I have taken from a data set the values of x and z of activity (e.g. walking, running) detected by an accelerometer. Since the data collected also contains the gravity values, I removed it with the following filter in Matlab:
fc = 0.3;
fs = 50;
x = ...;
y = ...;
z = ...;
[but,att] = butter(6,fc/(fs/2));
gx = filter(but,att,x);
gy = filter(but,att,y);
gz = filter(but,att,z);
new_x = x-gx;
new_y = y-gy;
new_z = z-gz;
A = magnitude(new_x,new_y,new_z);
plot(A)
Then I calculated the magnitude value and plotted the magnitude value on a graph.
However, every graph, even after removing gravity, starts with a magnitude of 1g (9.8 m / s ^ 2), why? Should not it start at 0 since I removed gravity?
You need to wait for the filter value to ramp up. Include some additional data that you don't graph at the beginning of the file for this purpose.
How accurate do your calculations need to be? With walking and running the angle of the accelerometer can change, so the orientation of the gravity vector can change throughout the gait cycle. How much of a change in orientation you can expect to see depends on the sensor location and the particular motion you are trying to capture.
I'm currently studying chemical engineering and for my Bachelor thesis, I'm supposed to model a heated pipe that can be used in a superheater by connecting two pipes via a heatport together. Even though I made a big effort on understanding how I code correctly in Modelica, my code is still not working and I'm getting pretty desperate.
So the model basically has to be applicable for both fluid water and overheated steam, so just one-phase flow in instationary conditions. Heat transfer is supposed to happen convectively. Also, I neglect pressure losses due to friction in this model.
Here´s my idea of how the model is supposed to work:
I'm pretty much trying to build a model like the one in the MSL, "Dynamic Pipe", just way more easier so that students who work on the same topic are able to understand my code quickly. So I splitted the pipe into a number of nodes n, the first volume being a inlet state, so basically that state does not really belong to the pipe. After that, the balance equations apply. I´m not quite sure about the momentum equations, so any help on them is highly appreciated. Convective heat transfer is defined by the Model "Convection" from the MSL, Thermal.HeatTransfer.Components.
When testing the model with a flow source, a boundary with fixed pressure and a fixed temperature at the wall, I also get the error "Failed to reduce the DAE index" and I have absolutely no idea what that means.
Also, here is my code:
model Pipe_base3
//Import
import Modelica.SIunits.*;
import Modelica.Constants.pi;
replaceable package Medium =
Modelica.Media.Interfaces.PartialTwoPhaseMedium annotation (choicesAllMatching = true);
parameter Integer n=2;
parameter Integer np=1;
// Geometry==================================================================//
parameter Diameter d_pipe = 0.05 "Inner diameter of pipe"
annotation (Dialog(tab="Geometry"));
parameter Length L = 1 "Length of unit"
annotation (Dialog(tab="Geometry"));
parameter Area A_hex = pi * d_pipe * L
"Shell surface of pipe for heat exchange" annotation (Dialog(tab="Geometry"));
parameter Area A_q = (pi/4)*d_pipe^2
annotation (Dialog(tab="Geometry"));
//Initialisation=============================================================//
parameter Medium.Temperature T_start = 403.15 annotation (Dialog(tab="Initialization"));
parameter Medium.SpecificEnthalpy h_start = Medium.specificEnthalpy_pT(p_start, T_start) annotation (Dialog(tab="Initialization"));
parameter AbsolutePressure p_start = Medium.saturationPressure(T_start) annotation (Dialog(tab="Initialization"));
parameter Medium.MassFlowRate m_flow_start = 0.5 annotation (Dialog(tab="Initialization"));
//Temperature, pressure, energy==============================================//
Medium.Temperature T[n+1]( each start=T_start, fixed=false);
Medium.SpecificEnthalpy h[n+1]( each start=h_start, fixed=false);
