Lecture 11: Feedback Systems Flashcards
1
Q
Definition of a System
A
- “A collection of component parts organizedfor a purpose”
- Contains interacting components connectedin such a way that the variation in one component affects the other components
- System is scoped by defining its boundary: i.e. choosing which entitiesare inside, and which are outside the boundary
- Environment affects system throughinput (cause), system responds (effect) in relation to the input
- How to structure a system:
o Determinewhat belongs to the system, and what is outside
o Defineinputs, outputs and internal dynamics
2
Q
Classification of Systems:Static vs. Dynamic Systems
A
Static System
- Output of the system is determinedonly by the current input
- The output does not change over timeif the input is held constant (time-invariant)
Dynamic System
- the output of the system depends onthe current and all previous input
- the output changes over time even ifthe input is constant (time-varying)
3
Q
Sequence of Events: Static vs dynamic systems
A
Static System
Information=> Action => Consequence
Dynamic System
Information ==Delay in knowledge==> Action ==Delay in choice==> Consequence ==Delay in state==> Information
^circle
4
Q
Why Do Systems Fail?
A
- It fails to achieve its purpose(system scope)
- The parts are poorly designed orpoorly connected (system structure)
- It is knocked off course by externalshock (perturbation)
- It is inherently incapable ofmeeting its purpose or it attempts to adjust to change (adaptation)
- Its policies are badly designed(interactions)
5
Q
Definition of System Dynamics
A
- System dynamics is the study of thetime-dependent behavior of a managed system
- Aims to describe the system andunderstand it (focuses on patterns of behavior, not events)
- Applies qualitative and quantitativemodels on how information feedback governs system behavior
- Designing robust informationfeedback structures and control policies through simulation and optimization
6
Q
System Dynamics and Dynamic Problem Analysis
A
System Dynamics are used to analyse “messy” dynamic problems:
- Self-organising – dynamics arise from internal structure
- Adaptive –actors change over time
- Counterintuitive – too focused on symptoms of difficulty rather than the underlyingcause
- Policy resistant – many obvious solutions fail or worsen the situation
- Characterized by trade-offs – high-leverage policies cause worst to better behavior, while lowleverage policies result in temporary improvement before getting worse
7
Q
Elements of a Dynamic Problem
A
- Dynamic behavior of important variables – identify and graph those variables in the systemthat are symptoms of the problem we wish to study
- Time horizon– period of time over which the problem plays itself out
- Reference behavior – patterns over time that will be referred to again and again
- Thinking in terms of graphs over time – looking for long-term dynamic consequences.Use graphs to describe, define and analyse a problem
8
Q
Common Modes of Behaviorin Dynamic Systems
A
- Exponential growth
- Goal-seeking
- S-shaped growth
- Oscillation
- Growth with overshoot
- Overshoot and collapse
9
Q
Questions to answer insolving dynamic problems
A
- What is the problem you are tryingto analyse?
- What are the important symptomvariables?
- What is the time horizon of yourproblem?
- What is the reference behavior mode youexpect to see?
- What are the long-term dynamicconsequences of the problem?
10
Q
Elements of System Dynamics
A
- System Definition
a. Definition of the problem understudy
b. System Boundaries, input and outputvariables - A model of the system
a. Definition of ystem components andtheir interrelations
b. Usually in the form of mathematicaland/or graphical relationship determined analytically or empirically - Analysis or simulation of thebehavior of the system
a. Effects of the inputs on systemoutputs - Formulation of recommendation
a. To improve system performancethrough modification of system structure or parameter values
11
Q
System Dynamics Modelling
A
- A model of a system is basically atool to study the behavior of a system withoutconducting experiments on the real system
- A model can be: physical model,mental model, linguistic model, graphical model, and mathematical model
- Formal model = collection of equationswhich represent behavior and characteristics of a real system
12
Q
Why do we need a model?
A
- To avoid a physical or social system
- Cantreat new processes, policies or technologies without real world experiments orprototype
- Doesnot interrupt operation of the existing system
- Easier to work with models than realworld
- Easyto test different approaches, parameter values
- Flexibleto time-scales (saves time)
- Canaccess immeasurable quantities (estimate component values)
- Support operational integrity
- Experimentsintroduce risks
- Actorsneed to be trained
=>Help to gain insights and buildunderstanding
13
Q
Model Characteristics
A
- A model captures only some aspectsof a system
- importantto know which aspects are modelled and which are noto makesure that the model is valid for its intended purposes
- all-encompassing models are often abad idea
- largeand complex – difficult to derive insights
- cumbersomeand slow to manipulate!Goodmodels are simple, yet capture the essentials
14
Q
Model Simulation
A
- we may define simulation as aprocess of imitating system dynamics using a computer in order to evaluateand/or improve the performance of the system
- a model can be used to compute how asystem will react to certain inputs (i.e. different parameter settings)
- this can be done by mathematicallysolving the equations that describe the system and study the solution OR
- with the power of a computer we canperform a numerical computation to solve the equations
15
Q
Causal Loop Diagrams
A
Causal LoopDiagrams are an important tool for representing the information feedbackstructure of systems
- quickly capturing your hypotheses aboutcauses of dynamics
- elicitating and capturing the mentalmodels of individuals or teams
- communicating the importantfeedbacks you believe are responsible for a problem
- testing scenarios and estimatinglong-term behavior of important variables
