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  1. 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...
  2. 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...
  3. 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...
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    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...
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    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...
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    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...
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    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 ?
  8. 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...
  9. 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...
  10. 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...
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    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...
  12. 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...
  13. 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 ??
  14. Z

    Full State Feedback question

    Below wikipedia page summarizes the full state feedback. Everything is clear but to be able to implement this controller I need to know my states. But What I know is just the A, B and C matrices. So, to be able to simulate this technique on simulink I need to observe the state, I think. Is this...
  15. Z

    Open loop vs Closed loop Transfer Functions

    Okay, I have a simple plant which is 1/s*(s+1) Two poles on 0 and -1 and no zeros. This is the case for open loop. But when I close the loop with unity feedback and add a K gain, I end up with following transfer function; K/s^2 + s + K So, clearly the poles are now at somewhere else. However...
  16. Z

    Simple dynamics equation

    Didn't get this equation which is written for the pendulum part of the cart. Must be easy but couldn't get it.
  17. Z

    2nd order characteristic equation standart form

    A second order system has the following standart form; http://controls-design.com/mathtex/mathtex.cgi?H%28s%29%3DK%5Cfrac%7B%5Comega_n%5E2%7D%7Bs%5E2%2B2%5Czeta%5Comega_n%20s%2B%5Comega_n%5E2%7D%20%5Cmbox%7B%20for%20%7D%200%20%5Cle%20%5Czeta%20%5Cle%201 [Broken] However, sometimes the...
  18. Z

    Standard Form for second order systems.

    Suppose there's a system with given uncertain parameters. And I would like to obtain certain Rise time, max. over shoot, settling time by adjusting those parameters. Let's say this is the second order system; T(s) = (ks + c) / (s2 + as + b) First of all; for a second order system there...
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    Final Value Theorem

    http://fourier.eng.hmc.edu/e102/lectures/Laplace_Transform/node17.html On that page about final value theorem, it says that; However at the bottom of the page, in order to find the DC gain, it uses Final value theorem. Ok, well, let's assume somehow he put "0" where he saw "s". How...
  20. Z

    Damping ratio and Maximum overshoot relation

    There is a certain equation relating both Mp (max. overshoot) and damping ration. Which is; Mp = e(-ζ*pi)/(1-ζ2)1/2 What I get from that equation is for every system a certain damping ratio will result the system in a certain amount of max. overshoot. That sounds ridiculous, because...
  21. Z

    DC gain of a transfer funct.

    What steps I have to follow to find the DC gain of the second order system with a transfer function ? Putting "0" where I see "s" or taking the limit as "s" goes to infinite ?
  22. Z

    Engineering Capacitor charge time on DC RLC circuit

    Homework Statement Inductor, resistor and a capacitor is connected to a DC source in series. DC source is 220 V Capacitance is 10F Inductance 5H Resistor 22 ohm Vc(0) = 50V Question is asking for the charge time of the capacitor, when it gets charged fully and then it starts to act...
  23. Z

    What is Power Electronics

    I'm an mechatronics engineer student. My university offers Power Electronics course. However, it's not compulsory. As a student not very interested in capacitor, diode, inductor and complex things like that in a circuit design, I'm kinda on the fence about taking that course. I'm kinda much...
  24. Z

    A problem with solution

    Have an equation; d2y(t)/dt2 + 5d2y(t)/dt2 + 4y(t) = 2e-2t Solved the complementary(homogenous) part and the function and got the roots of -1 and -4 so the yh(t) is A1.e-4t + A2.e-t Forcing function is 2.e-2t so yparticular(t) is A.e-2t Am I right here ? Or am I supposed to use...
  25. Z

    4th order DE

    I have a 4th order differential equation with given -2 +3i root. Now need to find the homogenous solution. Well, if the root was real, it would be easier but now I'm stuck and don't know how to proceed. What am I supposed to do to solve this ? Equation is : d4y(t)/dt4 +6d3y(t)/dt3 +...
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