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Diffstat (limited to 'third_party/webkit/PerformanceTests/MotionMark/tests/resources/math.js')
| -rw-r--r-- | third_party/webkit/PerformanceTests/MotionMark/tests/resources/math.js | 268 |
1 files changed, 268 insertions, 0 deletions
diff --git a/third_party/webkit/PerformanceTests/MotionMark/tests/resources/math.js b/third_party/webkit/PerformanceTests/MotionMark/tests/resources/math.js new file mode 100644 index 0000000000..9c2706e2a3 --- /dev/null +++ b/third_party/webkit/PerformanceTests/MotionMark/tests/resources/math.js @@ -0,0 +1,268 @@ +SimpleKalmanEstimator = Utilities.createSubclass(Experiment, + function(processError, measurementError) { + Experiment.call(this, false); + var error = .5 * (Math.sqrt(processError * processError + 4 * processError * measurementError) - processError); + this._gain = error / (error + measurementError); + }, { + + sample: function(newMeasurement) + { + if (!this._initialized) { + this._initialized = true; + this.estimate = newMeasurement; + return; + } + + this.estimate = this.estimate + this._gain * (newMeasurement - this.estimate); + }, + + reset: function() + { + Experiment.prototype.reset.call(this); + this._initialized = false; + this.estimate = 0; + } +}); + +PIDController = Utilities.createClass( + function(ysp) + { + this._ysp = ysp; + this._out = 0; + + this._Kp = 0; + this._stage = PIDController.stages.WARMING; + + this._eold = 0; + this._I = 0; + }, { + + // Determines whether the current y is + // before ysp => (below ysp if ysp > y0) || (above ysp if ysp < y0) + // after ysp => (above ysp if ysp > y0) || (below ysp if ysp < y0) + _yPosition: function(y) + { + return (y < this._ysp) == (this._y0 < this._ysp) + ? PIDController.yPositions.BEFORE_SETPOINT + : PIDController.yPositions.AFTER_SETPOINT; + }, + + // Calculate the ultimate distance from y0 after time t. We want to move very + // slowly at the beginning to see how adding few items to the test can affect + // its output. The complexity of a single item might be big enough to keep the + // proportional gain very small but achieves the desired progress. But if y does + // not change significantly after adding few items, that means we need a much + // bigger gain. So we need to move over a cubic curve which increases very + // slowly with small t values but moves very fast with larger t values. + // The basic formula is: y = t^3 + // Change the formula to reach y=1 after 1000 ms: y = (t/1000)^3 + // Change the formula to reach y=(ysp - y0) after 1000 ms: y = (ysp - y0) * (t/1000)^3 + _distanceUltimate: function(t) + { + return (this._ysp - this._y0) * Math.pow(t / 1000, 3); + }, + + // Calculates the distance of y relative to y0. It also ensures we do not return + // zero by returning a epsilon value in the same direction as ultimate distance. + _distance: function(y, du) + { + const epsilon = 0.0001; + var d = y - this._y0; + return du < 0 ? Math.min(d, -epsilon) : Math.max(d, epsilon); + }, + + // Decides how much the proportional gain should be increased during the manual + // gain stage. We choose to use the ratio of the ultimate distance to the current + // distance as an indication of how much the system is responsive. We want + // to keep the increment under control so it does not cause the system instability + // So we choose to take the natural logarithm of this ratio. + _gainIncrement: function(t, y, e) + { + var du = this._distanceUltimate(t); + var d = this._distance(y, du); + return Math.log(du / d) * 0.1; + }, + + // Update the stage of the controller based on its current stage and the system output + _updateStage: function(y) + { + var yPosition = this._yPosition(y); + + switch (this._stage) { + case PIDController.stages.WARMING: + if (yPosition == PIDController.yPositions.AFTER_SETPOINT) + this._stage = PIDController.stages.OVERSHOOT; + break; + + case PIDController.stages.OVERSHOOT: + if (yPosition == PIDController.yPositions.BEFORE_SETPOINT) + this._stage = PIDController.stages.UNDERSHOOT; + break; + + case PIDController.stages.UNDERSHOOT: + if (yPosition == PIDController.yPositions.AFTER_SETPOINT) + this._stage = PIDController.stages.SATURATE; + break; + } + }, + + // Manual tuning is used before calculating the PID controller gains. + _tuneP: function(e) + { + // The output is the proportional term only. + return this._Kp * e; + }, + + // PID tuning function. Kp, Ti and Td were already calculated + _tunePID: function(h, y, e) + { + // Proportional term. + var P = this._Kp * e; + + // Integral term is the area under the curve starting from the beginning + // till the current