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Systems Theory

Written by Darrell Anderson.

Note: Many thanks to Dr. Harvey Barnard for helping me write this. I miss you dearly my friend.

A “system” is model describing a collection or process of things or variables, all possessing certain interrelated observable characteristics and relationships. Systems theory is an interdisciplinary approach of evaluating how various parameters, characteristics, or phenomenon interact; and focuses primarily on the effects of those interactions. Systems theory is used to identify the overall process that will be the subject of the study.

Systems theory is not magical or written anywhere in stone. Systems theory is only a logical process of thinking about things, a checklist of sorts to see who is doing what to whom. By using such an approach, flaws and fallacies often are more easily discovered. More importantly, intelligent discussions become possible when both sides of a discussion agree to the terms of the discussion. When people do not stop to seek even a mutual agreement to what words or phrases mean, they almost always end up arguing endlessly. You might as well watch a dog chase its tail.

Basic Principles

  1. There are no “systems” in nature; that which is, is. Systems are arbitrary models helping humans understand the world around them.
  2. The most fundamental feature of any system is that a system has arbitrary boundaries.
  3. Systems are defined by creating arbitrary boundaries and listing the elements and relational rules associated with that system.
  4. System elements might be tangible or intangible, real or imaginary. Attributes or characteristics describe the perceived nature, features, or traits of the elements.
  5. System relational rules describe the relationship of how the elements interact, the system boundaries establish limits for how the relational rules affect the elements.
  6. A system with no elements and no relational rules is called a null system.
  7. In any system, changing any boundary, element or relational rule automatically creates a different system.
  8. Systems can exist within other systems, and sometimes are called sub-systems.
  9. Observations made in one system might, or might not, hold true for a different system.
  10. Differences in system parameters — both internal and external — drive systems; that is, generate dynamic responses.
  11. Identical actions traversing a system boundary in different directions (into or out of the system) might produce different results.
  12. A system where a relational rule becomes an element in that system and acts upon itself is called a recursive system. Strange things are possible in recursive systems.
  13. A momentary observation or analysis of a dynamic system is a static analysis, and is limited in usefulness in understanding that system.

Types of Systems

There are three types of systems:

  1. Closed system: nothing crosses the system boundaries, in or out.
  2. Open system: boundaries can be crossed and might experience uncontrolled inputs and outputs (also called system disturbances).
  3. Isolated system: an open system, but experiences changes under controlled, limited, or restricted conditions.

Controlling Systems

In systems theory, control means forcing a measurable parameter within a system to a desired value by adjusting some other system parameter known to cause an immediate, predictable response in the measured value. The requirements for system control include:

  1. A measurable parameter.
  2. A desired value for the measurable parameter.
  3. A specified time to achieve the desired value.
  4. An adjustable parameter which has an immediate, predictable effect on the measured parameter.

System Responses

There are three types of system responses:

  1. Positive system: positive stability, tends to be self-controlling, inherently stable.
  2. Neutral system: neither stable nor unstable, tends to produce “ramp” changes in output, the slope of the ramp depending on the input.
  3. Negative system: negative stability, tends to be self-destructive, inherently unstable.

System Changes

System output varies because of a change to the system. In all systems there are natural limits to the variation of physical parameters. These natural limits tend to clamp their associated measured variables, which usually limit system output.

There are two ways to change system output or, two types of forcing functions: 1) continual and 2) impulse. A continual force can be constant or periodic (repetitive). Impulse changes are non-periodic (non-repetitive). Changes can be caused internally or externally. Changes in a system input usually cause changes in system output.

  1. Continual or periodic effect: Ramp changes such as environmental effects or sinusoidal inputs are examples of continual and periodic changes. A shift change in any system variable is an example of a constant continual change. System output continually changes with periodic variable changes but usually stabilize after a variable shift change. The volume control of an audio device is an example of a shift change.
  2. Impulse effect: System output is affected by a sudden non-repetitive shock, such as a pulse or square wave input. The value of some parameters in positive systems might oscillate but usually quickly return to their steady state values (ring a bell). Negative systems tend to crash (snow avalanche). Neutral systems tend to ignore the impulse (water tank level).

