DC-DC converter

The invention discloses a two-loop controller architecture for digital control of a DC-DC converter regulating an output voltage configured to generate a pulse width

modulation (PWM) signal to control a power stage in

dependence of a voltage error signal.

Figure 1 shows the power stage of a buck converter, which is in this example the power plant to be controlled. Generally, there are two variables that can be used to control the power plant: the output voltage V _out , which is the main variable to be controlled, and the inductor current i _L .

Gv _d (s) is the transfer function of the power stage (fig. lb) from the input d to the output V _out of the power plant. Furthermore, there are two ways to control a DC-DC

converter power stage: by mean of a voltage mode controller or a current mode controller. When a voltage mode controller is used only one control loop is required to adjust the output voltage V _out to the desired value V _ref , as shown in fig. lc. Referring to figure lc) G _Vd is the transfer of the power stage, F _M = 1/V _M is the transfer function of the PWM block, used to convert the control signal d (i.e. the duty cycle) in a pulse width signal, C(s) is the main controller and V _ref is the reference voltage (or set-point voltage) to which V _out is adjusted to.

Alternatively, when a current mode controller is used both the inductor current i _L and the output voltage V _out are controlled to ensure V _out = V _ref . As shown in figure Id) two control loops 27, 28 are now required: an inner control loop Ti(s) 27 to adjust the inductor current I _L to a desired value (also called current loop) and one outer voltage loop T _v (s) 28 (also called voltage loop) to adjust V _out to V _ref by setting the target current for the inner control loop 27. Referring to fig. Id), Gi _d 31 is the transfer of the power stage from PWM to i _L , Z _c 29 is the transfer function of the power stage from i _L to V _out , F _M = 1/V _M is the transfer function of the PWM block, Ti(s) the inner current loop 27, Ci(s) 51 is the main controller of the inner current loop, T _v (s) the outer voltage loop and C _v (s) 52 is the main controller of the outer voltage loop 28, with Gi _d *Z _c = G _vd .

When voltage mode controllers are used the plant transfer function G _Vd (s) can be approximated to a second order system (fig. 2) and the design of C(s) requires good knowledge of the power plant, i.e. the values of the inductance L and the capacitance C, to achieve stable operation. When current mode controllers are used instead, the inner control loop regulates the inductor current i _L thus reducing the plant seen by the outer voltage loop to a first order system and therefore simpler to control. In such scenario knowledge of the power plant is still required for stable operation but the design of C±(s) and C _v (s) can be carried out to achieve stable operation over a wide range of power plants but with the cost of sacrificing regulation performance.

In fact modern digital PWM controllers used in Point Of Load (POL) applications are voltage mode controllers that deliver tight regulation of the output voltage by means of a

combination of two control techniques:

- A conventional linear Proportional Integral Derivative (PID) controller to provide robust, stable and predictable regulation of the output voltage and - A non-linear controller to break the performance

limitation of linear controllers during a sudden change of the load.

As mentioned before linear PID controllers, when used to control the power stage of a DC-DC converter, such as a buck converter for example, have the limitation that the

controller poles and zeros have to be specifically tailored to the power stage to which they are applied. This means that controller parameters are a function of the components values constituting the power stage itself. When the same

PID controller is used to compensate different power stages stability issues occurs. On the other side, the second order nature of the power plant being controlled allows the achievement of almost optimal regulation performance

compared to when a current mode controller is used.

Several attempts have been made to make controller

parameters independent from power stage components.

In digital PWM controllers a way to solve this problem is mean of auto-tuning algorithms, i.e. algorithms that would firstly try to identify the power stage being controlled extracting information from the converter behavior under specific stimuli; and secondly tailor controller poles and zeros to the identified power stage. Such auto-tuning algorithms are well described in the state of the art but have not being well accepted in the market because of one or more of the following problems:

1) Perturbations are injected in the system in steady state thus causing jitter on the PWM signal and unwanted noise on the output voltage;

2) Computational complexity of the algorithms used to identify the power stage is high;

3) The identification phase may require a long learning phase ;

4) Tailored controller parameters may lead to sub-optimal performance and in some cases to instability;

Using auto-tuning algorithms the parameters of C(s) in a voltage mode controller or parameters of Ci(s) and/or C _v (s) in a current mode controller can be estimated looking at how the power plant reacts to specific perturbations or how the power converter behaves compared to a known power plant.