time. + this._I += (this._Kp / this._Ti) * ((e + this._eold) / 2) * h; + + // Derivative term is the slope of the curve at the current time. + var D = (this._Kp * this._Td) * (e - this._eold) / h; + + // The ouput is a PID function. + return P + this._I + D; + }, + + // Apply different strategies for the tuning based on the stage of the controller. + _tune: function(t, h, y, e) + { + switch (this._stage) { + case PIDController.stages.WARMING: + // This is the first stage of the ZieglerâNichols method. It increments + // the proportional gain till the system output passes the set-point value. + if (typeof this._y0 == "undefined") { + // This is the first time a tuning value is required. We want the test + // to add only one item. So we need to return -1 which forces us to + // choose the initial value of Kp to be = -1 / e + this._y0 = y; + this._Kp = -1 / e; + } else { + // Keep incrementing the Kp as long as we have not reached the + // set-point yet + this._Kp += this._gainIncrement(t, y, e); + } + + return this._tuneP(e); + + case PIDController.stages.OVERSHOOT: + // This is the second stage of the ZieglerâNichols method. It measures the + // oscillation period. + if (typeof this._t0 == "undefined") { + // t is the time of the begining of the first overshot + this._t0 = t; + this._Kp /= 2; + } + + return this._tuneP(e); + + case PIDController.stages.UNDERSHOOT: + // This is the end of the ZieglerâNichols method. We need to calculate the + // integral and derivative periods. + if (typeof this._Ti == "undefined") { + // t is the time of the end of the first overshot + var Tu = t - this._t0; + + // Calculate the system parameters from Kp and Tu assuming + // a "some overshoot" control type. See: + // https://en.wikipedia.org/wiki/Ziegler%E2%80%93Nichols_method + this._Ti = Tu / 2; + this._Td = Tu / 3; + this._Kp = 0.33 * this._Kp; + + // Calculate the tracking time. + this._Tt = Math.sqrt(this._Ti * this._Td); + } + + return this._tunePID(h, y, e); + + case PIDController.stages.SATURATE: + return this._tunePID(h, y, e); + } + + return 0; + }, + + // Ensures the system does not fluctuates. + _saturate: function(v, e) + { + var u = v; + + switch (this._stage) { + case PIDController.stages.OVERSHOOT: + case PIDController.stages.UNDERSHOOT: + // Calculate the min-max values of the saturation actuator. + if (typeof this._min == "undefined") + this._min = this._max = this._out; + else { + this._min = Math.min(this._min, this._out); + this._max = Math.max(this._max, this._out); + } + break; + + case PIDController.stages.SATURATE: + const limitPercentage = 0.90; + var min = this._min > 0 ? Math.min(this._min, this._max * limitPercentage) : this._min; + var max = this._max < 0 ? Math.max(this._max, this._min * limitPercentage) : this._max; + var out = this._out + u; + + // Clip the controller output to the min-max values + out = Math.max(Math.min(max, out), min); + u = out - this._out; + + // Apply the back-calculation and tracking + if (u != v) + u += (this._Kp * this._Tt / this._Ti) * e; + break; + } + + this._out += u; + return u; + }, + + // Called from the benchmark to tune its test. It uses Ziegler-Nichols method + // to calculate the controller parameters. It then returns a PID tuning value. + tune: function(t, h, y) + { + this._updateStage(y); + + // Current error. + var e = this._ysp - y; + var v = this._tune(t, h, y, e); + + // Save e for the next call. + this._eold = e; + + // Apply back-calculation and tracking to avoid integrator windup + return this._saturate(v, e); + } +}); + +Utilities.extendObject(PIDController, { + // This enum will be used to tell whether the system output (or the controller input) + // is moving towards the set-point or away from it. + yPositions: { + BEFORE_SETPOINT: 0, + AFTER_SETPOINT: 1 + }, + + // The Ziegler-Nichols method for is used tuning the PID controller. The workflow of + // the tuning is split into four stages. The first two stages determine the values + // of the PID controller gains. During these two stages we return the proportional + // term only. The third stage is used to determine the min-max values of the + // saturation actuator. In the last stage back-calculation and tracking are applied + // to avoid integrator windup. During the last two stages, we return a PID control + // value. + stages: { + WARMING: 0, // Increase the value of the Kp until the system output reaches ysp. + OVERSHOOT: 1, // Measure the oscillation period and the overshoot value + UNDERSHOOT: 2, // Return PID value and measure the undershoot value + SATURATE: 3 // Return PID value and apply back-calculation and tracking. + } +}); |