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DC-DC Power Converter with Digital PID Controller

VaraPrasad Arikatla, Student Member, IEEE, and JaberA. Abu Qahouq, Senior Member, IEEE

The University of AlabamaDepartment of Electrical and Computer Engineering

Tuscaloosa, Alabama 35487, USA

Abstract This paper presents an approach for an adaptivePID controller in order to improve the dynamic performance

of DC-DC Power Converter. The control variables, namely the

proportional constant (Kp) and integral constant (Ki) are varied

as a function of the uncompensated error voltage which results

in improving the dynamic transient response of the power

converter. The experimental results show that there is a

reduction in overshoot/undershoot and settling time compared

to the conventional PID.

I. INTRODUCTIONDigital implementation of power controllers have gained

more popularity in recent days. This is due their severaladvantages compared to the analog counterpart. Digitalpower control has made the implementation of complex andsophisticated algorithms easier [1-4]. These algorithms helpin improving the performance of power converters. Digitalpower control can be implemented more easily and thecomponent variation and aging effects are negligiblecompared to the analog counterparts [3,4].

The dynamic response is an important factor thatdetermines the performance of the power converter [4,5].The design of controller with better dynamic performance isdesired. Conventional controllers have some inherentlimitations that limit the dynamic performance. Theseinclude, fixed bandwidth, fixed phase margin and gainmargin. The controller must satisfy the aforementionedcriteria during steady state in order to have a stable steadystate performance. However, during dynamic transientoperation, the bandwidth can be increased [6]. This paperexplores this point and provides a method to increase theclosed-loop bandwidth during the dynamic operation of thecontroller. Fig. 1 shows the general block diagram of powerconverter with digital controller. It is with a ProportionalIntegral Derivative (PID) closed-loop compensator type. Fig.2 shows the block diagram of a digital implementation of aPID controller. The conventional PID controller is usuallydesigned such that it satisfies the phase margin and gainmargin requirements using either bode plot or root locusmethods. Usually, the bandwidth is limited to 10-25 percentof the switching frequency. The design performances are

determined by the values of the proportional constant (Kp),the integral constant (Ki) and the derivative constant (Kd).

cV

eV

Figure 1. Block diagram of a Power Converter with Digital Controller.

In order to overcome the aforementioned limitations ofconventional PID controller certain modifications of thiskind of controller are proposed in [6-10]. In [6] the use oftwo different PID controllers is proposed resulting in two

different bandwidth values, a lower bandwidth during steadystate and a higher bandwidth which takes effect duringtransients. It might cause unnecessary oscillations due to alarge sudden change in bandwidth. In [8] a nonlinearimplementation of PID controller that behaves differentlyduring load transient condition is proposed. Itsimplementation is not straight forward and requirescalculation of many parameters. Moreover, the digitalimplementation requires more resources for the calculationof exponential terms.

In order to make a smooth PID transition from steady-state to transient state, an adaptive PID controller method ispresented in this paper. This paper proposes a controlstrategy that results in reduction in the overshoot/undershoot

and the settling time for the power converter output voltageduring dynamic transients. The proposed control methoddoes not require sensing any additional parameters that arenot already available in any conventional PID controller andis relatively simple to realize.

978-1-4244-8085-2/11/$26.00 2011 IEEE 327

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1Z1Z

( )refV z

( )outV z

( )ev z

pK

iK

dK

Figure 2. Block diagram of a Digital implementation of PID Controller.

Next section gives a description of the differencebetween conventional and adaptive PID control. Section IIIpresents the adaptive PID control law/method and algorithm.Section IV presents experimental results obtained for aproof-of-concept prototype. The conclusion is given inSection V.

II. CONVENTIONAL PIDAND ADAPTIVE PIDCONTROL

The conventional PID controller transfer function isgiven by (1).

1

1( ) (1 )

1

iPID p d

KG z K K z

z

= + +

(1)

The values of Kp ,Ki andKd are designed such that theloop bandwidth has a reasonable value which is generallyaround 10 to 25 percent of the switching frequency. In orderto improve transient performance, the bandwidth can beincreased during transient. This can be achieved by usingdifferent values for the proportional constant (Kp), theintegral constant (Ki) and the differential constant (Kd).Certain conditions have to be met for the variation of thesevalues in order to yield improvement and avoid oscillations

during the adaptive operation of the PID controller. Theseconditions are such as:

1. During steady-state operation the PID controller constantsare always the same.

2. The high bandwidth of the PID controller that is usedduring the dynamic operation should not drive the closed-loop system to instabilities.

