I can only answer question 1 here, based on the position of the Nichols plot rel

Question

I can only answer question 1 here, based on the position of the Nichols plot relative to the critical point (1, 3, 4 are closed loop stable systems). But I have no idea how to figure out the remaining points. What is the reasoning behind this type of problems?

Conceptual problem Problem 5: steady state analysis Consider the following Nichols plots of four different loop functions L(s) of a unitary negative feedback, cascade compensation control system configuration 2 50 Open-Loop Phase (deg) Open-Loop Phase (deg) 4 Open-Loop Phase (deg Suppose that, for each L(s), Kg lims- s° L(s) > 0, then, based on the Nichols plot only determine which of the four 1. corresponds to a closed loop stable system 2. guarantees a finite value of e? in the presence of a constant reference signal 3. guarantees ef- 0 in the presence of a constant reference signal 4. guarantees a finite value of lein the presence of a linear ramp reference signal 5. guarantees ef- 0 in the presence of a linear ramp reference signal 6. surely guarantees 0 in the presence of a constant actuator disturbance signal da(t)

Explanation / Answer

Given Nicholos plots are relating to openloop systems and he asked to determine closed loop error.We know that we can only determine error for open loop systems.

Here we have 3 condition by connecting type of system and applied input.

1) if type of system and applied input order is same then error is finite.

2)if system type is greater than applied input order then error is zero

3) if system type is less than applied input order then error is infinity.

We consider step input as zero order, ramp input as first order and parabolic as second order inputs.

We know that for one pole we get -90 degrees phase shift.

With this info we can answer questions now.

2)consta co reference signal means step input for step input finite error will be given by type zero system.Graph 3 ended with zero phase degrees hence it is matched.

4)first and second graphs ended qith-90degress that means type 1 system hence error is zero.

4)linear ramp input standard value means 2and 3 graphs are matched because type 1 systems.

5)erro e should be zero in presence of ramp signal menas type should be 2 or more hence from graph 4 we can say that it is type 2 system.

6)given input as constant actuator disturbance while doing multiple input problems we ignore remaining all signals and we consider only one signal ..so constant signal means type should be greater than zero to produce error zero hence from graph1 and 3 are matched.

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