In this respect, there are two types of auto-tuning

techniques. In a first technique the auto-tuning is based on a perturbation of the power stage where a perturbation is injected in one of the control loops and the reaction of the power plant to such perturbation is measured and used to tune the parameters of the controller. On a second

technique, the auto-tuning is based on a comparison of the behavior of the power plant with respect to the behavior of a reference model of it under the same control action. The difference in behavior is then used to tune controller parameters .

Referring to the latter technique the approximate knowledge of the power plant can be used to implement a filter G* _Vd (s) whose behavior represents the desired open loop behavior of the converter when a specific controller C* (s) 51 is used.

As shown in fig. le) the auto-tuning algorithm 26 is used to tune the parameters of C(s) 5 by means of a reference model G* _vd (s) 31 such that C ( s ) *G _vd ( s ) =C* ( s ) *G* _vd ( s ) .

Alternatively, the same principle can be used to implement filter T* (s) 25 by means of a reference model of the closed loop system whose behavior represents the desired closed loop of the converter when a specific controller C* (s) is used (see fig. If)).

On the other side manual optimization of controller

parameters is not a trivial task and requires power

expertise that is often not available at the user side.

Graphical User Interfaces (GUIs) provided together with digital PWM controllers try to overcome the lack of such expertise but fail to provide controller parameters

optimized for the specific application due to the limited accuracy of the models used to generate such control parameters. As a consequence a lot of support is required from the power companies to provide optimal controller solutions to their customers. Fig. la) shows a classical buck converter power stage 1 with the corresponding modeling in fig. lb) and a converter with a feedback 2 circuit forming a typical voltage control loop can be modeled as show in fig. lc) . The corresponding Bode plots for the transfer function 3 of the buck converter power stage 1 are shown in fig. 2 (magnitude and phase), whereas the compensation results with an integrator for ensuring that V _out 4 is regulated around a desired set-point (V _ref ) are shown in fig. 3. The disadvantage is that the integrator introduces a phase shift of -90 degrees on the frequency response of the power stage 1 making the closed loop unstable. Therefore, the compensation has been

performed with a PID controller in such a way that the controller zeros are placed around the LC double pole to achieve stable close loop operation (see figure 4) . It is obvious that the controller parameters 5 and power stage components, such as the inductor L 6 and the capacitor C 7 etc., are depending from each other. Therefore, the

controller 5 must be manually tuned to achieve an optimal performance, so a power expertise is required to achieve stable loop operation. As well, once the controller 5 has been tuned the same controller cannot be used with another power stage without deteriorating closed loop performance and eventually provoke closed loop instability. So far, the controller design is carried out in the frequency domain that requires also control loop expertise. Some considerations have been made to solve the

aforementioned problems. In order to compensate for load transients current 8 a derivative controller has been used. The bode plots are shown in figure 5. The derivative

controller boosts the phase of 90 degrees of the frequency response of the buck converter power stage 1 over the whole range of frequencies (see figure 2) . Compensation of the transfer function 3 using the derivative controller is shown in figure 6. It can be seen that the frequency response of the compensated transfer function is always stable.

Nevertheless figure 8 shows a drawback of this setup, namely the output voltage 4 does not settle back to the desired set-point value after the load transient. Figure 7 shows the bode plots of the output impedance for open and closed loop cases. The finite DC resistance in figure 7 indicates that the output voltage 4, once the load transient is over, will always differ from the set-point value by a factor

proportional to the dcr of the inductor and the step in the load current AI _0Ut .

Another possibility is to use a proportional-derivative (PD) controller 13 to compensate load transients 8. The result is shown in figure 9, whereas a phase boost in the range of wzl to wd occurs. In this case wzl is selected low enough to boost the phase of the power stage 1 at the LC double pole while wd is set to cancel out the effect of the ESR zero of the output capacitor 7 which is usually occurring at frequency higher than the intended controller bandwidth. Fig. 10 shows the frequency response obtained by

compensating the transfer function of the power stage G _Vd 3 with a PD controller. The control loop is also always stable and the dc resistance is smaller for the closed loop with the PD controller than using only a derivative controller

(figure 11) . Nevertheless the output voltage V _out 4 does not settle back completely to the desired set-point 14 (see figure 12) although the difference is smaller than by using only a derivative controller (compare figures 8 and 12) . Comparing the voltage closed loop (V _out /V _ref ) to the voltage open loop response, shown in figure 13, one can see that the output voltage V _out does not track changes of the set-point value V _ref when using a proportional-derivative controller in a voltage control loop. It is therefore the object of the invention to find an always stable controller architecture for digital control of DC/DC converters, like buck

converters that can compensate for load transients and for abrupt changes of the set-point voltage.

