Questions to solve belongs control and instrumentation - Coursework Example

. The characteristic equation will be  The critical gain of the system indicates the stability of a closed loop system developed by applying unit feedback to (Klee & Allen, 2011). The gain margin represents the increase or decrease needed to make the loop gain where the frequency is -180 degrees. Discreet time systems are characterized by difference equations. Examples of these are economic systems where the system behavior is recognized at discrete points of periods (Liu & Wang, 2012). Conversely in the system, some of the signals are continuous while others are discreet.

Some discreet time signal arises from the continuous signals via sampling. Digital computers accept signals on discreet points of period so that samplers transforms continuous time signal into discreet time signal. i) The derivative control increases the damping of the system. The derivative term also increases the present noise which can easily cause instability. Assuming the functions of closed transfer are outlined as shown, The integral affects the gain of low frequency and alters the frequency where proportional factor becomes more effective.

It would be best to raise KI, but when it gets higher a more negative stage is introduces in the range at a place where the servo bandwidth results. This lowers the phase margin of servo, causing ringing and overshoots. As shown below Ziegler Nichols and Modified Ziegler Nichols are tuning methods for PID. Ziegler Nichols uses the procedures of selecting proportional controls alone, increases the proportional gain until instability is attained. In addition, it measures the oscillation period to come up with critical time constant.

For certain control loops the oscillation measure, offered by ¼ decay ratios and their large overshoots for point alterations are not desired therefore, the modified Z-N is used (Olsson, 2002). The Z-N method does not give the final solution when compared to the