Medium.AbsolutePressure p[n+1](each start=p_start, fixed=false);
HeatFlowRate Q_flow[n](fixed = false);
Energy U[n](min=0);
Energy KE[n]; //Kinetic Energy
Medium.ThermodynamicState state[n+1];
// Nondimensional Variables + HeatTransfer===================================//
Medium.PrandtlNumber Pr[n](fixed=false);
ReynoldsNumber Re[n](fixed=false);
Real Xi[n];
NusseltNumber Nu[n];
CoefficientOfHeatTransfer alpha[n];
// Thermodynamic properties==================================================//
Medium.SpecificInternalEnergy u[n](fixed=false);
Medium.DynamicViscosity eta[n];
Density rho[n+1];
Medium.SpecificHeatCapacity cp[n];
Medium.ThermalConductivity lambda_fluid[n];
//Segmental properties
Mass ms[n]; //Mass per Segment
MassFlowRate m_flow[n+1]( each start=m_flow_start/np, fixed=false);
Velocity w[n+1](fixed=false);
// Momentum
Force F_p[n];
Momentum I[n];
Force Ib_flow[n];
parameter Boolean init = false;
Modelica.Fluid.Interfaces.FluidPort_a fluidin( redeclare package Medium = Medium, m_flow(start = m_flow_start, min = 0), p(start = p_start))
annotation (Placement(transformation(extent={{-90,-100},{-70,-80}}),
iconTransformation(extent={{-90,-100},{-70,-80}})));
Modelica.Fluid.Interfaces.FluidPort_b fluidout( redeclare package Medium = Medium, m_flow(start = -m_flow_start, max = 0), p(start = p_start), h_outflow(start=h_start))
annotation (Placement(transformation(extent={{70,-100},{90,-80}}),
iconTransformation(extent={{70,-100},{90,-80}})));
Modelica.Thermal.HeatTransfer.Interfaces.HeatPort_a[n] heatport
annotation (Placement(transformation(extent={{-10,60},{10,80}}),
iconTransformation(extent={{-10,60},{10,80}})));
Modelica.Blocks.Interfaces.RealOutput[n] alpha_output annotation (Placement(
transformation(extent={{-100,38},{-140,78}}), iconTransformation(extent={{-100,
38},{-140,78}})));
protected
parameter Volume vn = (A_q * L) / n; //Volume per segment
parameter Real x[n] = linspace((L/n), L, n);
parameter Length length = L/n;
initial equation
for i in 1:(n+1) loop
//h[i] = Medium.specificEnthalpy_pTX(p_start, T_start, {1});
p[i] = p_start;
end for;
equation
//Port equations=============================================================//
fluidout.p = p[n];
//fluidin.p-fluidout.p=p[1]-p[n+1];
fluidout.h_outflow = h[n];
fluidout.m_flow = -m_flow[n+1];
//===========================================================================//
h[1]=inStream(fluidin.h_outflow);
p[1]=fluidin.p;
state[1]=Medium.setState_ph(p[1],h[1]);
T[1]=Medium.temperature(state[1]);
rho[1]=Medium.density(state[1]);
m_flow[1]=fluidin.m_flow/np;
m_flow[1]=A_q*rho[1]*w[1];
for i in 1:(n) loop
// Heatport equations======================================================//
T[i] = heatport[i].T;
Q_flow[i] = heatport[i].Q_flow;
// Momentum Balance =======================================================//
der(I[i]) = Ib_flow[i] - F_p[i];
I[i]=m_flow[i]*length;
Ib_flow[i] = (p[i+1]*w[i+1]*w[i+1] - p[i]*w[i]*w[i])*A_q*np;
F_p[i] = (A_q*p[i+1]-A_q*p[i]);
// Energy Balance=========================================================//
U[i] = ms[i] * u[i];
KE[i] = 0.5*ms[i]*w[i+1]*w[i+1];
der(U[i]+KE[i])=m_flow[i]*(h[i]+0.5*w[i]) - m_flow[i+1]*(h[i+1]+0.5*w[i+1]) + Q_flow[i];
der(rho[i+1])= -((rho[i+1]-rho[i])*w[i+1] + (w[i+1]-w[i])*rho[i+1]); //Konti
ms[i]=vn*rho[i+1];
T[i+1]=Medium.temperature(state[i+1]);
state[i+1] = Medium.setState_ph(p[i+1], h[i+1], 1); //Sets thermodynamic state from which other properties can be determined
u[i] = Medium.specificInternalEnergy(state[i+1]);
cp[i] = Medium.specificHeatCapacityCp(state[i+1]);
rho[i+1] = Medium.density(state[i+1]);
eta[i] = Medium.dynamicViscosity(state[i+1]);
lambda_fluid[i] = Medium.thermalConductivity(state[i+1]);
Re[i] * eta[i] = (rho[i+1] * abs(w[i+1]) * d_pipe);
Pr[i] *lambda_fluid[i] = (eta[i] * cp[i]);
Xi[i] = (1.8 * log10(abs(Re[i])+1) - 1.5)^(-2);
Nu[i] = ((Xi[i]/8)*Re[i]*Pr[i])/(1+12.7*sqrt(Xi[i]/8)*((Pr[i])^(2/3)-1))*(1+(1/3)*(d_pipe/x[i])^(2/3));