The object of the invention will be solve by a two-loop controller architecture for digital control of a DC-DC converter regulating an output voltage configured to generate a pulse width modulation (PWM) signal to control a power stage in dependence of a voltage error signal, the voltage error signal being a difference between a reference voltage and the output voltage; the controller architecture comprising an inner voltage loop comprised an error amplifier, a main controller C(s) configured to compensate for load transients and for abrupt changes of a set-point value and a digital pulse width modulator, and an outer voltage loop comprised a second error amplifier, a second main controller F(s) configured to compensate a voltage error of the inner voltage loop to achieve a regulation of an output voltage around the desired set-point value and providing an input for the first error amplifier of the inner voltage loop, wherein the combination of the inner voltage loop and the outer voltage loop are configured to eliminate the dependency of the main controllers parameters with respect to components values of the power stage of the DC-DC converter.

The linear controller architecture eliminates the dependency of the controller parameters with respect to the components values of the power stage. This means that controller parameters can be tuned to shape controller regulation performance but do not affect the stability of the control loop. In this way non power experienced users can easily tune the controller without the risk of incurring into stability problems. In order to eliminate the dependency of controller parameters from the power stage components a two loop architecture is employed: A first loop, called inner voltage loop, is used to provide a fast reaction to changes of the regulated output voltage; a second loop, called outer voltage loop, is used to provide slower but more accurate regulation of the output voltage to meet the accuracy requirement dictated by the application. As stated before the inner voltage loop provides a fast but coarse regulation of the output voltage. Such control action is required to suppress the effect of sudden load changes on the output voltage. The outer voltage loop is then taking care of tightly regulating the output voltage to the desired set- point value. In conventional digital PID controllers

typically employed digital PWM controllers the controller parameter providing such accurate control action, i.e. the integral parameter, is the cause of control loop instability in DC/DC converters. For example, the integrator gain can be made small enough to achieve stability for a wide number of power stage scenarios with the drawback of poor regulation performances.

In a preferred embodiment the inventive two-loop controller architecture is an analogue or digital implementation, which only requires two controllers, C(s) and F(s) to operate. A digital implementation is preferred, because an analogue implementation has limitations due to the fact that C(s) has gains lower than 1 at DC and in the low frequency range. When C(s) is implemented as an analogue controller an operational amplifier has to be used. Operational amplifier cannot implement gains lower than 1 within their frequency range of operation and do not work well with gains close to 1. Therefore, a digital implementation of the proposed controller architecture is preferred, as in figure 22.

Controllers F(s) and C(s) are easily implemented in digital and require no external components for their implementation. Moreover switching ripple can be completely filtered out in digital controllers due to the availability of moving average filters or other type of filters that are not implementable in analogue fashion.

In a preferred embodiment of the two-loop controller

architecture the main controller C(s) of the inner voltage loop is configured as a pure derivative controller. The inner voltage loop is stable as long as C(s) is a derivative controller, i.e. has a transfer function

C (s) = (K _d* s) / (1+s/wd) , where K _d is a gain and wd is a high frequency pole placed at high frequency. With C(s) being a derivative controller the inner voltage loop is always stable and the poles and zeros of the power stage do not affect its stability. In fact parameters of C(s) can be determined to work within a wide range of power stages used in the specific application. The idea here is that V _out inherently contains information about the output current and the output current information is used by C(s) to roughly adjust V _out . The transfer function of C(s) determines how good V _out is adjusted to V _ref upon a load change. When C(s) has the above mentioned transfer function and a load step is applied V _out differs from V _ref of a value dcr*AI _0Ut (see fig. 8) while when C (s) = ( (1+s/wz) K _d ^* s) / (1+s/wd) V _out differs from V _ref for a smaller amount than dcr*AI _0Ut as shown in fig. 12.

The switching ripple in the inner voltage loop has no influence on the stability of the loop because it is

attenuated by the pole wd in C(s) and in a digital

implementation can be properly filtered out by the use of specific filtering techniques.

The outer voltage loop with the controller F(s) is only required to achieve precise V _out regulation, i.e. V _out = V _ref , and therefore to compensate for the small difference between V _out and V _ref left over by the inner voltage loop.

