7/30/2019 SN 3 What is Robust Control

1/24

Dr. S. UshakumariAssociate Professor

Department of Electrical EngineeringCollege of Engineering Trivandrum

1

7/30/2019 SN 3 What is Robust Control

2/24

It is the analysis and design of

control systems in the presence of

uncertainty.

2

7/30/2019 SN 3 What is Robust Control

3/24

1. Obtain a mathematical model of the system

2. Use a control design method together withthe system model to come up with acontroller with certain parameters and

structure.3. Simulate the closed loop system to verify

that specifications are met.

4. Implement the controller in the real system

and tweak the controller parameters if necessary.

3

7/30/2019 SN 3 What is Robust Control

4/24

7/30/2019 SN 3 What is Robust Control

5/24

Signal uncertainty.

Eg. Unknown disturbances, measurementnoise.

Model uncertainty.Eg. Unknown parameters, unmodelled high

frequency dynamics, ignorednonlinearities.

Uncert ain t y cann ot b e avoided, bu t i t can b emanaged.

5

7/30/2019 SN 3 What is Robust Control

6/24

1. Identify and quantify uncertainty

2. Analyse the impact of uncertainty on controlsystem performance (Analyse the robustnessof the control system)

3. Design control systems that provide goodperformance in the presence of uncertainty(Design robust control systems)

6

7/30/2019 SN 3 What is Robust Control

7/24

One degree of freedom controller

7

7/30/2019 SN 3 What is Robust Control

8/24

8

7/30/2019 SN 3 What is Robust Control

9/24

9

7/30/2019 SN 3 What is Robust Control

10/24

Upto page 8 of what I robust

10

7/30/2019 SN 3 What is Robust Control

11/24

11

7/30/2019 SN 3 What is Robust Control

12/24

12

The term complementary followsfrom the identity S +T = I

7/30/2019 SN 3 What is Robust Control

13/24

13

7/30/2019 SN 3 What is Robust Control

14/24

14

7/30/2019 SN 3 What is Robust Control

15/24

Stability is one of the main issues in controldesign.

Two methods commonly used to determineclosed loop stability are:

Evaluate the poles of the closed loop system

(1+L(s) = 0). Plot the frequency response of L(s) in the

complex plane and use Nyquist's stabilitycriterion.

15

7/30/2019 SN 3 What is Robust Control

16/24

16

Time domain performance (step response)

Rise time

Settling time

Overshoot

Steady stateoffset

7/30/2019 SN 3 What is Robust Control

17/24

17

Gain and phase margins

Typically, we require GM > 2 and PM > 300

7/30/2019 SN 3 What is Robust Control

18/24

18

7/30/2019 SN 3 What is Robust Control

19/24

The concept of bandwidth is important inunderstanding the benefits and trade-offsinvolved with feedback.

The closed loop bandwidth, B, is the

frequency where first crosses

from below.

19

)3(707.02/1 dB)( jS

7/30/2019 SN 3 What is Robust Control

20/24

20

7/30/2019 SN 3 What is Robust Control

21/24

Loop shaping

21

7/30/2019 SN 3 What is Robust Control

22/24

e = y - r = -Sr +SGdd - Tn

where S = 1/(1+L) and T = L/(1+L).

The following trade-offs exist:

Good command following L large.

Good disturbance rejection L large

Good noise attenuation L small. Small input u K,L small.

Nominal stability (stable plant) L small

Robust stability (stable plant) L small

22

7/30/2019 SN 3 What is Robust Control

23/24

23

7/30/2019 SN 3 What is Robust Control

24/24

24