Voltage Regulation in Power Stage

We use Simulink to model the voltage controller in the power stage for an electronic device:

open_system('rct_powerstage')

The power stage amplifier is modeled as a second-order linear system with the following frequency response:

bode(psmodel) grid

The controller must regulate the voltageVchipdelivered to the device to track the setpointVcmdand be insensitive to variations in load currentiLoad. The control structure consists of a feedback compensator and a disturbance feedforward compensator. The voltageVingoing into the amplifier is limited to. The controller sampling rate is 10 MHz (sample timeTmis 1e-7 seconds).

Performance Requirements

This application is challenging because the controller bandwidth must approach the Nyquist frequencypi/Tm= 31.4 MHz. To avoid aliasing troubles when discretizing continuous-time controllers, it is preferable to tune the controller directly in discrete time.

The power stage should respond to a setpoint change in desired voltageVcmdin about 5 sampling periods with a peak error (across frequency) of 50%. Use a tracking requirement to capture this objective.

Req1 = TuningGoal.Tracking('Vcmd','Vchip',5*Tm,0,1.5); Req1.Name ='Setpoint change'; viewGoal(Req1)

The power stage should also quickly reject load disturbancesiLoad. Express this requirement in terms of gain fromiLoadtoVchip. This gain should be low at low frequency for good disturbance rejection.

s = tf('s'); nf = pi/Tm;% Nyquist frequencyReq2 = TuningGoal.Gain('iLoad','Vchip',1.5e-3 * s/nf); Req2.Focus = [nf/1e4, nf]; Req2.Name ='Load disturbance';

High-performance demands may lead to high control effort and saturation. For the ramp profilevcmdspecified in the Simulink model (from 0 to 1 in about 250 sampling periods), we want to avoid hitting the saturation constraint. Use a rate-limiting filter to model the ramp command, and require that the gain from the rate-limiter input tobe less than.

RateLimiter = 1/(250*Tm*s);% models ramp command in Simulink% |RateLimiter * (Vcmd->Vin)| < VmaxReq3 = TuningGoal.Gain('Vcmd','Vin',Vmax/RateLimiter); Req3.Focus = [nf/1000, nf]; Req3.Name ='Saturation';

To ensure adequate robustness, require at least 7 dB gain margin and 45 degrees phase margin at the plant input.

Req4 = TuningGoal.Margins('Vin',7,45); Req4.Name ='Margins';

Finally, the feedback compensator has a tendency to cancel the plant resonance by notching it out. Such plant inversion may lead to poor results when the resonant frequency is not exactly known or subject to variations. To prevent this, impose a minimum closed-loop damping of 0.5 to actively damp of the plant's resonant mode.

Req5 = TuningGoal.Poles(0,0.5,3*nf); Req5.Name ='Damping';

Tuning

Next usesystuneto tune the controller parameters subject to the requirements defined above. First use theslTunerinterface to configure the Simulink model for tuning. In particular, specify that there are two tunable blocks and that the model should be linearized and tuned at the sample timeTm.

TunedBlocks = {'compensator','FIR'}; ST0 = slTuner('rct_powerstage',TunedBlocks); ST0.Ts = Tm;% Register points of interest for open- and closed-loop analysisaddPoint(ST0,{'Vcmd','iLoad','Vchip','Vin'});

We want to use an FIR filter as feedforward compensator. To do this, create a parameterization of a first-order FIR filter and assign it to the "Feedforward FIR" block in Simulink.

FIR = tunableTF('FIR',1,1,Tm);% Fix denominator to z^nFIR.Denominator.Value = [1 0]; FIR.Denominator.Free = false; setBlockParam(ST0,'FIR',FIR);

Note thatslTunerautomatically parameterizes the feedback compensator as a third-order state-space model (the order specified in the Simulink block). Next tune the feedforward and feedback compensators withsystune. Treat the damping and margin requirements as hard constraints and try to best meet the remaining requirements.

rng(0) topt = systuneOptions('RandomStart',6); ST = systune(ST0,[Req1 Req2 Req3],[Req4 Req5],topt);

最后:软= 1.29,= 0.99651, Iterations = 373 Final: Soft = 1.29, Hard = 0.98195, Iterations = 407 Final: Soft = 1.29, Hard = 0.91128, Iterations = 351 Final: Soft = 1.29, Hard = 0.99834, Iterations = 399 Final: Soft = 1.3, Hard = 0.99571, Iterations = 360 Final: Soft = 1.28, Hard = 0.99752, Iterations = 504 Final: Soft = 1.29, Hard = 0.97842, Iterations = 368

The best design satisfies the hard constraints (Hardless than 1) and nearly satisfies the other constraints (Softclose to 1). Verify this graphically by plotting the tuned responses for each requirement.

figure('Position',[10,10,1071,714]) viewGoal([Req1 Req2 Req3 Req4 Req5],ST)

Validation

首先验证设计的线性区域形成n using theslTunerinterface. Plot the closed-loop response to a step commandVcmdand a step disturbanceiLoad.

figure('Position',[100,100,560,500]) subplot(2,1,1) step(getIOTransfer(ST,'Vcmd','Vchip'),20*Tm) title('Response to step command in voltage') subplot(2,1,2) step(getIOTransfer(ST,'iLoad','Vchip'),20*Tm) title('Rejection of step disturbance in load current')

UsegetLoopTransferto compute the open-loop response at the plant input and superimpose the plant and feedback compensator responses.

clf L = getLoopTransfer(ST,'Vin',-1); C = getBlockValue(ST,'compensator'); bodeplot(L,psmodel(2),C(2),{1e-3/Tm pi/Tm}) grid legend('Open-loop response','Plant','Compensator')

The controller achieves the desired bandwidth and the responses are fast enough. Apply the tuned parameter values to the Simulink model and simulate the tuned responses.

writeBlockValue(ST)

The results from the nonlinear simulation appear below. Note that the control signalVinremains approximately withinsaturation bounds for the setpoint tracking portion of the simulation.

Figure 1: Response to ramp command and step load disturbances.

Figure 2: Amplitude of input voltageVinduring setpoint tracking phase.