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Without P, the controller just doesn't reliably do what a control system is supposed to do: drive the error to 0. …

$H_2$ minimizes error function 2-norm while $H_{\infty}$ minimizes maximum error Very complicated The somewhat longer answer: $H_2$ and $H_{\infty}$ control are both advanced robust-control strategies … For such systems, these controllers have the advantages of: (sub)optimal control robust1 performance and stability guarantees A more complete description of $H_{\infty}$is here. …

That only works when the desire roll angle is 0. What happens if you are trying to turn and have a desired roll angle of 1deg? Even changing your sum to match the angle error, $w_1 (\theta - \theta_d) …

For a rough calculation of natural frequency, you could create an bode plot. Starting at low frequencies, command a sin wave and measure the amplitude of the output motion (which will be a phase-shi …

In short, adaptive control and robust control (Hinf) are the difficult combination of computationally expensive and complicated to understand. … There are applications though; for example robust control is common harddrive servos. …

If everything were ideal, then your thinking is correct. In practice, though, there are many accumulated errors both in the sensors and in the real vs modelled Jacobian. So if what you care about most …

At each timestep you would separately compute the control action using the $K_j$ computed for each of these linearization points and then interpolate between those values based on the current $\theta$. …

If I remember correctly, LQR minimizes the total energy, which usually means a large initial correction followed by a slop back to zero for the control signal (as opposed to lots of oscillation). … There are other techniques that can focus on the maximum peak instead of total energy (e.g. generic optimal control or $\mathcal{H}_2$ robust-control techniques, which Matlab has commands for) but they …

2 comments ... First, as many people said in answer to your other question, you need to understand that your transfer function is not the real transfer function of the motor. Real motors have nonline …

Pole/zero cancellation is discouraged primarily because in practice it is almost impossible to do perfectly. Real systems have variation and uncertainty so you can't know for sure where the poles/zero …

The most straightforward approach is to use a Kalman filter with a memory of recent state history. While waiting for measurements you do the standard time update. When a new measurement arrives, you r …

I've implemented this algorithm before but I found a different paper easier to read. Try find the paper by Hamel and Mahoney (with Hamel listed as the first author). From that paper, which I don't h …

The point of a complementary filter is combine the low-pass parts of some measurements (e.g. accelerometer) with the high-pass parts of other measurements (e.g. gyro). If the accelerometer perfectly r …

I'm a little confused, are you trying to control each wheel's exact position or the overall position of the robot. … For the former, a cascaded structure makes sense where the robot position control loop defines desired velocities for each motor. …

Quite often in vehicle control this is actually the biggest challenge. …