Recent content by vicjun

Do you mean what I did previously, i.e. integrating the quaternion derivatives? In this case I am constrained to quaternions as a final result (interpolation polynomials), starting from Euler angles and Euler angle rates. I know about Rodrigues parameters, though I've never used them in...

Thanks for the reply, I should have been clearer about the context. I found a method to numerically integrate quaternions, in a book. It basically involves integrating the kinematic equation \dot{Q}=\frac{1}{2} Q \, \Omega where \Omega is the pure quaternion representation of the angular...

I need to revive this thread, yet again, for another related question. Sorry. At least I won't have to re-explain the problem and all the parameters. Thanks for the help with the quaternion derivatives, I understand them much better now. I now wish to integrate the angular velocity...

I hesitated between posting this in the Mathematics forum or here, but since it's fairly applied, I chose this place. Sorry if it should've gone somewhere else. I posted another thread earlier (https://www.physicsforums.com/showthread.php?t=599737), about having trouble finding the quaternion...

I understand the difference now. I agree, it is probably about finding out which frame the angular velocities are expressed in. But if I manage to calculate the quaternion derivative from one frame to another, as I did, i.e \dot{\mathcal Q}_{I \to O} as well as \dot{\mathcal Q}_{O \to B}...

OK, so I got an idea on how to test the handedness of the quaternions. First, a correction. The quaternion describing the orientation of the Body-fixed frame relative the Inertial frame is given by the quaternion multiplication \mathcal Q_{I \to B} = \mathcal Q_{I \to O} \cdot \mathcal...

I calculated the quaternion product \dot{Q}=\frac{1}{2} Q \cdot \Omega where I assumed that \Omega is a pure imaginary quaternion, so that \Omega = \begin{bmatrix} 0 \\ \omega_1 \\ \omega_2 \\ \omega_3 \\ \end{bmatrix} This does indeed give the matrix you...

I've tested the interpolation methods in two different ways, and they're unlikely to be the source of error. It's obvious the \dot{q_1}, \dot{q_2} and \dot{q_3} components are wrong. If I look at how the quaternion changes with time by printing out the component values at every point, they do...

You're absolutely right, sorry. I understand the proof through the dot product, I had forgotten the quaternions were unitary. It seems my derivatives are correct at least in direction, as I get inner products which are either 0, or in the order of 10-19 and 10-20, which can be considered...

I have been trying to find evidence of this relationship in literature. Why should the inner product of the quaternion and its derivative be zero? In other words, why is the derivative normal to the quaternion? I do understand how this leads to the relationship though, since it is just the...

I don't mean to gravedig, sorry, but I have another question about quaternion derivatives that does not deserve its own thread, and it is within the topic of the discussion. I have now figured out how to calculate the quaternion derivatives from the quaternions and the angular velocities...

I thought I would find my PID controller by identifying step response, using a Silab Xcos diagram (similar to Matlab's Simulink), and play around with the PID parameters until I get a good result. I've included the feed-forward part and set the disturbance as a step function that goes from 0...

OK thanks, I think I've figured out how to calculate the transfer functions from the heater to the oven. I still don't understand how to find the transfer function from the disturbance to the oven, however. Is it just 1, or is there a more complex relationship, involving \alpha? As for...

Thanks, I'll look into it later. The problem requires me to, as you wrote, produce a block system diagram and calculate all the transfer functions in it. But I'm not sure I need to introduce new variables such as TR or the heat output, especially if I don't know their value (I am already...

Homework Statement I am supposed to design a control system with feedback and disturbance feed-forward, with all relevant transfer functions. The system consists of an oven where the temperature T is controlled by an electric heater that dissipates power P_{in}. The temperature outside...