Hot plate PID control according to measured graphs

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Dan Richter 2023-3-28

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https://ww2.mathworks.cn/matlabcentral/answers/1936924-hot-plate-pid-control-according-to-measured-graphs

评论： Dan Richter 2023-3-29

I would like to control electric hot plate by PID control. Please can you advise me on how to identify system, calculate the PID parameters and let me know the equation by which I can control the temperature of the hotplate by reading the measured temperature in 1 s intervals and by means of MCU to control the SSR (PWM) accordingly to follow JEDEC reflow profile?

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Star Strider 2023-3-29

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Identifying the system is straightforward. Coinverting the identified system to a PID representation does not appear to be possible.

THP = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1338819/Esperanza_Hotplate.xlsx', 'VariableNamingRule','preserve')

THP = 490×2 table

Time [s] T [°C] ________ ______ 1 27.032 2 26.966 3 26.909 4 26.859 5 26.818 6 26.784 7 26.759 8 26.742 9 26.733 10 26.731 11 26.738 12 26.752 13 26.774 14 26.804 15 26.842 16 26.887

VNTHP = THP.Properties.VariableNames;

figure

plot(THP{:,1}, THP{:,2})

grid

xlabel(VNTHP{1})

ylabel(VNTHP{2})

Ts = diff(THP{[1 2],1}) % Sampling Interval (Assumed Constant)

Ts = 1

HPData = iddata(THP{:,2},[],Ts)

HPData = Time domain data set with 490 samples. Sample time: 1 seconds Outputs Unit (if specified) y1

HPss = ssest(HPData,3)

HPss = Continuous-time identified state-space model: dx/dt = A x(t) + K e(t) y(t) = C x(t) + e(t) A = x1 x2 x3 x1 -0.009696 0.00484 0.005199 x2 -0.01001 0.00952 0.01666 x3 -0.01958 0.002297 -0.00606 C = x1 x2 x3 y1 -2743 99.72 1.013 K = y1 x1 -0.0002048 x2 0.01029 x3 -0.08902 Parameterization: FREE form (all coefficients in A, B, C free). Disturbance component: estimate Number of free coefficients: 15 Use "idssdata", "getpvec", "getcov" for parameters and their uncertainties. Status: Estimated using SSEST on time domain data "HPData". Fit to estimation data: 100% (prediction focus) FPE: 1.1e-06, MSE: 1.061e-06

figure

compare(HPData, HPss)

grid

.

Dan Richter 2023-3-29

Thank you very much for your advice. That's great.

What equation with PID coefficients should I use to control the SSR so that the resulting temperature matches the JEDEC temperature profile, see attached graph? When the peak of the curve is reached, I take the PCB off the hot plate.

I will measure the hot plate temperature each second.

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