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7/30/2019 Control of Technical Systems
1/37
OC 5.1
S.
Mostaghim,
H.
Schmeck
Organic Computing
Chapter 5: Control of technical Systems
7/30/2019 Control of Technical Systems
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OC 5.2
S.
Mos
taghim,
H.
Schmeck
Overview
This chapter focuses on the basics of control of technical systems:
Basics of control engineering
Adaptive controllers
Uncertainties in design
Robustness
Reliability
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Basics
Process
Input Output
If we have an exact knowledge of the process (controlled variable behavior),
we can use a Feedforward Control.
OutputProcess
Input Control
System
Feedforward is being used to maintain some desired state of the system.
Everything is predefined
The control system responds to a known disturbance.
The control system does not observe the output of the process it is controlling.
A Process:
The main goal of control systems is to improve the behavior of the system
Disturbance
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Feedforward
Example:
The task is to control the system
such that the shafts rotate with equal speeds in spite of different possible
friction levels (disturbances).
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Feedforward
A desired speed should be achieved.
The torque to accelerate the mass to a desired speed can be easily computed if
we assume a frictionless system.
T
SpeedProcess
Speed
referenceControl
System
Computes the correct Torque value
Disturbance
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Speedreference
Feedforward vs. Feedback
Unfortunately the real world is full of non-linearities that
limit the effectiveness of such feed forward control schemes:
Different friction levels come from different sources and vary over time,
therefore some feedback is introduced:
SpeedProcess
Control
System
Disturbance
Computes the correct Torque value
to control the speed.
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Schmeck
Feedback
Feedback Control:
In every feedback loop,
information about the result of a
transformation or an action is sent
back to the input of the system inthe form of input data.
ProcessOutput
Disturbance
Control
System
Input
Feedback
OpinionFeedback systems also appear
in non-technical systems.
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H.
Schmeck
Positive vs. Negative Feedback
Positive Feedback: If the feedback to the system influences the output of theprocess in the same direction as the preceding observed changes, it is
positive feedback - its effects are cumulative: there is exponential growth or
decline.
Time
Ou
tput Explosion
Blocking
Start
Positive Feedback: exponential growth or decline
(diverging behavior)
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H.
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Positive vs. Negative Feedback
Negative Feedback: If the feedback to the system influences the output of theprocess in the opposite direction, it is negative feedback - its effects stabilize
the system: there is maintenance of the equilibrium.
Time
Output
Start
Goal
Start
Negative Feedback: Maintenance of equilibrium and convergence
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Adaptive systems and control systems
An adaptive system is a system that is able to adapt its behavior according tochanges in its environment or in parts of the system itself.
Control systems utilize feedback loops in order to sense conditions in their
environment and adapt accordingly.
The aim of control engineering, beside the others, is to determine:
the model of the controller
the parameters of the controller
It is desirable that the controllers adapt their parameters to the changing
environment parameters
Adaptive Controllers
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Adaptive Control
Adaptive Controllers:
In Adaptive Control, the controller parameters are variable and there is a
mechanism to adjust them online based on the signals in the system.
Example: A robot carrying an unknown load (a load of uncertain mass properties).
There are two ways to construct the adaptive controllers:
1- Model-reference adaptive control
2- Self-tuning method
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Schmeck
Adaptive Control
Model-reference adaptive control:
requires a reference model for the controller in order to compute
the error of the systems output and the adaptation law sets the
parameters of the controller so that the error is minimized.
Process
Disturbance
Control
System
Ref.
Adaptation
law
Reference
model
error
Estimates the parameters
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Adaptive Control
Self-tuning adaptive control:
Based on the input and output of the process, the estimator
estimates parameters of the controller.
Process
Disturbance
ControlSystemRef.
Estimator
The selected Parameters must be robust with respect to the changes
caused by the disturbance.
This is an on-line estimator
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Robustness
Searching for robust solutions:
In many real world applications the adaptation is not possible:
1- the environment changes too quickly
2- the environment cannot be monitored closely enough
3- the changes happen after the commitment to a particular solution has been
made.
In such cases, one must search for solutions that perform well in all possible
future scenarios.
The property of being insensitive to the slight changes of the
environment or noise in the decision variables is called
Robustness.
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x
f(x)
Robustness
Example:
A change affects the
quality of the solution onthe thin peak much more
that the solution on the
plateau.
We consider the disturbance to appear indesign variables.
