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  1. Z

    Flow rate of a syringe

    Given ##\dot{V}_{\mathrm{b}} = \frac{\pi}{4}d_{\mathrm{b}}^2\dot{x}## Then ##\dot{x}_{\mathrm{n}} = \frac{4\dot{V}_{\mathrm{b}}}{\pi d_{\mathrm{n}}^2}## where subscript ##n## stands for needle. Asking just to make it sure. Thanks for the help, this is quite straightforward compared to...
  2. Z

    Flow rate of a syringe

    So, what you are suggesting is considering the height of the liquid in the barrel and the radius of the plunger along with the length of the needle with its radius. I am ignoring the hub, since its the intermediate part. Volumebarrel = Volumeneedle + Volumeoutput rbarrel2 * dhbarrel/dt =...
  3. Z

    Flow rate of a syringe

    I am trying to come up with a mathematical model so that, when the displacement of the plunger of a syringe is know, I can calculate the amount of a specific liquid in the barrel. Or the relationship between the speed of the plunger and flow rate at the tip of the needle (Again assuming that the...
  4. Z

    Adaptive PID controller implementation

    All the files related to simulation were already attached my first post but anyways here's the screenshot of the model Here's the function that runs inside the interpreted matlab function block And those are the initializations;
  5. Z

    Adaptive PID controller implementation

    Hello, What I mean is, given reference signal is not tracked as expected. Here is the reference signal. Just a square wave. And the output of the plant as the response (I just limited it to 1 second, it goes with the same fashion up to 10 seconds) So the tracking is way out of the...
  6. Z

    Adaptive PID controller implementation

    Hello, I am trying to implement a simple adaptive PID controller paper. However, I am having some problems which I could not find out due to what.. Paper is the following; http://www.aedie.org/9CHLIE-paper-send/337_CHAINHO.pdf Quite simple. Using the Tagaki-Sugeno fuzzy system, in accordance...
  7. Z

    Inverted pendulum system order

    I am considering a simple inverted pendulum system given in the following page; http://ctms.engin.umich.edu/CTMS/index.php?example=InvertedPendulum&section=SystemModeling System has two degree of freedom but the control input can be only applied as force to the chart. I am not sure about the...
  8. Z

    Difference equation solution

    Actually that's the point confusing me. u(k+2) is there in the equation. However, When I start plugging values for k, starting from 0, I will always get 1. So, I would treat u(k+2) as step function and take its inverse z transform as z/(z-1)
  9. Z

    Difference equation solution

    If u is equal to 1 for every k values, it is a step function and then z/(z-1) should be the z-transform. Am I correct ?
  10. Z

    Difference equation solution

    Yes, it is. My mistake sorry. I think it should be z2 [z/(z-1)] but I'm not sure
  11. Z

    Difference equation solution

    Homework Statement Given the following difference equation; x(k+2)-x(k+1)+0.25x(k)=u(k+2) where x(0)=1; x(1)=2; u(k)= 1 for k=1,2,3,… Homework Equations Z- transformation The Attempt at a Solution To be able to solve this difference equation, I think I need to transform it into z domain...
  12. Z

    Lead compensator for double integrator

    Thank you so much. I was sure that I was missing something.
  13. Z

    Lead compensator for double integrator

    I'm trying to design a lead compensator for a double integrator plant, which is plant = tf([1],[1 0 0]) I started with the angle condition. So, poles contribute (+) angle and zeros contribute (-) angle and that sums to 180 Desired pole location is 4.4 +- 4.4j So, 45 + 45 = 90 degrees comes...
  14. Z

    Linear Quadratic Regulator

    I have pantograph simulation on simulink. The dynamic model of the system is given as a C code. So the input is torque and output is motor angles and velocities. I need to build a QLR controller and to do so I need to come up with state space model of the system, right ? I have the following...
  15. Z

    Solution for two unknowns with two equations

    lb*cos(qb) - lc*cos(qc) = ld*cos(qd) - la*cos(qa) lb*sin(qb) - lc*sin(qc) = ld*sin(qd) - la*sin(qa) Those are the equations I have. I know all the parameters but qb and qc. How can I solve for qb and qc ?
  16. Z

    Computed Torque Control vs. PID

    Thank you for your answer. So, let me tell what I got from your answer; Since I use the joint angle as output and torque as input, which are not the same parameter, I get a slow response. Is this correct ? If so, you suggested a torque observer so that I can compare the torque input with torque...
  17. Z

    Computed Torque Control vs. PID

    I'm working on a pantograph device, which is not a linear plant, and implemented 2 different control schemes. First one is computed torque; For this control technique, I modeled nonlinear terms in the equation of motion and canceled them by injecting their model within the control input, which...
  18. Z

    Transfer function of the state space model

    x_head' = (A-LC)x_head + Bu + Ly Where x_head is the estimated state array
  19. Z

    Motion level forward kinematics on Simulink

    I have built a Forward kinematic block with s-function on simulink. This FK is for a pantograph. Input is two angles of the motors and output is the position and 4 angles, which are the inputed motor angles along with angles of two elbows. Now, I need a motion level FK which will output the...
  20. Z

    Transfer function of the state space model

    I have a state space model along with an observer and state feedback. I need to find the transfer function connecting the r (reference) to the y (output) I have this model on simulink. I know the A,B,C,D matrices. So, I can get the TF for the stateSpace with ss2tf function of matlab...
  21. Z

    Kinematics of pantograph device

    I need to obtain the forward and inverse kinematics of a pantograph device. It is easy when only the one side of the pantograph is considered; So, it becomes a 2DOF planar elbow mechanism, which is easy to solve. However, there is symmetry on pantograph, so I kinda need to combine two planar...
  22. Z

    State space representation

    Perfect ! Thanks a lot
  23. Z

    State space representation

    JL*QL'' + BL*QL' + k(QL - Qm) = 0 Jm*Qm'' + Bm*Qm' - k(QL - Qm) = u This is the equation set I have for a motor with a load. QL'' means second derivative and QL' means first derivative. I need to be able to obtain the state space representation of this model where X = [QL;QL';Qm;Qm'] (This is...
  24. Z

    Full State Feedback question

    How do you do exactly ? You only have the input and output. So, how can you plot the bode ? And then how do you deduce the poles and zeros from bode plot ?
  25. Z

    Inertia with gearhead

    I have a motor with rotor inertia of 140gcm2 with 71:1 gearhead. Considering this configuration what would my inertia be at the output ? 140*(1/71)2 ??
  26. Z

    Full State Feedback question

    Yes I built the observer intentionally. It's clear that the pre-scaling works as I wished. But I just want to inspect the dynamics of the observer as well. So, that's why I am looking for close loop transformation.
  27. Z

    Full State Feedback question

    Ok, I got it. I designed an observer over my model which is simply; x'_head = Ax_head + Bu + L(y-Cx_head) and used the x_head from the observer's output to multiply with K gain and feed back to the system with negative sign. It worked perfectly, but now I want to inspect the poles and zeros...
  28. Z

    Full State Feedback question

    Oh I see, then this is the trade-off between steady state error and being able to put the poles anywhere you wish as long as the plant is controllable
  29. Z

    Full State Feedback question

    But if I am controlling the system, it should track the reference with the desired criteria. So, what else can I change in the system to get it track the reference ?
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