Controls Tutorial for Motion Profiling

source/_extensions/controls_js_sim/__init__.py

@@ -91,6 +91,8 @@ def setup(app: Sphinx) -> Dict[str, Any]:
     app.add_js_file("pid-tune.js")
     app.add_css_file("pid-tune.css")
 
+    print("Done.")
+
     return {
         "parallel_read_safe": True,
         "parallel_write_safe": True,

source/_extensions/controls_js_sim/base/base-visualization.js

@@ -27,6 +27,9 @@ class BaseVisualization {
 
     window.addEventListener("resize", this.updateSize.bind(this));
     window.addEventListener("load", this.updateSize.bind(this));
+
+    this.position = 0;
+    this.positionPrev = 0;
   }
 
   updateSize() {
@@ -43,8 +46,8 @@ class BaseVisualization {
     this.timeS = timeS;
   }
 
-  setCurPos(positionRad) {
-    this.positionRad = positionRad;
+  setCurPos(position) {
+    this.position = position;
   }
 
   setCurSetpoint(setpoint) {

source/_extensions/controls_js_sim/plant/vertical-elevator-plant.js

@@ -0,0 +1,91 @@
+class VerticalElevatorPlant {
+  constructor(TimestepS, heightM) {
+    this.TimestepS = TimestepS;
+
+
+    this.mass = 20.0; // in kg
+
+    // Gains estimated by ReCalc (http://reca.lc) with the specs below
+    // motor: 1x REV Neo
+    // gearing: 3:1
+    // Pulley Diameter: 1 in
+    // efficiency: 75
+    // moving mass: 20 kg
+    this.kGVolts = 2.28;
+    this.kVVoltSecondPerM = 3.07;
+    this.kAVoltSecondSquaredPerM = 0.41;
+
+    //Factor for loosely-modeled air resistance for some unmodeled disturbance
+    // See https://www.grc.nasa.gov/www/k-12/VirtualAero/BottleRocket/airplane/falling.html
+    let r = 1.225; //Air density at sea level
+    let Cd = 1.42; // Drag Coefficient for a hollow hemisphere pointed the "wrong way" into the wind
+    let A = 1.5; //Exposed Area (m^2)
+    this.airResistanceCoef = Cd * r * A / 2.0;
+
+
+    //Maximum height the elevator travels to
+    this.heightM = heightM;
+
+    this.state = [0, 0];
+
+    this.systemNoise = false;
+    // Simulate half volt std dev system noise at sim loop update frequency
+    this.gaussianNoise = gaussian(0, 0.5);
+  }
+
+  acceleration([posM, velMPerS], inputVolts) {
+    if (this.systemNoise) {
+      inputVolts += this.gaussianNoise();
+    }
+
+    const gravityAcceleration = -this.kGVolts / this.kAVoltSecondSquaredPerM;
+    const EMFAcceleration = -this.kVVoltSecondPerM * velMPerS / this.kAVoltSecondSquaredPerM;
+    const controlEffortAcceleration = inputVolts / this.kAVoltSecondSquaredPerM;
+    const airResistanceAccel = -1.0 * Math.sign(velMPerS) * Math.pow(velMPerS, 2) * this.airResistanceCoef / this.mass;
+
+    var springAccel = 0.0;
+    var dashpotAccel = 0.0;
+
+    //Apply hard-stops as a combo spring + dashpot
+    if(posM > this.heightM){
+      //Top limit
+      springAccel = (posM - this.heightM) * -100000.0;
+      dashpotAccel = -100.0 * velMPerS;
+    } else if(posM < 0.0){
+      //Bottom limit
+      springAccel = (posM) * -100000.0;
+      dashpotAccel = -100.0 * velMPerS;
+    }
+
+    const accelMPerSSquared = gravityAcceleration + EMFAcceleration + controlEffortAcceleration + airResistanceAccel + springAccel + dashpotAccel;  
+
+
+    return [velMPerS, accelMPerSSquared]
+  }
+
+  reset() {
+    this.state = [0, 0];
+  }
+
+  update(inputVolts) {
+    // Simulate system noise
+    if (this.systemNoise && inputVolts > 0) {
+      // apply system noise
+      inputVolts += this.gaussianNoise();
+    }
+
+    this.state =
+      secondOrderRK4((state, inputVolts) => this.acceleration(state, inputVolts),
+      this.state,
+      inputVolts,
+      this.TimestepS);
+  }
+
+  getPositionM() {
+    return this.state[0];
+  }
+
+  setSystemNoise(enabled) {
+    this.systemNoise = enabled;
+  }
+}