3. There should not be any abrupt change in controllerparameters, as this may cause unnecessary oscillations.

In this paper, these conditions are met by varying thecontrol variables (Kp andKi) with the use of a parameter thatvaries smoothly during the dynamic transient operation andremains constant during steady-state operation. One of the

parameters that is readily available in the converter and thatcan be used to meet the aforementioned requirements is theerror signal/voltage (Ve). The values ofKp andKi are variedin accordance with (2).

1

1

( )( ) ( ) (1 )

(1 )

i

c p e e d e

KV z K v v K z v

z

+= + + +

(2)

III. ADAPTIVE CONTROL LAW AND ALGORITHMThe proposed adaptive PID controller given by (2) is

implemented by varying the values of and smoothly inaccordance with (3) and (4), respectively. This is illustratedin Fig. 3 waveforms.

minoI

maxoI

outV

pK

iK

0

0

Output

Current

Output

Voltage

Figure 3. Illustration of the Adaptive PID Controller Operation.

1

0,0 ( )

( ) , ( )

e th

e th e

v n V

v n V v n

< =

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No Yes

Start

Obtain the value of

error signal

( )eV n

0 =

0=

0 =

0 =

( 1) ( )e eV n V n =

( )e tV n V>

1( )

ev n =

1 ( )ev n =

Figure 4. Algorithm for the implementation of Adaptive PID Control.

The algorithm for the implementation of the AdaptivePID controller is shown in Fig. 4. The algorithm tracks theerror signal and whenever the absolute value of error signalis beyond the threshold value (Vt), the values of and arevaried as given by (3) and (4) in a smooth manner. Thisresults in a system that has a higher bandwidth than thatduring the steady state and hence the transient response isimproved, i.e., the settling time and overshoot/undershoot ofthe output voltage are reduced.

IV. EXPERIMENTAL RESULTSA proof of concept experimental prototype is developed

in the laboratory in order to verify the Adaptive PID

controller. The prototype is a single phase buck converterwith input voltage of 10V and output voltage maintained at anominal value of 1.5V. The power stage capacitance is 1mF

and the inductor value used is 440nH . The switching

frequency used is 350KHz. The PID controller is

implemented with the help of Altera FPGA Altera CycloneII EP2C35F672C6.

The experimental results are shown in Fig. 5 and Fig. 6.Fig. 5(a) shows the variation of output voltage during a stepdown load transient of 8A to 0A with conventional PID. Fig.5(b) shows the response during the same load condition, butwhen the Adaptive PID controller is used. Fig. 6(a) showsthe variation of output voltage during a step up load transientfrom 0A to 8A with conventional PID control. Fig. 6(b)shows the response during the same load condition but whenthe Adaptive PID controller is used.

It can be observed from experimental results of Fig. 5and Fig. 6 that the Adaptive PID controller results in animproved dynamic behavior during transient compared toconventional PID. Also, the transition of the controlleroccurs without any additional oscillations or ringing in theoutput voltage. For this particular design example, there is animprovement of 8mV (about 16%), during step up loadtransients and an improvement of 8mV (about 16%), duringstep down load transient and a reduction of 20 s (> 40%) in

the settling time.

(a)

(b)

Top Trace: Output Voltage (50mV/div, 20s/div.) and Bottom Trace:

Inductor Current (5A/div., 20s/div.)

Figure 5. Experimental results of the prototype with zoomed in viewunder dynamic load step-down transient of 8A-0A (a) with conventional

PID controller and (b) with Adaptive PID controller

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(a)

(b)

Top Trace: Output Voltage (50mV/div, 20s/div.) and Bottom Trace:

Inductor Current (5A/div., 20s/div.)

Figure 6. Experimental results of the prototype with zoomed in viewunder dynamic load step-down transient of 8A-0A (a) with conventional

PID controller and (b) with Adaptive PID controller

V.CONCLUSION

This paper presented a digital controller implementationof an Adaptive PID controller in order to improve thedynamic response of power converters. The Adaptive PIDcontrol law/method dynamically and adaptively varies the

proportional and integral constants as a function of the errorsignal resulting in a reduction in the settling time andovershoot/undershoot of the power converter output voltage.The transition between steady-state operation and dynamictransient operation is made smoothly in order to avoid anyringing and oscillations. The principle of operation andexperimental results of the Adaptive PID controller are

presented in this paper and compared with the conventionalPID controller.

ACKNOWLEDGEMENT

This work was supported in part by the National Science

Foundation (NSF) of USA under Grant No. 0927104 and in

part by The University of Alabama. Any opinions, findings,

and conclusions or recommendations expressed in this

material are those of the author(s) and do not necessarily

reflect the views of the National Science Foundation.

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