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Schmeck
Uncertainties in the design
Different kinds of uncertainties:
1. Aleatory Uncertainty
describes the inherent stochastic variation of the physical system.
such variation is usually caused by the random nature of the input data.
Variations can occur in the form of manufacturing tolerances or
uncontrollable variations in the external environment.
They are usually modeled as random phenomena characterized by probability
distributions. The probability distributions are constructed using the relativefrequency of the occurrence of events, which requires large amounts of
information. Most often such information does not exist and designers usually
make assumptions on the characteristics (mean, variances, correlation
coefficients) of the random phenomena causing the variation.
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Schmeck
Uncertainties in the design
2. Epistemic Uncertainty
Epistemic uncertainty also known as subjective uncertainty arises due to
ignorance lack of knowledge
incomplete information
decision making (due to trade-offs)
In engineering systems, the epistemic uncertainty can be
Parametric: uncertain parameters for which the available information is
inadequate
Model-based: improper model of the systems usually due to the lack of
knowledge about the physics of the system
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Schmeck
Uncertainties in the design
3. Numerical Uncertainty (Error)
commonly associated with the numerical models used for modeling and
simulation.
typical examples:
- round-off errors
- truncation errors- error associated with the solution of ODEs and PDEs which typically uses
discretization schemes.
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Definitions of Robustness
Possible definitions for a Robust Solution assuming a certain range of
uncertainties:
1- Maximize the minimum possible outcome:
This is appropriate for problems like when:
- an investment strategy is sought that in no possible way leads to bankruptcy.
- flight control strategies must not crash the airplane.
2- Trade-off between quality and variance:If the focus is on small variance, one might explicitly look at the trade-off
between quality and variance.
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x
f(x)
Robustness
3- Maximize the expected performance:
The expected performance (effective quality) can be calculated as follows:
+
+=+= d)f(x).()E(f(x(x)feff
p
Probability density function of disturbance
Because fis not known in a closed form, feffcannot be easily computed.
But it can be estimated by methods like Monte Carlo integration.
Monte Carlo Integration:Sampling over a number of realization of.Each sample corresponds to one fitness evaluation.
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Schmeck
Sampling methods
=
+=n
1i
0n
10eff )f(x)(xf
Integral Approximation:For a given point x0 the integral can be estimated by evaluating a set ofn
samples xi = x0+ in the neighborhood ofx0:
Sampling methods:
1- Random Method
2- Antithetic3- Stratified
4- Latin Hypercube
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staghim,
H.
Schmeck
Sampling Methods
1- Random Method
2- Antithetic
Random Method:
Samples points at random
Antithetic:
produces pairs of disturbances which lead to
negatively correlated estimation.
For uniformly distributed disturbances, the
first vector is selected at random (), thesecond is then chosen as -.
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staghim,
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Schmeck
Sampling Methods
3- Stratified
4- Latin Hypercube
Stratified:
Divides the space of possible disturbances
into possible equal properties.
Draws one disturbance from every region.
Latin Hypercube:
In order to draw k samples, every dimension is
divided into k parts.
k samples are chosen such that each quantile in
each dimension is covered by exactly one
sample.
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Schmeck
x
f(x)
Robustness vs. Reliability
Robust designs are designs at which
the variation in the performance
functions is minimal.
Reliable designs are designs at which
the chance of failure of the system is
low.
x
f(x)
constraints
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Schmeck
Reliability
x1
x2
Deterministic Optimum
Feasible region
Reliable solution A
Infeasible regionInfeasible region
Example :
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Schmeck
How to compute the reliability of a solution?
A desired reliability value R can be measured for solution A:
The probability of having an feasible solution created through uncertainties
from solution A is:
( ) JjRdxgP jj ,,2,10, K=
Where gj denotes thejth
constraint (e.g. the distance from some infeasible region).x and dare the vectors of uncertain and deterministic design parameters.
The quantity Rj is the required reliability (within [0, 1] )
for satisfying the jth constraint.
A computational method is required to estimate the probability.
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Schmeck
How to compute the reliability?
Simulation method
A set of Ndifferent parameter
settings is created by following theknown distribution of variation ofx.
For each sample each constraint gjisevaluated and checked for
possible constraint violation.
Ifrcases (ofN) satisfy all gjconstraints, we can replace
with RNr
From [H. Agrawal 2004]
( ) JjRdxgP jj ,,2,10,K
=
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staghim,
H.
Schmeck
How to compute the reliability?
