1 ASE-1256 Introduction to Control and Automation E13 Root Locus Definition. A nominally stable CT (Continuous-Time) LTI system with poles is said to have Pole Margin if and only if the right-most pole has (poles have) the real part ( ) and so lie in the horizontal distance to the Im axis. 1. Consider the familiar Hard Disk Drive Read-Write Head application with the motor parameters given below. Use Routh-Ziegler-Nichols Test to identify condition for marginal stability as well as the angular frequency and the period of the critical oscillation. 20 , 1 , 5 , 1 , 001 . 0 b J K R L 2. A process together with the actuator are modelled using a positive Time Constant T and Gain K . The sensor is regarded as ideal. Assume an I controller with the Integral Gain I K . a) Study the condition 0 Re s for the closed-loop poles ( 0 ). What is this proposing about Pole Margin? b) Sketch the root locus for variation of I K using exact root formulae. Can you here see issues related to Pole Margin? 3. The ÅM book discusses Inverted Pendulum on e.g. pages 35-37 (Ex 2.1, 2.2), 263 (T8.3), 265 (T8.13) and 276-277 (Ex 9.6). Sketch the root locus after identifying start points, end points, Im axis crossings, Re axis segments as well as departure points and arrival points of Re axis. 4. The charpo of a system is given below. Which tf would you give to rlocus to get a root locus plot vs. define for use of Root Locus rules e.g. to find Re axis segments as well as departure and arrival points? 1 ) ( 2 s a s s P , a 5. The mass flowrate of a stuff from a belt conveyor is controlled by adjusting the mass flowrate (of a stuff) onto the conveyor using an ideal sensor and a P controller. What kind of root loci will we get if a) The process delay is fixed but the controller gain can be varied? b) The controller gain is fixed but the process delay will change? 6. Consider again the belt conveyor control but now using an I controller. Identify for the root loci a) Start and end points. b) Re axis segments. c) Departure and arrival points of Re axis. 7. Consider again the disk drive application of Problem 1. a) Identify for the root loci Re axis segments b) Identify departure points and arrival points of Re axis. c) Which value of the controller gain gives the departure point? d) What would happend and why if a poor engineer tried a negative controller gain?
1 ASE-1256 Introduction to Control and AutomationE13 Root Locus
Definition. A nominally stable CT (Continuous-Time) LTI system with
poles is said to have Pole Margino if and only ifthe right-most
pole has (poles have) the real part(o ) and so lie in the
horizontaldistance oto the Im axis.
1.ConsiderthefamiliarHardDiskDriveRead-WriteHeadapplicationwiththe
motorparameters given below.Use Routh-Ziegler-NicholsTestto
identify condition for marginal stability as well as the angular
frequency and the period of the critical oscillation. 20 , 1 , 5 ,
1 , 001 . 0 = = = = = b J K R L 2.A process together with the
actuator are modelled using a positiveTime ConstantT and GainK .The
sensor is regarded as ideal. Assume an I controller with
theIntegral Gain IK .
a)Study the condition{ ; 0 Re < ). What is this proposing
about Pole Margin? b)Sketch the root locus for variation ofIKusing
exact root formulae. Can you here see issues related to Pole
Margin? 3.TheM book discussesInverted Pendulumon e.g. pages 35-37
(Ex 2.1, 2.2), 263 (T8.3),265 (T8.13)and 276-277 (Ex 9.6). Sketch
the root locus after identifying start points, end points, Im axis
crossings, Re axis segments as well asdeparture points and arrival
points of Re axis. 4. The charpo of a system is given below. Which
tf would you give to rlocus to get a root locus plot vs. define for
use ofRoot Locusrules e.g. to find Re axis segments as well as
departure and arrival points? 1 ) (2+ + = s a s s P, < < a
5.The mass flowrate of a stuff from a belt conveyor is controlled
by adjusting the mass flowrate (of a stuff) onto the conveyor using
an ideal sensor and a P controller. What kind of root loci will we
get if a)The process delay is fixed but the controller gain can be
varied? b)The controller gain is fixed but the process delay will
change? 6.Consider again the belt conveyor control but now using an
I controller.Identify for the root loci a)Start and end points.
b)Re axis segments. c)Departure and arrival points of Re axis.
7.Consider again the disk drive application ofProblem 1. a)Identify
for the root loci Re axis segments b)Identify departure points and
arrival points of Re axis. c)Which value of the controller gain
gives the departure point? d)What would happend and why if a poor
engineer tried a negative controller gain?
