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Depending on the plant, a reduction in phase margin could happen. Here is a theoretical example. Consider a plant with a double integrator and an additional pole: $$\frac{K_1}{s^2(1+s/\omega_P)}$$ Now let's have a PD controller, which could be written either $[K_P(1+{K_D}s)]$ , or as $[K_P + {K_D}s]$ . For convenience, both of these could be re-written in ...


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Perhaps this is an X/Y problem. But here are some suggestions. 1 Design an over damped PID closed loop system. An over damped system will have poorer rise time. Assumptions required for this to work are The target pressure is a constant; i.e. the command to the system is a step input. The PID (particularly the D) can be designed to result in a stable over ...


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If the flexibility and mass of the cables are small compared to the masses, the early stage could be just winding the cables around the hub. Basically, we need to calculate the equation of a system of 4 whips lashing. The mass per unit length and bending moment stiffness in relation to the 4 end masses will plug into a differential equation with a large ...


1

SMALL SIGNAL Let's assume a typical loop. Controller and plant in forward path, unity feedback. Let's add a pre-filter. Let C = controller transfer function; P = plant transfer function; F = input filter transfer function (side note: it's possible to put part of the controller in the reverse path. Those configurations could be rearranged to small-signal-...


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