System Stability

There are two basic types of control methods: open loop and closed loop. Open loop systems are used when the outcome is known and predictable. Such systems provide no mechanism to regulate the output with respect to the input. An open loop system is good for static systems. Dynamic systems require a means to stabilize the output within expected parameters. Stabilizing systems is performed in one of two ways:

  1. Feedback: Feedback is a process of partially returning output back into a system. Systems can have internal or external feedback loops that can be active or inactive. That is, one parameter in a system changes value, which forces a change in a second system parameter, which in turn forces a change in the first parameter. When this feedback is in phase (reinforces) the first parameter, the system exhibits positive feedback; when out of phase (impedes or balances) the system exhibits negative feedback. If the positive feedback loop gain is greater than one, the system variables oscillate or drive to a limit. Negative feedback with gains less than one reduces oscillations and tends to stabilize system variables. External system feedback is used to automatically correct and maintain system output at a desired level.
  2. Feedforward: Whereas negative feedback control uses one system parameter against another to stabilize a system, feedforward control measures an external change about to enter and possibly upset a system, and therefore creates and injects an offsetting change to maintain system stability.

Practical Applications

Engineers and scientists use these principles daily in their vocation. Yet, understanding these principles can help lay people as well. Understanding the fundamentals of systems theory helps people appreciate the meaning of the adage that “the quality of an answer is directly related to the quality of the question.”

For example, consider survey polls where respondents are limited to only a few options. By providing a limited number of choices, boundaries are purposely established. Add another option and a new system appears — with new boundaries. Add an option of “none of the above” or “all of the above” and a new relational rule appears for how the elements (options) might interact. Purposely limiting the number of options is called a false dilemma.

Thus, by understanding systems theory, an individual can grow to learn that all polls are usually rigged to control the outcome of the answers. Indeed, ask a professional pollster to help run a poll, and the pollster likely will ask you what kind of outcome you desire.

Another example is a pure economic system of supply and demand. Such a system is self-stabilizing positive system. However, introduce artificial elements into that system, such as banking, monetary, and tax systems, and a new system is defined that might or might not remain self-stabilizing.

Another example is the common effort used by some “teachers” to demonstrate a point of theory: the “island” scenario game.

Island scenarios are often static snapshots of dynamic systems. Often only one element of a complex system is discussed, further limiting usefulness of the discussion. A static snapshot of a dynamic system controls the outcome of the scenario. In other words, the “teacher” rigs the outcome of the game (usually unintentionally because they do not understand the basics of systems theory, but sometimes intentionally too).

Therefore, before participating in any discussions about island scenarios, you might want to inspect how they (intentionally or unintentionally) rigged the game. Although most island scenarios typically are a limited static analysis of a complex dynamic system (economic or monetary systems, for example), sometimes these “intellectual” exercises also break natural limits, or they cross system boundaries, or they make the system self-referential (recursive).

Static snapshots also often ignore the effects of other elements of the original complex system. Sometimes people try to explain complex systems by reducing the system into a “simpler” system. This is called reductionism. However, when people do this they create a new system; along with new boundaries, elements, and relational rules. Thus, whether intentional or unintentional, they have rigged the outcome of their “simpler” system; and often, those outcomes do not correspond well to how the original complex dynamic system functions. Worse, begin to reintroduce into the “simpler” system some of the elements of the original complex system and the author is continually creating a new and different system, with new boundaries, elements, and relational rules.

When people present island scenarios, simply ask them to first clarify the system, the boundaries, elements, and relational rules. Most definitely ask the “teacher” to fully explain all definitions to ensure everybody is talking about one thing and not another. Be sure the relational rules are clearly defined, such as ethical vs. moral. More than likely the “teacher” will return a blank stare. Then, after a few moments of the blank stare, tell them they have rigged the game and that the boundaries, elements, and relational rules they have created limit your options.

Or, if you want to have fun, you can re-rig the game by adding your own elements, relational rules, or boundaries, then hand the scenario back to them!

Finis.

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