In another preferred embodiment of the inventive controller architecture the main controller C(s) of the inner voltage loop is configured as a proportional-derivative controller. In another preferred embodiment of the inventive controller architecture the main controller C(s) of the inner voltage loop is configured as a proportional-integrative-derivative controller with an integral gain, whereas the integral gain is configured such that close loop stability is achieved for a wide number of power stage scenarios despite the poor regulation performance of the closed loop system.

The main idea behind the controller architecture is based on the property of any closed loop system to suppress the poles and zeros of the plant/power stage once the control loop with enough gain is closed around it. In this way a pure derivative (D) or a proportional-derivative controller (PD) as well as a proportional-integral-derivative controller (PID) stabilizing a wide number of power stages can be used for the fast inner voltage loop to compensate for load transients and for abrupt changes of the set-point voltage.

In a further preferred embodiment the second main controller F(s) of the outer voltage loop is configured as a pure integrator controller to compensate the closed inner loop.

Alternatively, the second main controller F(s) can be configured as any other controller type having an integrator behavior at frequencies lower than an inner voltage loop bandwidth can be used for the same purpose.

In the preferred implementation an integral controller (I) can be used to compensate the closed inner voltage loop to achieve regulation of the output voltage around the desired set-point value. Since the integral controller employed in the outer voltage loop compensates the closed inner voltage loop the use of such controller does not have any effect on the stability of the control loop as in a conventional linear PID controller. The implementation of the inventive controller architecture succeed therein that the outer voltage loop comprising a feedback loop feed backing the output voltage to the second error amplifier calculating an internal voltage error signal as a difference between the reference signal and the output voltage .

The outer voltage loop is a slower loop than or as fast as the inner voltage loop, whereas the controller F(s) is a pure integrator or alternatively a controller of an

integrator type that compensates the closed inner voltage loop. With the use of the outer voltage loop and the

integrator the cross over frequency can be pushed up to the bandwidth of the inner voltage loop. Therefore, the

integrator is required to ensure that the output voltage is regulated around the desired set-point of the converter. So the outer voltage loop compensates the residual error between a reference voltage V _ref and the output voltage V _out , whereas the inner voltage loop provides a fast reaction to load transients. Furthermore, the inner voltage loop comprising a feedback loop feed backing the output voltage to the first error amplifier calculating the voltage error signal as a

difference between an internal reference signal of the outer voltage loop and the output voltage. The output voltage is controlled by the inner voltage loop in order to suppress load transients. The inner voltage loop is a fast voltage loop that regulates the output voltage with a proportional-derivative controller. The voltage loop is always stable up to very high bandwidths where the stability boundary is given by delay introduced by the control loop itself. By closing the inner voltage loop the two poles of the power stage are eliminated due to the fact that the closed control loop suppresses the power stage poles and zeros up to the control loop bandwidth. From the bode diagram of the compensated system it can be seen that the phase curve is very far from -180 deg, therefore, the control loop is always stable. In another embodiment the inner voltage loop comprising a feedback loop feed backing the output voltage to the second error amplifier and feed forwarding a difference of the output voltage signal and the reference voltage signal as the internal voltage error signal as an input to the first error amplifier. The

advantage of this implementation is that only a single flash Analog-to-Digital converter is used while the summing node or the first error amplifier is implemented in the digital domain .

The main controller C(s) of the closed inner voltage loop and the main controller F(s) of the outer voltage loop have controller parameters that are tunable in the time domain. The advantage of performing the tuning of controller parameters in the time domain is that this does not require the notion of poles and zeros and their location in

frequency and therefore, no power expertise is required to achieve control loop stability. Additionally, the

implementation of the inventive two-loop controller

structure fits typical control loop architecture of a digital PWM controller, i.e. the proposed controller architecture just replaces the linear PID controller architecture without requiring any additional hardware. It is very advantageous that a stability of the controlled converter is independent of a choice of the controller parameters. In this way controller parameters do not

influence any longer the stability of the converter but only shape the regulation behavior of the converter. So, the controller architecture eliminates the dependency of the controller parameters from the value of power stage

components .

The invention will be explained in more detail using

exemplary embodiments.