This is a simple method and works well when the desired reliabilityR is not
very close to one.
A major drawback is that the sample sizeNneeded for finding rmust belarge enough, such that at least one infeasible case is present in the sample
Computationally expensive
Biased Monte-Carlo simulation can be used to solve this.
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Schmeck
Output from
observer
Controller in the generic architecture
The task of controller is to :
Select an observation model
Control the SuOC
Input
Control
System
Goals. SuOC
Process
Observer
Output
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Schmeck
Model Predictive Control (MPC)
Predictive control is a form of control which incorporates the prediction of a
system behavior into its formulation.
The prediction serves to estimate the future values of system variablesbased on the available information on the current status of the system.
The prediction is used to optimize necessary control actions: meaning to drive
or maintain the system in a state which satisfies the objectives.
MPC is used when the future behavior of the system might be quite different
from that currently perceived. In particular, the current model for prediction
might be just a currently feasible simplified abstraction of a much more
complex system, i.e. the model has to be updated whenever the realbehavior of the system deviates too much from the predictions.
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MPC
Prediction and control horizon in MPC:
control horizon
time
FuturePast
Input
time
now
desired
output
measured
output
predicted
outputReference
trajectory
prediction horizon
output
Process
Input output
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MPC
Procedure in predictive controller:
1. Sample the output of the process.
2. Check for necessary updates of the model due to deviations between
observed and previously predicted behavior.
3. Use the model of the process to predict its future behavior over a prediction
horizon, when the control action is applied for a control horizon.4. Calculate the optimal control sequence (Input to the process) that minimizes
the error between Input, output and reference.
5. Apply the input to the process and repeat the procedure for the next sampling
time.
Process
Disturbance
Predictive
controller
desired output
(reference)
model
outputInput
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MPC
MPC is a particularly attractive option, if the system behavior over time is not
adequately modeled by one linear model, but may be approximated with a
certain accuracy by a sequence of linear models M1, M2, , Mi,
Without using prediction, it would not be feasible to detect online whether it is
necessary to transform model Mi
into model Mi
+1.
Process
Disturbance
Predictive
controller
desired output
(reference)
model
outputInput
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Distributed control
A distributed control system (DCS) refers to a control system, in which the
controller elements are not centralized but are distributed throughout the
system.
In each subsystem,
local control inputs are computed using the measurements and reduced-order
models.
the sub-system is controlled by one or more controllers. The entire system
may be networked for communication and monitoring.
Process
Dist.
Control
Process
Dist.
Control
Process
Dist.
ControlProcess
Dist.
Control
Central Control Distributed Control
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Distributed control
In large-scale applications, it is useful (or sometimes necessary) to have
distributed or decentralized control schemes, as the global measurement of
the system parameters is not possible.
The main challenge in distributed control is to achieve some degree ofcoordination among the controllers.
In distributed control, we have the same problems of emergent phenomena as
outlined for self-organizing systems.
Distributed control systems (DCSs) are used in many industrial applications to
monitor and control distributed systems, like:
Electrical power grids
Traffic signals
Sensor networks Economic systems
Large scale distributed telescopes (in astronomy)
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Organic Computing and Controllers
In OC, we have different kinds of controllers:
Central, distributed, and Multi-level.
Model-predictive controllers might help to efficiently control the behavior ofhighly complex systems.
observer controller
SuOC
observer controller
SuOC
SuOC
O C
SuOC
O C
SuOC
O C
SuOC
O C
SuOC
O C
SuOC
O C
SuOC
O C
SuOC
O C
SuOC
O C
SuOC
O CSuOC
O C
SuOC
O C
SuOC
O C
SuOC
O C
SuOC
O C
central distributed Multi-level
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Summary
In this chapter we had a very brief view on different aspects of controlengineering:
Basics in control
In dynamic environments, adaptive controllers can adjust the controllerparameters to achieve desirable controller model and parameters. An essential task of control engineering is to guarantee robust and reliable
system behavior. Model-predictive controllers incorporate a prediction of the future system
behavior and support the stepwise linear (or simplified) control of highlycomplex systems.
Distributed control is an essential aspect dealing with large scaleapplications, but has to cope with the problems of emergence.
All these issues can be used effectively in OC systems. So far, control engineering does not provide adequate answers to the key
problems addressed in OC systems related to controlled self-organization.
Next:
As learning plays an important role in organic computing, the next chaptersurveys different machine learning methods.