Usually we have to compromise among many conflicting and damaging specifications and have to adjust the system parameters to achieve a suitable performance although it is not possible to obtain all desired optimum specifications…
Download file to see previous pages...
Although the prime objective of a control system is to have optimum performance yet without any adjustment it is rare indeed. Usually we have to compromise among many conflicting and damaging specifications and have to adjust the system parameters to achieve a suitable performance although it is not possible to obtain all desired optimum specifications. The control system adjustment or stabilization and alteration is carried out by introducing a compensating block within the control loop that will not allow the steady state error to exceed to a certain limit. This compensating block is called compensator or filter and physically it may be an electric network or mechanical equipment containing levers, springs, dashpots, etc. The compensator may be placed cascade with forward transfer function Gx(s) or in feed back path as shown in fig.1.1. The selection of location for inserting the compensator largely depends on the control system, the necessary physical modifications and results desired (D’Azzo, 1995, pp. 319-320). The available techniques to achieve improvement in the response of feedback control system are time domain, frequency domain, root locus and disturbance rejection technique. In next section we will examine cascade and feed back path compensators using frequency domain technique and a comparison is made relative to merits of each design.
Let we consider a system as shown in fig. 1.2, then forward transfer function in
terms of frequency domain with a compensator be,
G(j) = Gc(j) Gx(j)
or, Gc(j) = .(1)
Now for lag compensators, the equation (1) in terms of frequency domain becomes
(D'Azzo, 1995, pp. 333),
Lag Compensator Gc(j) = .(2)
Also for Lead Compensator Gc(j) = . .(3)
Fig. 1.1 Block Diagrams of Control Systems with Feedback Compensators
Fig. 1.2 Feedback System with Compensators
The polar plots of equations (2) and (3) can be plotted as shown in fig. 1.3. From
graph we observe that the cascade lag compensator results in a clockwise rotation of
G(j) and can produce a large increase in gain (Km) with a small decrease in m where
as cascade lead compensator results in the counter clockwise rotation of G(j) and
produce a large increase in m with small increase in Km where both Km and m
determine the transit response of a feedback system.
Fig. 1.3 Polar graphs of Cascade Compensator
Also from equation (1), Gc(j) = Gc(j)
Solving for ', we have (Dorf, 1989, p. 266), (D'Azzo, 1995, pp. 370-371).
= tan-1T - tan-1T
= tan-1 . (3)
or T + T + = 0 . (4)
Where for lag compensator > 1 and < 1 for lead compensator. Differentiating
equation (3) w.r.t. and setting it equal to '0, we have,
m = . (5)
Substituting the value in (3) we have the max. phase shift,
() max = sin-1 . (6)
From equation (6) we can calculate typical shift values as given in table (a) which are
very useful in design application of lead compensator as we will see in design examples.
Design Example of Phase - lag Compensator Network
Let we consider an uncompensated transfer function give as,
GH(j) = (where Kv = K/20)
Let we compensate this network to Kv = 20 with phase margin of 45.
If we observe the uncompensated Bode diagram as given in fig. 1.4 we see it has as
Fig. 1.4 Bode Diagram
shown in solid lines then we see that uncompensated system has a phase margin of 20.
Allowing 5 for an increase in phase -lag compensator, we relocate the frequency,
(where = -130) which is to be our crossover
...Download file to see next pagesRead More
It is a company that has been in existence since the year 1911. It has over the years been charged with the responsibility of constructing numerous buildings in the US. It has of course adopted several developments in its construction process thanks to the relentless technological advancements.
Automation, as defined by Moray, Inagaki and Itoh (2000, Para. 1), “is any sensing, detection, information processing, decision-making, or control action that could be performed by humans but is actually performed by machine.” Therefore, automation involves changing the way people do work and thus affects operations management.
Using Assessment and Feedback
Among these barriers include “(a) degree of differentiation required, (b) need to provide advanced learning opportunities beyond grade level, (c) philosophical barriers and antipathy of many teachers toward the gifted learner and their needs, (d) lack of understood services for the gifted population, and (e) lack of service mandates in many states to support services for gifted learners leading to greater neglect” (VanTassel-Baska & Stambaugh, 2005).
As per the study, Drew has exhibited vulgar traits in the responses that he gives to the other employees. In this regard, the employees have expressed displeasure in this behavior despite the fact that Drew is one of the company’s best performers in task execution.
The author states that intrinsic motivation is driven by an individual’s personal interest in an activity. The intrinsic motivation is spurred by an individual’s personality or behavior rather than external pressure. The intrinsically motivated students are willingly involved in the activities.
Comparison of software
Aglione is a powerful business intelligence tool that is also easy to use as a dashboard tool and a marketing intelligence application. It allows for a single view into one’s data across every source, as well as pre-calculated key metrics like revenue by channel and acquisition, customer retention over time and by value, and lifetime value by segment or acquisition source (Agilone.com 1).
The student exhibited clarity in the language used in the explanations as well as clarity in the answering of the questions posed.
From the responses given, the student exhibited the ability to reflect on the unit in question. The student also appears
1 Pages(250 words)Assignment
GOT A TRICKY QUESTION? RECEIVE AN ANSWER FROM STUDENTS LIKE YOU!
Let us find you another Research Paper on topic Feedback Control and Automation for FREE!