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Control

Applying input to cause system variables to
conform to desired values called the reference.
Cruise-control car:
f_engine(t)=?  speed=60 mph
 E-commerce server:
Resource allocation?  T_response=5 sec
 Embedded networks:
Flow rate?  Delay = 1 sec
 Computer systems: QoS guarantees

Feedback (close-loop) Control
Controlled System
( “plant” )
Controller
control
function
control
Acturator
input
(efector, etc)
error
+
-
reference
manipulated
variable
Sensor
(monitor etc)
sample
controlled
variable
Open-loop
control
Controlled System
( “plant” )
Controller
control
function
control
input
Acturator
manipulated
variable
(efector, etc)
error
+
-
controlled
variable
reference

Compute control input without continuous variable
measurement



Simple
Need to know EVERYTHING ACCURATELY to work right
 Cruise-control car: friction(t), ramp_angle(t)
 E-commerce server: Workload (request arrival rate?
resource consumption?); system (service time? failures?)
Open-loop control fails when



We don’t know everything
We make errors in estimation/modeling
Things change
Feedback control theory, vs …

Adaptive resource management heuristics



Queuing theory



Laborious design/tuning/testing iterations
Not enough confidence in face of untested workload
Doesn’t handle feedbacks
Not good at characterizing transient behavior in overload
Feedback control theory


Systematic theoretical approach for analysis and design
Predict system response and stability to input
Control design methodology
System
model
Controller
Design
Dynamic model
Control algorithm
Satisfy
Requirement
Analysis
Performance Specifications
Linear vs. non-linear
Time-invariant vs. Time-varying
Are coefficients functions of time?
Continuous-time vs. Discrete-time
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Feedback Control of Computing Systems: M1 - Introduction
© 2004 Hellerstein
Example: Control of Lotus Notes
Architecture
Admin Controller
MaxUsers
RPCs
Server
Desired
RIS
RIS = RPCs in System
Actual RIS
Control Model
MaxUsers
Desired
RIS +
r(k)
e(k)
-
u(k)
Controller
Notes
Server
Actual
RIS
y(k)
Control error: e(k)=r(k)-y(k)
System model: y(k)=(0.43)y(k-1)
+(0.47)u(k-1)
P controller: u(k)=Ke(k) ?
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Feedback Control of Computing Systems: M1 - Introduction
© 2004 Hellerstein
Example: Control & Response
in an Email Server
Response
(queue length)
Good
Bad
Control
(MaxUsers)
Slow
Useless
Feedback Control of Computing Systems: M1 - Introduction
© 2004 Hellerstein
Control System Architecture
Reference
Input
Controller
Transduced
Output
Control
Input
Disturbance Input
Target
System
Measured
Output
Transducer
Components
Given target system, transducer
Target system: what is controlled
Control theory finds controller
Controller: exercises control
that adjusts control input
Transducer: translates measured outputs
to achieve measured
Data
output in the presence of
Reference input: objective
disturbances.
Control input: manipulated to affect output
Disturbance input: other factors that affect the target system
Transduced output: result of manipulation
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Feedback Control of Computing Systems: M1 - Introduction
© 2004 Hellerstein
Administrative
IBM Lotus Domino Server Tasks
Notes
RPC
RPCs
Client
Records
Notes
Server
Server
Log
Notes
Architecture
Client
MaxUsers
Administrative
Tasks
Target System
MaxUsers
Reference
RIS
Controller
Actual
Notes RIS
Sensor
Server
Measured
RIS
Block Diagram
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Feedback Control of Computing Systems: M1 - Introduction
© 2004 Hellerstein
Properties of Control Systems – SASO
Stability
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Accuracy
Unstable System
Short settling
Feedback Control of Computing Systems: M1 - Introduction
Small Overshoot
© 2004 Hellerstein
Performance specifications
Controlled
variable
Overshoot
Steady state error
%
Reference
value
Transient State
Settling time
Steady State
Time
Control Theory in Two Slides: System Identification
MaxUsers
u (k )
Notes Server
Actual RIS
y (k )
Model of System Dynamics
y(k )  a1 y(k -1) + b1u(k -1)
Predicted RIS
100 a  0.913
1
80
60 b1  0.055
40
2
R
 .97
20
0
0
20
40
60
80 100
Measured RIS
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Transfer Function
b1
N ( z) 
z - a1
Feedback Control of Computing Systems: M1 - Introduction
© 2004 Hellerstein
Control Theory in Two Slides: Control Design
+ e(t ) Controller
r*
Notes Server
Sensor
-
G(z)
N(z)
S(z)
H(z) = Closed Loop Transfer Function
Integral Control Law
u (t )  u (t - 1) + Ke(t )
K=.1
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Poles
of
H(z)
K=1
Feedback Control of Computing Systems: M1 - Introduction
K=5
© 2004 Hellerstein