![]() ![]() ![]() Incidentally, the distance from the real axis to the pole, the distance along the imaginary axis, is equal to Wd, the damped angular frequency which is the frequency that the closed loop system will oscillate at in response to a step input before settling down to its steady state value. Hence we can see how the the position of the poles are determined by the values of zeta and Wn. This tracing of the movement of the poles of a closed loop system in response to the increase of some system parameter, such as open loop gain, from 0 to infinity is the basis of the Root Locus technique.Īs K is increased and the poles move away from each other parallel to the S-plane's imaginary axis we can say that the distance from the origin to the pole is equal to Wn the undamped natural angular frequency and the cosine of the angle which that line makes with the real axis is equal to zeta, the damping ratio and so we can see that, as K increases, the poles move further from the real axis causing a reduction in damping ratio (angle gets closer to 90 degrees so cosine of the angle and hence zeta reduces) and the distance from the origin increases, increasing Wn. Oscillatory does not mean unstable, it means that, in response to a step input, the closed loop system will oscillate a bit before the output settles down to a steady state value. The two poles now have an imaginary component, they have become complex conjugate poles and the system is now oscillatory with some overshoot in response to a step input in the time domain. If the open loop gain is increased further, zeta will become less than one (underdamping), and the two poles will diverge away from each other moving away from each other at right angles to the real axis and parallel to the imaginary axis. At this value of K, the poles have the same value. As the open loop gain,K is increased the poles will move towards each other (converge) until they meet, still on the real axis. The two poles on the S-plane will be real and spaced apart on the real axis. So ultimately, the behavior of the closed loop system depends solely on the values of zeta and Wn in the closed loop transfer function.Ĭonsidering a closed loop system with a low value of open loop gain,K such that the value of zeta is greater than one (over damping). That is true and it is true because changing the value of K in the open loop transfer function alters the values of zeta and Wn in the closed loop transfer function. Well, you might say, I've already said that closed loop system behavior changes with the value of K, the open loop gain. These two variables determine the position of the poles on the S-plane and so you can also say that the behavior of a 2nd order system is determined by the position of the poles on the S-plane. The behavior of a closed loop system with just 2 poles (2nd order system) is totally determined by the combination of the values of zeta, the damping ratio and Wn, the undamped natural angular frequency. Interestingly, increasing k reduces the damping ratio, zeta but increases the undamped natural frequency,Wn and so changing k has no effect on settling time. So, increasing k moves the system closer to the point of instability and so phase margin and gain margin are reduced. Increasing k increases percentage overshoot and reduces rise time (faster response). Increasing k moves the closed loop system closer to the point of instability. ![]() With regard to a simple 2nd order transfer function with 2 poles. I don't know what woofer I'll use, so I'll use a sheet of plywood for now to get baseline idea of how this stacks up and possibly try them in a random cab I have lying around.It may become more understandable if you relate it to the open loop gain, k. Next I'll make a test baffle and measure these on the weekend. I'll keep these wrapped in plastic until they're ready to install. I image this is a good design for the sake of cooling and breathing (low wind noise) but I'm worried any debris will get in the gap and rub. If you look close in this next photo, you can see the voice coil barely sticking out of the gap. Cast frame is nice and the way the surround comes up onto the frame is attractive, but the cone luster and dark black doesn't match the matte grey-black of the frame. Neo mag is small compared to the ferrite I'm use to seeing, and the frame is quite open. Just got these in and I haven't seen much info on them, so figured I'd share my experience. ![]()
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