open loop system and now what they have added is a sense circuit which should measure the output voltage which should be controlled properly amplified or attenuated and then filtered and then delivered to the comparator which compares the feedback signal to a reference if gnal this is actually the set point this is our wish I knew what the V zero should be eventually it is compared to that and an error signal is generated which is the difference between the reference value set point and the input word feedback that has given the error the controller and the controller will generate an output control output which is VC which is compared to a port triangle generator generates the PWM and turns the transistor on and off according to ii-era in such a way that the error here becomes 0 once the other here goes 0 so we don't feed back and V doesn't reference or say and then we can say the output is a regulated constant regardless of changes in V changes in temperature or even changes and being low so this is our goal and this is what the control system would look like later on probably what you could do is to replace this blue part of the powers heal with different DC DC converters you could connect the boost converter you could replace e this with the boost converter but appropriately provide the control input to the specific power semiconductor device on your specific position for it to do the job of turning the particular converter on and off and act as a single pole double throw switch and the likewise, too you could give it to isolated converters such as forward-back converters and other types of converters.Now, let's examine this aspect of the controller a bit more before we go into the simulation. Now consider the controller and let's focus on these three variables. e vc and the controller play I have indicated P I have proportional integral integral controller but let me delete this and replace it with an overall gain K so let me put the K value here so now this was the controller gain and let's try to see the controller play these three variables e K and BC he is the error input to the controller VC is the old age control so they are related as follows II era is equal to we see bike a direct relationship now when will be when is and equal to zero now this is an important question that we need to answer can i tell when is it equal to zero now looking at the equation e ket 0 in the first case VC is equal to 0 or in the second case K tends to infinity now let's take the first case if VC is equal to zero which means I am grounding it at this point this point is grounded now by the time you graph at that point it means there is no point in putting all this controlled r as in open loop operation where we are given a fixed value of voltage to VC this becomes open loop operation the whole circuit is open loop so what is the meaning of making it closed loop so that the operation closed loop cease to exist? we can't make VC zero so let's stick with the other option K which tends to infinity if K is infinity whatever the value of VC VC divided by infinity will give me an error of zero so in the case of PID controller the PA controller has a gain K which is infinity as asked the system tends towards a DC situation or a stabilized situation so let me take for example a fresh page in the case of for example , this is Omega versus Omega and let's say this is a gain of DB on the gain of DB of ie DB so let us first take I what I is I I is integral I is the integral and let's say nothing more than 1 times s, so 1 times s is nothing more than a Bode plot going to minus 20 DB per decade minus 20 DB per decade and what is the value at Omega equals 0 at Omega equals 0 here the gain is final, so if you put an integral, the game is finite in it or in a stable region, which means the error is 0 so an integral integrator will give you a means to achieve a steady state error of 0 due to infinite gain whatever BC is equal to 0 because VC times infinity will be 0 so if puts a scalar scale value K high, what basically happens is depending on whether K is greater than greater than 1 or less than 1 gain or attenuation will be chosen sing different parallels which will change the bandwidth, so if you have a measure of control over speed of response so ki is one aspect so let's say instead of allowing this instead of allowing this to be brought up like this somewhere this point I try to flatten it out so the high frequency in the high frequency regions of Omega I have a little more gain and this can improve my dynamics which means if you have to flatten the curve my integral action is here the integrator and at this point you want to shape it you want to shape the l to curve gain like this instead of allah allah instead of letting it cool down to minus 20 DB per decade you make it zero DB per decade what do you mean? you're putting a zero here you put that zero in at this point so let's say i put in a proportional part KP and you add it to the integral part now let's say this is e and this is VC so what's the transfer function between VC? and D now this is KP plus s ki times s KP plus ki times s now this equals KB yes plus ki simplifying further it will say KP yes plus ki times KP times itself so just entering a proportional gain which you have now entered as 0 in s equals minus K over K so this in ki times the corresponding KP ratio yes Omega you have a zero and that has flattened this curve and then you have an added high frequency gain advantage which will improve the response transient a little better so this is the structure of the VI controller when viewed from the frequency domain and the pi controller is seen to have a finite value potential at TCR at finite steady state gain because they are in finite steady state k torque controller is capable of giving 0 steady state error, it's going to add a much higher deal to improve transient response, but most of the time it's not necessary, so you don't need to have a PID controller, the most ca sos the VI controller comes out when you are a dad be careful because you are boosting the gain or your input introduces a shunt component into the high noisy frequency zone and can amplify the noise so be very careful when inputting while introducing D or the derivative so this is the concept of P I so going back to the previous page now I'll delete this usually k now and say I'd like to put a P I here because P I will give me a value of K equals the infinity at a gain of Phi at a finite value after DC, therefore the constant -state value of the other will be equal to zero, therefore it is good practice to start with the DIA topology for most drivers and then take it from that drive and take it from there

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