The appended drawings show

Fig. 1 a) classical buck converter power stage; b)

modeling of the buck power stage; c) typical voltage mode control loop; d) typical current mode controller; e) auto-tuning algorithm to tune the parameters of C(s) by means of a reference model G*v _d of the power plant; f) implementing a filter T* (s) by means of a reference model of the closed loop system;

Fig. 2 Bode plot of the transfer function of the buck converter power stage;

Fig. 3 Open loop compensated frequency response of the buck converter power stage with an integrator as controller;

Fig. 4 Open loop compensated frequency response of the buck converter power stage with a PID as controller;

Fig. 5 Bode plot of the frequency response of a

derivative controller; Fig. 6 Compensation of the power stage transfer function by means of the derivative controller in fig. 5;

Fig. 7 Bode plot of the output impedance for open and

closed loop with the derivative controller; Fig. 8 Drawback of using only a derivative controller to compensate for load transients;

Fig. 9 Bode plot with the frequency response of a

proportional-derivative controller;

Fig. 10 Frequency response of the compensated transfer function of the power stage G _Vd with a PD controller;

Fig. 11 Frequency response of the output impedance when using a PD controller;

Fig. 12 Drawback of using only a PD controller for

regulating an output voltage to compensate for load transients;

Fig. 13 Comparison of the voltage closed loop (V _out /V _ref ) to the voltage open loop response when a PD controller is used; Fig. 14 a) Basic idea of the inventive two-loop controller architecture, a closed inner voltage loop with a PD-controller and a I-controller as a function of the error voltage, and an output voltage loop, b) the corresponding V _ref (t) and V ^* _ref (t) or I _out (t) diagrams;

Fig. 15 Inventive inner voltage loop to control the output voltage with a reference voltage and to suppress load transients;

Fig. 16 Frequency response of the closed voltage loop

( out / re _f ) of circuitry shown in fig. 16;

Fig. 17 Inventive outer voltage loop to compensate for voltage drops;

Fig. 18 Frequency response of the compensated inner

voltage loop and the controller used to compensate the outer voltage loop;

Fig. 19 Frequency response of the voltage loop (V _out /V _ref ) of the circuitry shown in fig. 17 with the inner voltage loop closed and outer voltage loop being open (VOpenLoop) and closed (VClosedLoop) ;

Fig. 20 Frequency response of the output impedance of the circuitry shown in fig. 17 if the inner and outer voltage loops are closed (solid) compared to the open loop output impedance (dashed) ;

Fig. 21 Exemplary embodiment of the inventive controller architecture: Expected load transient V _out (t) for the inner and outer voltage loop; Fig. 22 Schematic drawing of the implementation of the inventive two-loop concept a) using two summing nodes, b) using a single summing node;

Fig. 23 a) Inner voltage loop in the proposed embodiment using two summing nodes; b) Inner voltage loop in the proposed embodiment using a single summing node ;

Fig. 24 a) Outer voltage loop in the proposed embodiment using two summing nodes; b) Outer voltage loop in the proposed embodiment using a single summing node .

Figure 14 presents the basic idea of the inventive two-loop controller architecture, whereas an inner voltage loop is closed by feed backing 2 the output voltage 4 back to the first error amplifier 10 of the power converter circuitry whereas the inner voltage loop is configured with a PD- controller 19 in order to compensate for load transients 8 and for abrupt changes of a set-point value of the output voltage 4. Secondly, parameters of an I-controller 16 as a function of the error voltage e (t) 24 is determined to compensate for voltage error e (t) = V _ref -V _out . Fig. 14 b) shows the corresponding V _ref (t) and V ^* _ref (t) or I _out (t) diagrams with the influences of the PD- 19 and I- controller 16.

The embodiment as presented in figure 14 cannot be easily implemented by a digital controller because of the two summing nodes 15 and 10 that would require digital to analog and analog to digital conversion of the quantities V _ref 11 - V _out 17, V* _ref 18 - V _out 2 and the voltage error e 20. In fact as shown in figure 22a) a typical digital controller

architecture for DC-DC converters implements a flash ADC to implement the summing node V _ref 11 - V _out 17 while summing node 10 is not available. Figure 15 shows the inventive inner voltage loop 21 which comprises an error amplifier 10, a PD-controller 19, a digital pulse width modulator 9 configured to regulate the output voltage 4 of a power stage 1 and a feedback loop 2 feed backing the output voltage 4 back to the error

