It has been impossible over the last few years to ignore thetransition in electronics from analogue to digital technologies. Thischange has been driven largely by the speed that digital devices arenow capable of reaching, allowing them to compare favourably withtheir analogue counterparts in high frequency applications, such asmobile communications and broadcasting. However, the inherentadvantages of digital signals in these applications; high noisetolerance, use of advanced compression techniques, increased channelcapacity etc do not directly apply to system control, andspecifically to closing the loop in switched-mode power electronics.
The digital advantage
Using a digital signal processor (DSP), controllers of identicalspecification to their analogue counterparts can be realised in a fewlines of code. The processing power of the modern DSP chip is suchthat further functionality can be added to the device, such asin-built fault detection, load/line management or online monitoringcapabilities. Because the controller itself is software based, abasic set of algorithms can be modified to stabilise any powerconverter topology and the parameters of the control algorithm can befine-tuned easily at any time. The control design is also hiddeninside the DSP chip, giving added design security. The cost of DSPtechnology is reducing and its power increasing constantly, such thatdigital control can now compete strongly in terms of cost and boardspace with its analogue equivalent. However, it is the possibilitiesfor realisable advanced or adaptive algorithms that set digitalcontrol apart as the way forward in converter control.
Conventionally, a switched-mode power supply is stabilised bymonitoring variables such as the output voltage or inductor current,and using these measurements to govern the duty ratio of theswitching process.
A compensation network is used to process the feedback signalgenerated by the measurements, shaping the overall frequency responseof the converter and providing good transient responsecharacteristics. To design this compensation network, a transferfunction, or mathematical model, of the power stage of the converteris required. If this model can be manipulated into a form that islinear and that does not change over time (a linear time-invariant(LTI) model) then many simple and effective classical methods can beused to design the controller. This is conventionally the approachadopted by converter designers.
Unfortunately, the technique of pulse width modulation (PWM) usedin switched-mode devices to regulate the output power is neithertime-invariant nor linear; the model of the device changes dependingon the state of the switching transistor and can also depend on the(time-varying) input voltage and load impedance. Because theswitching frequency of the PWM device is typically much greater thanthat of the output filter, its inter-cycle behaviour can be wellapproximated by a time average and the small output ripple ignored inany analogue model. Likewise, in a digital control scheme, a sampleddata model can be derived that samples the measured variables at theend of each switching cycle.
The issue of time-variance is therefore dealt with equally in bothcases, neither scheme being any better or worse than the other, andthe averaged models work to a good degree of accuracy. The non-linearnature of the PWM scheme can be handled in several ways. Often, it isassumed that the device will function over a small range of valuescentred around a nominal operating condition. A linear approximationcan then be made, resulting in a model to which PID or lead-lagcontrol designs can be applied. This approach can also be taken inorder to design a digital controller and is one of the methodssuccessfully implemented by GSPK Design.
Fig 1: Comparison of frequency responses – discrete-continuous.The behaviour of a digitised system and its analogue equivalent areidentical up to 1/2 the sampling frequency.
A Texas Instruments C24x series DSP chip running at 40MIPs wasused to implement a digital controller to allow the current drawn by250W converter to follow the mains voltage, providing power factorcorrection without an additional front-end boost converter. Thiscontroller was a digital version of a PID control loop and includedintegrator windup and inductor current limiting functions. Altogetheronly 30% of the available processing power was used to run thecontrol software, leaving plenty of available processing time to putmore complex algorithms into action. The test application managed toperform in line with the equivalent analogue control, at a comparableprice and using less board space.
For designs of this type, an automated design tool for a genericsecond order digital controller is under development at GSPK – seefigure 2. Given the topology and component values of a converter,this will provide designers with a control algorithm to implement aDSP controller.
Fig 2: Beta version of the DSP control algorithm designtool
Current-mode control is a widely adopted control method thatimproves on the inherently slow response of simple voltage-modecontrollers. The technique utilises an inductor current measurementto set the switching time of the power transistor. Because there isno delay present between the transistor switching and its effect oninductor current, a fast inner control loop can be used inconjunction with a simplified outer voltage loop to improve thecontrol action – see figure 3.