Nu[i] = Modelica.Fluid.Pipes.BaseClasses.CharacteristicNumbers.NusseltNumber(alpha[i], d_pipe, lambda_fluid[i]);
alpha_output[i] = alpha[i] * (A_hex/n);
m_flow[i+1] = A_q * w[i+1] * rho[i+1];
// der(p[i]) = - w[i]*der(w[i]) * rho[i];
// 0 = m_flow[i-1] - m_flow[i];
// der(rho[i]) = -((rho[i]-rho[i-1])*w[i] + (v[i]-v[i-1])*rho[i]);
//m_flow[i] = A_q * w[i] * rho[i]; //Calculation of flow velocity
//ms[i] = vn * rho[i]; //Mass per segment
//Calculation of thermodynamic properties for each segment=================//
//Heat Transfer============================================================//
end for;
fluidin.h_outflow = h[1]; //
annotation (Icon(coordinateSystem(preserveAspectRatio=false, extent={{-100,-100},
{100,100}}), graphics={Line(
points={{-80,-80},{-80,94},{-80,100},{0,20},{80,100},{80,-80}},
color={0,0,255},
smooth=Smooth.None), Line(
points={{-60,-60},{-60,-48},{-60,0},{60,0},{60,-60},{48,-40},{72,-40},
{60,-60}},
color={0,0,255},
smooth=Smooth.None)}), __Dymola_selections);
end Pipe_base3;
Thank you so much in advance!
I was in the same situation when I started using Modelica: I wanted the features of Modelica.Fluid.Pipes.DynamicPipe but with less complexity (I wanted the code to be more readable and less hierarchical). So, like you, I started building my own pipe model from scratch. However, because I wanted to be able to replace the pressure drop and heat transfer correlations and have great flexibility I ended up with a model of nearly the same complexity as Modelica.Fluid.Pipes.DynamicPipe.
My recommendation to you is to
build your own simple dynamic pipe model without any complex
features. This will only be usable for educational purposes (e.g.
letting other students understand your coding principles)
learn how to use Modelica.Fluid.Pipes.DynamicPipe for problems where you need vary model complexity (number of segment, replaceable pressure drop and heat transfer methods etc.). Modelica.Fluid.Examples.HeatExchanger is an example of how you can use Modelica.Fluid.Pipes.DynamicPipe to model a heat exchanger like the one you request.
Here I've shared an example of a very simple dynamic pipe that can be used as a heat exchanger. The pipe is made from n pipe segments and takes advantage of the fact that you can instantiate an array of components and connect the elements in a for loop.
As for the momentum balance, the correct/complete way is to account for the change in momentum by summing all the forces acting on each control volume (Newton's Second law). However, in most lumped models a steady-state momentum balance is adequate which reduces the equation to a linear or quadratic relation between mass flow rate and pressure drop. Modelica.Fluid.Pipes.DynamicPipe has a number of different presssure/flow correlations to choose from.
Best regards,
Rene Just Nielsen
I have built a small example/test that uses your model. It should be a very simple application of your model. Unfortunately I get the same error message:
Cannot find differentiation function:
Modelica.Media.Water.IF97_Utilities.waterBaseProp_ph(boundary1.p, pipe_base3_1.h[2], 0, 1)
with respect to time
Index reduction basically means that the model contains equations that have no unknown. This is solved by differentiation of these equations with respect to time (which can happen multiple times). For more information you can check
https://www.inf.ethz.ch/personal/cellier/Lect/NSDS/Ppt/nsds_ppt_engl.html
especially lecture 16 and probably the ones before it :)
Therefore the Modelica tool will have to know how to do this differentiation. For equations this is usually done automatically, but for functions it has to be specified by the developer. It seems this is not done for Modelica.Media.Water.IF97_Utilities.waterBaseProp_ph()
which is why you get the error message.
There are basically two possibilities to solve this problem:
You change your model to get rid of or revise the constraint equation (the one which has no unknown). It should be the one shown in the error message: der(pipe_base3_1.rho[2]) = ...
