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To add a little to Petrus' answer, for systems with constituitive nonlinearities, the effects of those nonlinear terms become significant at large amplitudes and in general shift the system resonances to higher frequencies. Therefore, you can get a satisfactory approximation by assuming small amplitudes throughout- and remember, in putting together a dynamic ...

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Simple answer: tune the controller such that it avoids saturation / rate limits at all cost, then use standard stability analysis techniques. Complex answer: Stability techniques like bode and nyquist are more or less a Rule-Of-Thumb method. Actual stability guarantees are based upon the logic that the energy in the system stays finite. The most broadly ...

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Picking up from NMech's answer: For the step response, integration constants can be expressed in terms of $\zeta$ and $\omega_0$ According to swarthmore.edu Where $\omega_0 = \sqrt{\omega_1\omega_2}$ with $(\omega_1,\omega_2)$ being the two characteristic frequencies, and $K$ is the step amplitude After that, I believe $\zeta$ can be extracted from any two ...

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The logarithmic decrement is not applicable to the overdamped systems because there are no oscillations. Also, there is not (at least to my knowledge) an equivalent to the logarithmic decrement approach to calculate the damping ratio $\zeta$ for overdamped systems. Free vibration measurement As AJN proposed what you can do is given the equation that ...

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If I read it correctly (i.e. the plant has a single zero but not pole at the origin), then the issue I think is being solved, is that the plant RHP pole we are trying to manipulate is unpaired. Thus its RL would travel along the real axis. However the zero at the origin, being its destination at infinite gain, effectively blocks this pole's RL from ever ...

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The nyquist plot is nothing more than just a polar representation of the bode plot (assuming we neglect negative frequencies). So if you know how $e^{-Ts}$ affects the bode plot, you can essentially just pick a certain amount of frequencies, get their phase and magnitudes from the bode plot, and compute its corresponding position in the Nyquist plot. Just ...

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Foreword/disclaimer: This is my derivation (as I mentioned I've never seen this procedure written ), so I would appreciate any constructive feedback. I am assuming that the viscous "damping" coefficient for this system produces a torque which is proportional to the angular velocity. $$M(\omega(t) ) = c_t \omega(t) \tag{eq.1}$$ (this is an analogy ...

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It will depend on your application, but I would consider a hall effect sensor with one or more magnets the "default" sensor for rotation speed. The dynamic range is essentially infinite, since a digital timer can record short (uS) intervals all the way up to months fairly easily. The only limitation is that you need to measure for some fraction of ...

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You can use an IIR filter after you have taken the derivative of the encoder signal. the iir filter will smoothen the pulses and will give you a good enough velocity estimate

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Maybe? Without knowing ourselves anything about the system you have, it's mostly impossible for us to be able to answer the question. However, I can say that in general it is certainly possible to consider the inner (stable) control loop to be continuous (namely fast enough) that you could simply consider it part of your system, and run an outer control loop ...

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The controllability matrix of the discrete time system is of full rank. When I calculate the controllability matrix for the discrete time system with Matlab, I get at first glance the same eigenvalues as you. However, the last two are not actually 0, Matlab just cuts off after 4 decimals. The last two eigenvalues are 2.0366e-7 and -3.0627e-5, so the matrix ...

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