Presentation #1Group 3 Carlos Domene, Keshav K Rangan, Wonyup SongJanuary 20151Problem #1Overview of Simulink Modelu Graphy GraphKc Graph

OutlineINDEXProblem #2

2IIntroduction to MIT Rule23

Model Reference Adaptive Control / MIT strategy is used to design the adaptive controller that works on the principle of adjusting the controller parameters so that the output of the actual plant tracks the output of a reference model having the same reference input.

MIT Rule3

MIT RULEThe aim of the this approach is to minimize J().Objective function: Min.J() = e2 where, e = y y* => error = adjustable parameter from the objective function, 4

MIT RULE is known as the sensitivity.We dont want the sensitivity of the controller to be too high as that will lead to the controller picking up noise from the controller itself as an error and try to nullify it. This would then lead to oscillations.On differentiation, we get the value of the controller gain, Kc : c = Gm * e * ys * From here on it is a simple question of taking the Laplace Transform and solving. 56

. Problem #1Design of MIT Rule based model6

7Overview

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8u graph

Mu = -0.1

Mu = -1.0

Mu = -5.0

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9y graphMu = -0.1

Mu = -1.0

Mu = -5.0

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10Kc graphMu = -0.1

Mu = -1.0

Mu = -5.0

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11error graphMu = -0.1

Mu = -1.0

Mu = -5.0

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. Problem #2Determine the condition for stability12

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Problem #2Step 1:Express the given Gp in the characteristic form.

Characteristic Equation:

5s2 + 6s2 + (1-)s + = 0Step 2:Substitute all the coefficients of the characteristic equation into the Routh array.13

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Routh-Hurwitz Criterion:For the characteristic equation,The Routh array is:Thus, for the given problem:an = a2 = (1-)b1 = (6-11)/6c1 = For the system to be stable, > 06/11 > 14

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STABILITY = Kp y*2

Thus,

0 < < 6/(11Kpy*2)

Considering the gain margin to be 2, we get:

0 < < 3/(11Kpy*2)

The expression has different values of Kp and y* substituted into the equation (from the question) and we determine the value of at which we can achieve stability.

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Thank you!Question/suggestion? 06-708 Advanced Process Dynamics & ControlTeam 3Carlos Domene, Keshav K Ragan, Wonyup Song16