You add the function for differentiation to the medium (I'm not much into the Fluid/Media so I have no idea how complicated that is, so I would try to go with 1. first). How this can be done is shown in https://modelica.org/documents/ModelicaSpec33Revision1.pdf section 12.7
Here is the code of the example:
model PipeTest
Pipe_base3 pipe_base3_1(redeclare package Medium = Modelica.Media.Water.WaterIF97_R1pT)
annotation (Placement(transformation(extent={{-10,-10},{10,10}})));
Modelica.Fluid.Sources.FixedBoundary boundary(
nPorts=1,
p=100000,
redeclare package Medium = Modelica.Media.Water.WaterIF97_R1pT)
annotation (Placement(transformation(extent={{-60,-40},{-40,-20}})));
Modelica.Fluid.Sources.FixedBoundary boundary1(
nPorts=1,
p=100000,
redeclare package Medium = Modelica.Media.Water.WaterIF97_R1pT)
annotation (Placement(transformation(extent={{60,-40},{40,-20}})));
Modelica.Thermal.HeatTransfer.Sources.FixedHeatFlow fixedHeatFlow[2](Q_flow={0,0})
annotation (Placement(transformation(extent={{-40,20},{-20,40}})));
equation
connect(boundary.ports[1], pipe_base3_1.fluidin) annotation (Line(points={{-40,-30},{-8,-30},{-8,-9}}, color={0,127,255}));
connect(boundary1.ports[1], pipe_base3_1.fluidout) annotation (Line(points={{40,-30},{8,-30},{8,-9}}, color={0,127,255}));
connect(fixedHeatFlow.port, pipe_base3_1.heatport) annotation (Line(points={{-20,30},{0,30},{0,7}}, color={191,0,0}));
annotation (
Icon(coordinateSystem(preserveAspectRatio=false)),
Diagram(coordinateSystem(preserveAspectRatio=false)),
uses(Modelica(version="3.2.2")));
end PipeTest;
Hope this helps...
I have a problem with the quadrature encoder mode on timer TIM3 of my
STM32F446RE /
NUCLEO-F446RE:
TIM3 counts on every rising edge on the first signal.
The CNT register counts up and I read the value with 1 Hz and then
I set the register to 0.
When I look on the
oscilloscope
the frequency is half as high as the value from the
CNT register output (1hz).
Why?
TIM3 counts on both edges on the first signal.
The
CNT register output (1 Hz)
is completely wrong.
My configuration is:
GPIO_InitTypeDef sInitEncoderPin1;
sInitEncoderPin1.Pin = pin1Encoder.pin; // A GPIO_PIN_6
sInitEncoderPin1.Mode = GPIO_MODE_AF_PP;
sInitEncoderPin1.Pull = GPIO_PULLUP;
sInitEncoderPin1.Speed = GPIO_SPEED_HIGH;
sInitEncoderPin1.Alternate = altFunctionEncoder; // GPIO_AF2_TIM3
GPIO_InitTypeDef sInitEncoderPin2;
sInitEncoderPin2.Pin = pin2Encoder.pin; // A GPIO_PIN_7
sInitEncoderPin2.Mode = GPIO_MODE_AF_PP;
sInitEncoderPin2.Pull = GPIO_PULLUP;
sInitEncoderPin2.Speed = GPIO_SPEED_HIGH;
sInitEncoderPin2.Alternate = altFunctionEncoder; // GPIO_AF2_TIM3
HAL_GPIO_Init(GPIOA, &sInitEncoderPin1);
HAL_GPIO_Init(GPIOA, &sInitEncoderPin2);
encoderTimer.Init.Period = 0xffff;
encoderTimer.Init.Prescaler = 0;
encoderTimer.Init.CounterMode = TIM_COUNTERMODE_UP;
encoderTimer.Init.ClockDivision = TIM_CLOCKDIVISION_DIV1;
encoderTimer.Init.RepetitionCounter = 0;
HAL_NVIC_SetPriorityGrouping(NVIC_PRIORITYGROUP_4);
HAL_NVIC_SetPriority(SysTick_IRQn, 0, 1);
encoder.EncoderMode = TIM_ENCODERMODE_TI1;
encoder.IC1Filter = 0x0f;
encoder.IC1Polarity = TIM_INPUTCHANNELPOLARITY_RISING; // TIM_INPUTCHANNELPOLARITY_BOTHEDGE
encoder.IC1Prescaler = TIM_ICPSC_DIV1;
encoder.IC1Selection = TIM_ICSELECTION_DIRECTTI;
encoder.IC2Filter = 0x0f;
encoder.IC2Polarity = TIM_INPUTCHANNELPOLARITY_RISING;
encoder.IC2Prescaler = TIM_ICPSC_DIV1;
encoder.IC2Selection = TIM_ICSELECTION_DIRECTTI;
HAL_TIM_Encoder_Init(&encoderTimer, &encoder);
HAL_TIM_Encoder_Start_IT(&encoderTimer, TIM_CHANNEL_ALL);
The
oscilloscope screenshot
shows a frequency of about 416 Hz.
