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This is an open loop PID autotuner using a novel s-curve inflection point test method. Tuning parameters are typically determined in about ½Tau on a first-order system with time delay. Full 5Tau testing and multiple serial output options are provided. SeeWiKi for test results and more.

This open-loop tuning method is used when the controller action is set todirectIP orreverseIP. This method works best on processes that respond with an S-shaped reaction curve to a stepped output. Being an open-loop test, there is no setpoint and PID correction involved. The process gain, dead time, time constant and more is determined by doing a shortened step test that ends just after theinflection point has been reached. From here, the apparent maximum PV (input) is mathematically determined and the controller's tuning parameters are calculated. Test duration is typically only ½Tau.

Accurate determination of the inflection point was given high priority for this test method. To accomplish this, a circular buffer for the input readings is created that's sized to 6% of the samples value. The buffer is used as a moving tangent line where the "head" of the tangent is based on the average of all readings in the buffer and the "tail" is based on the oldest instantaneous value in the buffer. The tangent line moves along the reaction curve one sample at a time. The slope of the tangent line is checked at every sample. When the sign of the change in slope changes (i.e. slope goes from increasing to decreasing or from decreasing to increasing), this is the point of inflection (where the tangent turns red here). After 1⁄16 samples has occurred with the new slope direction, then it's known that the point of inflection has been reached. Final calculations are made and the test ends.

• First, the PID controller is placed inmanual mode.

• The tuner action is set todirectIP orreverseIP, then configure sTune:

• tuner.Configure(inputSpan, outputSpan, outputStart, outputStep, testTimeSec, settleTimeSec, samples);

• Its expected that the user is already familiar with the controller and can make a rough estimation of what the system's time constant would be. Use this estimate for thetestTimeSec constant.

• Thesamples constant is used to define the maximum number of samples used to perform the test. To get an accurate representation of the curve, the suggested range is 200-500.

• settleTimeSec is used to provide additional settling time prior to starting the test.

• inputSpan andoutputSpan represent the maximum operating range of input and output. Examples:

  • If your input works with temp readings of 20C min and 220C max, theninputSpan = 200;If the output uses 8-bit PWM and your using its full range, thenoutputSpan = 255;If the output is digital relay controlled by millis() with window period of 2000ms, thenoutputSpan = 2000;

• outputStart is the initial control output value which is used for thesettleTimeSec duration and sample 0.

• outputStep is the stepped output value used for sample 1 to test completion.

• after test completion, the setup can be updated for the next test andtuner.Configure() can be called again.

• TheoutputStep value is applied at sample 1 and inflection point discovery begins.

• Dead time is determined when the averaged input has increased (or decreased) beyond one resolution value from the starting instantaneous input value.

• When the point of inflection is reached, the test ends. The apparentpvMax is calculated using:

• pvMax = pvIp + slopeIp * kexp;// where kexp = 4.3004 = (1 / exp(-1)) / (1 - exp(-1))

• The process gainKu and time constantTu are determined and the selected tuning rule's constants are used to determineKp, Ki, Kd, Ti and Td. Also,controllability and other details are provided (see comments insTune.cpp).

• In the user's sketch, the PID controller is set to automatic, the tuning parameters are applied the PID controller is run.

A full test to pvMax is used when the controller action is set todirect5T orreverse5T. Use this method if theIPtesting isn't a good fit to the process or if you'd like to get test data for the complete input response. Here, it is assumed the test will complete at about 3.5τ, from which point the apparentpvMax is estimated and the tuning parameters are calculated.

sTune(float *input,float *output, TuningRule tuningRule, Action action, SerialMode serialMode);

• input andoutput are pointers to the variables holding these values.
• tuningRule provides selection of 10 various tuning rules as described in the table below.
• action provides choices for controller action (direct or reverse) and whether to perform a fast inflection point test (IP) or a full 5 time constant test (5T). Choices aredirectIP,direct5T,reverseIP andreverse5T.
• serialMode provides 6 choices for serial output.

Open Loop Tuning Methods	Autotune Plot (using PWM output)	Description
ZN_PID		Open Loop Ziegler-Nichols method with ¼ decay ratio
DampedOsc_PID		Damped Oscillation method can solve marginal stability issues
NoOvershoot_PID		No Overshoot uses the C-H-R method (set point tracking) with 0% overshoot
CohenCoon_PID		Open loop Cohen Coon method approximates closed loop response with a ¼ decay ratio
Mixed_PID		Mixed method averages the gains forZN_PID,DampedOsc_PID,NoOvershoot_PID andCohenCoon_PID
ZN_PI		Open Loop Ziegler-Nichols method with ¼ decay ratio
DampedOsc_PI		Damped Oscillation method can solve marginal stability issues
NoOvershoot_PI		No Overshoot uses the C-H-R method (set point tracking) with 0% overshoot
CohenCoon_PI		Open loop Cohen Coon method approximates closed loop response with a ¼ decay ratio
Mixed_PI		Mixed method averages the gains forZN_PI,DampedOsc_PI,NoOvershoot_PI andCohenCoon_PI

sTune tuner =sTune(&Input, &Output, tuner.ZN_PID, tuner.directIP, tuner.printALL);/*                                         ZN_PID           directIP     serialOFF                                           DampedOsc_PID    direct5T     printALL                                           NoOvershoot_PID  reverseIP    printSUMMARY                                           CohenCoon_PID    reverse5T    printDEBUG                                           Mixed_PID                                           ZN_PI                                           DampedOsc_PI                                           NoOvershoot_PI                                           CohenCoon_PI                                           Mixed_PI*/

This function applies the sTune test settings.

voidConfigure(constfloat inputSpan,constfloat outputSpan,float outputStart,float outputStep,uint32_t testTimeSec,uint32_t settleTimeSec,constuint16_t samples);

voidSetEmergencyStop(float e_Stop);voidSetControllerAction(Action Action);voidSetSerialMode(SerialMode SerialMode);voidSetTuningMethod(TuningMethod TuningMethod);

floatGetKp();// proportional gainfloatGetKi();// integral gainfloatGetKd();// derivative gainfloatGetTi();// integral timefloatGetTd();// derivative timefloatGetProcessGain();// process gainfloatGetDeadTime();// process dead time (seconds)floatGetTau();// process time constant (seconds)uint8_tGetControllerAction();uint8_tGetSerialMode();uint8_tGetTuningMethod();voidGetAutoTunings(float * kp,float * ki,float * kd);

When the test ends, sTune determineshow difficult the process is to control.

float controllability = _Tu / _td + epsilon;

• Comparison of PID Controller Tuning Methods
• Ziegler-Nichols Open-Loop Tuning Rules
• Inflection point
• Time Constant (Re: Step response with arbitrary initial conditions)
• Sample Time is a Fundamental Design and Tuning Specification