amplifier respective summing node 10. The voltage loop is always stable up to very high bandwidths where the stability boundary is given by delay introduced by the control loop itself. By closing the inner voltage loop 21 the two poles of the power stage 1 are eliminated due to the fact that a closed control loop suppresses the power stage poles and zeros up to the control loop bandwidth. From the bode diagrams in figure 16 it can be seen that the phase curve of the closed inner voltage loop is very far from -180 deg, therefore, the inner control loop is always stable. Figure 17 shows the inventive outer voltage loop 22 which comprises a second error amplifier 15, an I-controller 16, whereas the output V* _ref of the I-controller F(s) 16 is used as an input for the first error amplifier or summing node 10 a feedback loop 17 feed backing the output voltage 4 back to the said second error amplifier or second summing node 15. The integrator controller F(s) 16 is used to compensate for the closed inner voltage loop 21 in such a way that the integrator controller 15 ensures that V _out is regulated around a desired set-point value as shown in figure 18. Figure 19 shows the frequency response of the voltage loop ( Vout /Vre _f ) of the circuitry shown in figure 17 if the inner 21 and outer voltage loop 22 being closed, whereas the magnitude of the output voltage 4 tracks set-point changes up to the outer voltage loop bandwidth and the phase

response in dependency of the frequency shows that the phase is very far from -180 degrees, thus the system is always stable .

Figure 20 shows the output impedance of the circuitry shown in figure 17 if the inner voltage loop 21 is closed (solid line) compared to the open loop output impedance (dashed line) . The DC output impedance Z _out is -infinity meaning that the output voltage settles back to the desired set-point value after a load transient. The dashed line shows Z _out for an open loop and the solid line shows Z _out for the closed loops.

Figure 21 shows the influence of the inventive controller architecture for an exemplary embodiment: The inner loop 21 provides a fast reaction to load transient meaning that a change in the output voltage V _out due to a change in the load 8 is compensated very fast, and the outer voltage loop 22 compensates for residual error (V _ref - V _out ) and settles the output voltage 4 back to a desired set-point value. Thereby, the proportional controller parameter K _p controls residual error to be compensated by the outer voltage loop 22, the derivative controller parameter K _d controls the maximum undershoot and the integral controller parameter of the outer voltage loop 22 controls the settling time.

Figure 22 a) and b) shows the schematic drawings of two possible implementation procedures for the two-loop

controller architecture. For calculating the difference between the reference voltage 11 and the output voltage V _out 4 a flash Analog-to-Digital converter (ADC) is used. The advantage by using a flash ADC is to achieve high resolution of the sensed voltage 17 around the desired set-point value V _ref 11.

The control loop diagram in figure 22a) is reworked to the one in figure 22b) where the inner voltage loop comprising a feedback loop feed backing the output voltage to the second error amplifier is now implemented by feed forward 23 of the output of the summing node 15, whereas the summing node is implemented by a flash ADC as in a typical digital

controller architecture for PWM converters.

Figure 23 a) shows a first implementation of the inner voltage loop 21, whereas the output voltage 4 is feed backed 2 to the first error amplifier 10. Figure 22 b) shows a second implementation of the inner voltage loop 21, whereas for the second implementation the result of the difference between the reference voltage V _ref 11 and the output voltage V _out 4 is used as an input value for the first error

amplifier 10. The advantage of the second implementation is that only a single flash Analog-to-Digital converter is used while the summing node 10 is implemented in the digital domain .

Figures 24 a) and b) show a first and a second

implementation of the outer voltage loop 22.

The proposed two-loop controller architecture eliminates the dependency of the controller parameters from the value of the power stage components 1. Furthermore, the stability of the controlled DC/DC converter is not any longer influenced by the choice of controller parameters. Rather, the

controller parameters only "shape" the regulation behavior of the digital PWM controller. Thereby, the tuning of the controller parameters can be performed in the time domain without requiring any power expertise to achieve control loop stability.

The implementation of the controller fits the typical control loop architecture of digital PWM controller, i.e. the proposed controller architecture replaces the linear PID controller architecture without requiring changes on the existing architectures. Two-loop controller architecture for digital control of DC- DC converter

Reference signs 1 buck converter stage

2 feedback loop

3 transfer function of the buck power stage

4 output voltage

5 digital filter, controller

6 inductor of the power stage

7 capacitance of the power stage

8 load current

9 digital pulse width modulator

10 error amplifier, summing node

11 reference voltage

12 derivative controller parameter

13 proportional-derivative controller

14 desired set-point

15 second error amplifier, summing node

16 outer loop integrator controller

17 outer feedback loop

18 internal reference voltage

19 inner loop PD-controller, D-controller

20 error voltage

21 inner loop or first loop or fast loop

22 outer loop or second loop or slow loop

23 second embodiment of the inner loop, feed forward

24 internal voltage error signal

25 filter

26 auto-tuning algorithms

27 inner control loop outer current loop

transfer function of the power stage Z _c

specific transfer function G* i ₀ r v _d

specific controller Ci(s)

specific controller C _v (s) of the outer voltage loop