The values shown in the
first shell output
are (very roughly!) twice as high (as the question points out already).
This appears (nearly...) correct to me since the shown configuration
encoder.EncoderMode = TIM_ENCODERMODE_TI1;
selects the "X2 resolution encoder mode", which counts 2 CNT increments per signal period.
In an application note on
timer overview,
(Sec. 4.3.4 / Fig. 7) there is an illustrative diagram how the encoder mode works in detail.
The
second screenshot
results from an incorrect TIM3 configuration:
The encoder mode (TIM_ENCODERMODE_TI1) assumes that both channels trigger only upon directed flanks in an alternating way (see the AN link above).
If one of the two channels triggers twice as many events due to
configuration
encoder.IC1Polarity = TIM_INPUTCHANNELPOLARITY_BOTHEDGE,
the counter will only count up one position and then "recognize" a "reversal" event (= change of direction).
Keeping in mind that
65535u = 0xFFFF = -1
the second screenshot only shows values -1, 0, +1 - which fits perfectly with this explanation.
The question remains why the first screenshot shows (reproducible) measurements between 800 and 822.
I assume that
the physical source of the encoder signal runs at a constant pace
the 1 Hz timer that triggered shell output is independent from TIM3, and
it has been started before the encoder timer
(i.e., above the shown code sample).
This may explain why the first two values look like nonsense (0: TIM3 has not been started yet. 545: TIM3 has been started during the shell output timer period).
Discarding the first two measurement samples, the average and standard deviation, resp., of the measured signal frequency are
808,9091 +/- 0,5950 [X2 increments per second]
404,4545 +/- 0,2975 [Hz]
which corresponds to a period of
2,4331 +/- 0,003 [ms].
Hence, the measured frequency is too low by about 11 Hz, i.e., measured period too high by nearly 30 µs, and this error is clearly beyond the statistical noise.
The question gives a hint where this error might come from:
The CNT register counts up and I read the value with 1 Hz and then I set the register to 0.
Whenever the 1 Hz "polling timer" expires, it triggers an interrupt
(or a logical event in polling software).
Processing of this interrupt/event may be delayed a little,
depending on other software (IRQ: deactivation times elsewhere in the software,
Polling: loop duration until event is polled).
Software reads CNT value.
Software resets CNT value to zero,
discarding further increments since the CNT value has been read.
TIM3 continues counting (from zero).
This hints that software needs 30 µs between (3.) and (4.), which would be quite a lot of time on an STM32F4.
Edit: I just re-checked the oscilloscope screenshot. The error is visible, but I believe it is smaller than I originally assumed (from counting flanks in the picture).
I'm trying to present a 4Hz flickering stimuli in PsychToolbox for 5 seconds followed by a 500Hz tone. Does anyone have an idea of how to do this? I've been using the vbl or screen refresh rate to calculate the flicker frequency but I'm not sure if I'm on the right track at all. I also have no idea how to present an auditory stimuli in PTB (I tried the sound function already). Any help is greatly appreciated!
I'm not sure about sound presentation in PTB (I've never done it), but you seem to be on the right track for the flicker frequency.
The way I do it is to determine the screen refresh rate, divide the total length of time you want the stimulus presented by this refresh rate (this will give you the number of frames that will be drawn during this time), and then have a frame counter that increases by 1 after every flip. You can then use this frame counter to switch commands on or off.
A minimal example (randomly changes the background colour at 4Hz for 5 seconds):
[w, wRect]=Screen('OpenWindow', 0);
MaxTime = 5; %Set maximum time for all stimuli to be presented in seconds
Hz = 4; %Set Hz for stimulus flicker
Screen('Flip',w);
Frametime=Screen('GetFlipInterval',w); %Find refresh rate in seconds
FramesPerFull = round(5/Frametime); % Number of frames for all stimuli
FramesPerStim = round((1/Hz)/Frametime); %Number of frames for each stimulus
StartT = GetSecs; %Measure start time of session
Framecounter = 0; %Frame counter begins at 0
while 1
if Framecounter==FramesPerFull
break; %End session
end
if ~mod(Framecounter,FramesPerStim)
randomcolour = rand(1, 3)*255; %Change background stimulus colour
end
Screen('FillRect', w, randomcolour, wRect);
Screen('Flip',w);
Framecounter = Framecounter + 1; %Increase frame counter
end
EndT = GetSecs; %Measure end time of session
Screen('CloseAll');
EndT - StartT %Shows full length of time all stimuli were presented
The timing precision will depend on your particular refresh rate.
Hope this helps!