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Euler method is horrible for general ODE timestepping because it is globally only first order accurate. This means that to decrease the error by a factor of 1/2, you'll need to decrease the timestep …

I argue that because feedforward control still uses sensor values to produce a control signal, it is still reactive to the conditions that the system finds itself in. … So, how can feedforward control possibly be any different from feedback if both are forms of reactive control? What really separates the two from each other? …

To understand this interpretation, you have to remember that the system that we want to control is really one of two things: either a differential equation or a difference equation. …

When setting up an optimal control problem using a linear quadratic regulator, one often chooses semi-definite matrices Q and R such that the objective function J has the form $$J=\int_{t_0}^{t_f}(x … In practice, I can’t think of a situation where a non-diagonal semi definite matrix would be better than a diagonal one for an LQR control problem. …

Assuming no filter is used to measure error (or rate of change in error) with respect to a desired state, would a PI controller more/less/about equally robust to signal input noise compared to a PD co …

The equations of motion for a cart-pole (inverted pendulum) system are given as $$(I+ml^2)\ddot{\theta}+mglsin(\theta)+ml\ddot{x}cos(\theta)=0$$ $$(M+m)\ddot{x}+ml\ddot{\theta}cos(\theta)-ml\dot …

As far as i can tell, both LQR and PID controllers can both be applied to the cart-pole (inverted pendulum) problem. What are the pros/cons to using one controller over the other for this particular …

Now that I've done this, I want to take the next step and turn my PID control commands into electrical commands onto a DC motor to give the desired linear acceleration $\ddot{x}$. … $\ddot{x}(t)$, and chose this control command as $\ddot{x}(t)=K_1\theta(t) + K_2\int_0^t\theta(t) dt + K_3\dot{\theta}$, where $K_i$ are the PID gains. …

You need both: gyroscopes react quickly to fast changes in orientation, but lose accuracy in the long run. Accelerometers are better in the long run, but are too sensitive to short term. Combining …