Fig 3: Two loop current-mode controlstructure.
The following analysis shows the effect the inner current loop hason the transfer function seen by the outer voltage loop:
The above expression is a new, single loop system, representingthe transfer function between the input reference voltage and theconverter output voltage. If |C1G|>>1, as is the case for mostpower converters, then the above expression reduces to:
For the Buck converter:
The inner current loop has reduced the system seen by the voltageloop to a single order transfer function with no dependence on theinput voltage (note that due to the assumptions made this is an idealcase). This model can be used to design the outer loop controller C2.Because this is now a single order, input independent system, thistask is made considerably easier.
Such two-loop control systems are easily handled in the digitalrealm. The TI C24x and C28x DSPs handle up to 16 time-sequencedanalogue input channels via their on-chip ADC. They also include upto 16 PWM outputs, making them ideal for applications such as this.The processing power available even on the cheapest DSP device is nowsuch that plenty of time is available to compute the algorithmsrequired for current-mode control schemes.
However, in order to obtain further improvements in controlperformance, it would be desirable to take a step back and reconsiderthe stabilising of power converters from a non-linear model,applicable to a less restrained range of operating conditions.
Because the design of switched mode control systems is usuallybased on a small-signal linearised model, the behaviour of suchdevices when subject to variations in load characteristics or currentlevels is unpredictable. Increasing the complexity of the controlbased solely on this model is useful only to a limited extent, sincethe control performance cannot extend beyond the accuracy of theinitial model. The best way to improve the control is therefore touse a more accurate model. With the added complexity involved innon-linear control schemes based on such a model, analogue methodsbecome difficult and expensive to implement, as well as requiringmore and more silicon to perform the task. In contrast, the same DSPset-up used to implement the PID controller in this application canbe reprogrammed to perform more advanced algorithms simply bychanging the software code. This ease of implementation is the keyadvantage of digital technology for development of convertercontrol.
The concept of sliding-mode control is that the controllerstructure is altered such that the position of the state of theoverall system is forced onto a 'surface' in state-space of orderless than that of the system. Upon reaching this surface, the designof the controller must ensure that for all subsequent time, the stateof the system remains on (or close to) this surface. If this can beensured, a reduced-order, equivalent model of the system can becomputed, this equivalent model can then be used to design a controlscheme with desirable closed-loop response. Because of the simplifiednature of the equivalent model, this design task is made considerablyeasier. In current-mode control, a similar strategy is used; theinductor current is forced by a fast inner-control loop to follow areference. This is the equivalent to driving the state of the systemto a sliding surface. This gives a reduced-order, simplifiedstate-space model and a slower outer-control loop can be designed toregulate the converter output voltage.
The difference between the current-mode control scheme and that ofsliding-mode control is that the former uses the approximatelinearised model, whereas sliding-mode controllers can be applied tonon-linear models. An adaptive scheme such as sliding-mode controllends itself well to digital implementation, where controllerstructures can easily be altered during operation. Achieving thisusing an analogue method would not be straightforward.
Figure 4 shows the basic concept. The controller structure isaltered depending on which side of the sliding surface the systemhappens to be, this forces the state trajectory to converge on thedesired surface. Once on this surface the control action is such thatthe trajectory remains fixed to it. A common problem with this methodis 'jitter', where rather than fix itself to the surface the systemoscillates around it.
Fig.4 Sliding-mode control
Once the system has reached the surface, an equivalent reducedorder model can be used, this can be seen to be the case in figure 4,since on the surface: x1 = k.x2+c. The design problem is then splitinto two distinct aspects, definition of the sliding surface (andcontroller partitioning in order to gain these surfaces) and designof the reduced order controller based on the reduced order systemdynamics.
The simple implementations of digital controllers can easily matchthe performance of analogue systems. Also that much-improvedperformance is possible with no additional hardware by use ofnon-linear modelling and sliding-mode control schemes. Otheradvantages are possible with digital control such as reducingswitching losses and EMI