source/_extensions/controls_js_sim/sim/vertical-elevator-sim.js

@@ -0,0 +1,154 @@
+class VerticalElevatorSim extends BaseSim {
+  constructor(divIdPrefix) {
+    super(divIdPrefix, "M", -0.5, 2.5);
+
+    this.simDurationS = 5.0;
+    this.simulationTimestepS = 0.005;
+    this.controllerTimestepS = 0.02;
+
+    this.elevHeightM = 1.0;
+
+    this.plant = new VerticalElevatorPlant(this.simulationTimestepS, this.elevHeightM);
+
+    this.visualization = new VerticalElevatorVisualization(
+      this.visualizationDrawDiv,
+      this.simulationTimestepS,
+      this.elevHeightM,
+      () => this.iterationCount - 1,
+      setpoint => this.setSetpointM(setpoint),
+      () => this.begin()
+    );
+    this.visualization.drawStatic();
+
+    this.timeSinceLastControllerIteration = 0.0;
+
+    this.accumulatedError = 0.0;
+    this.previousPositionError = 0.0;
+
+    //User-configured feedback
+    this.kP = 0.0;
+    this.kI = 0.0;
+    this.kD = 0.0;
+
+    //User-configured Feed-Forward
+    this.kG = 0.0;
+    this.kV = 0.0;
+    this.kA = 0.0;
+
+    //User-configured Profiling
+    this.maxVelMps = 0.0;
+    this.maxAccelMps2 = 0.0;
+
+    this.inputVolts = 0.0;
+
+    //Default starting setpoint
+    this.goal = new ProfileState(0.0, 0.0, 0.0);
+
+    // Reset at least once right at the start
+    this.resetCustom();
+  }
+
+  setSetpointM(setpoint) {
+    this.goal = new ProfileState(setpoint, 0.0, 0.0);
+    document.getElementById(this.divIdPrefix + "_setpoint").value = setpoint;
+  }
+
+  resetCustom() {
+    this.plant.reset();
+    this.timeS = Array(this.simDurationS / this.simulationTimestepS)
+      .fill()
+      .map((_, index) => {
+        return index * this.simulationTimestepS;
+      });
+
+    this.visualization.setCurPos(0.0);
+    this.visualization.setCurTime(0.0);
+    this.visualization.setCurSetpoint(0.0);
+    this.visualization.setCurControlEffort(0.0);
+
+    this.accumulatedError = 0.0;
+    this.previousPositionError = 0.0;
+    this.inputvolts = 0.0;
+    this.iterationCount = 0;
+
+    this.makeProfile()
+
+    this.positionDelayLine = new DelayLine(13); //models sensor lag
+
+  }
+
+  makeProfile(){
+    var constraints = new ProfileConstraints(this.maxVelMps, this.maxAccelMps2);
+    this.profile = new TrapezoidProfile(constraints)
+    this.start = new ProfileState(0.0,0.0,0.0);
+    this.setpoint = this.start;
+    this.profile.init(this.start, this.goal)
+  }
+
+  iterateCustom() {
+
+    this.curSimTimeS = this.timeS[this.iterationCount];
+
+    let measuredPositionM = this.positionDelayLine.getSample();
+
+    // Update controller at controller freq
+    if (this.timeSinceLastControllerIteration >= this.controllerTimestepS) {
+      this.setpoint = this.profile.calculate(this.curSimTimeS, this.setpoint)
+      this.inputVolts = this.updateController(this.setpoint, measuredPositionM);
+      this.timeSinceLastControllerIteration = this.controllerTimestepS;
+    } else {
+      this.timeSinceLastControllerIteration = this.timeSinceLastControllerIteration + this.simulationTimestepS;
+    }
+
+    this.plant.update(this.inputVolts);
+
+    this.positionDelayLine.addSample(this.plant.getPositionM());
+
+    this.visualization.setCurPos(this.plant.getPositionM());
+    this.visualization.setCurTime(this.curSimTimeS);
+    this.visualization.setCurSetpoint(this.setpoint.pos);
+    this.visualization.setCurControlEffort(this.inputVolts);
+
+    this.procVarActualSignal.addSample(new Sample(this.curSimTimeS, this.plant.getPositionM()));
+    this.procVarDesiredSignal.addSample(new Sample(this.curSimTimeS, this.setpoint.pos));
+    this.voltsSignal.addSample(new Sample(this.curSimTimeS, this.inputVolts));
+
+    this.iterationCount++;
+
+    if (this.iterationCount >= this.timeS.length) {
+      this.end();
+    }
+  }
+
+  updateController(setpoint, measurement) {
+
+    // Calculate error, error derivative, and error integral
+    let positionError = setpoint.pos - measurement;
+
+    this.accumulatedError += positionError * this.controllerTimestepS;
+
+    const derivativeError =
+      (positionError - this.previousPositionError) / this.controllerTimestepS;
+
+    // PID + gravity/Profiled feed-forward control law
+    let controlEffortVolts =
+      this.kG  +
+      this.kV * setpoint.vel +
+      this.kA * setpoint.accel +
+      this.kP * positionError +
+      this.kI * this.accumulatedError +
+      this.kD * derivativeError;
+
+    // Cap voltage at max/min of the physically possible command
+    if (controlEffortVolts > 12) {
+      controlEffortVolts = 12;
+    } else if (controlEffortVolts < -12) {
+      controlEffortVolts = -12;
+    }
+
+    this.previousPositionError = positionError;
+
+    return controlEffortVolts;
+  }
+
+}