Div>So lustrous, if you recollect, the rust mixture, we have covered what is called the internal stability of a linear time-invariant system. What is this? You have a plant and a controller. In addition to this, we have input disturbance, output disturbance, and measurement noise. Generally, measurement noise is a high-frequency signal and disturbances are low-frequency signals. How do we check the stability of this system in the presence of all disturbances and noises? We have discussed that since there are four inputs (1, 2, 3, 4 inputs), all internal signals must be stable. We have considered the internal signals, the summer output II, the summer output u P, and the summer output Y. Even all internal signals must be stable. Then we have this problem, and we have seen that there are 4 inputs and 4 outputs, so we will get a total of 16 transfer functions. Each transfer function must be stable for the internal stability of the system. We have derived this. Next, we have seen the detailed derivation of that one output. The output is due to the reference input, the disturbance, the output disturbance, the input disturbance, and the measurement noise. That output is expressed as follows. Then we have considered how the effect of disturbances at the output can be reduced by police designing a controller that C(s). The design objective is to achieve good output disturbance rejection. In order to achieve this, the loop gain (GS and CS) must be high at low-frequency range to reject all disturbances. For a good setpoint, we need to make the transfer function or the transforms and T0 nearly equal to zero. We have proven this. Next is noise suppression for high noise separation. At high-frequency signals, the loop gain is very small. If you can design...
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