Distributed parameter system
Under the system characteristics is a set of properties that are characteristic of a system. They arise in part from the properties of the elements of the system and on the other from the system structure, ie their mutual relations.
Complexity
It is characterized by the type and number of elements as well as type, thickness, number and density of interactions at the micro level.
The complexity and intricacy is determined by the number of elements and the number and the type of relations. A distinction (ratio of number of relations and elements; complexity measure = K = nr / ne ) between structural complexity and Time complexity. That is, the number of possible states, which may take a period of time in the system.
Description of the extremes:
Between simple and complex systems, all degrees of severity of the extremes are possible.
The complexity of a system depends on the definition of system boundaries, the number of elements considered to be relevant and of the interactions considered as relevant ( interdependencies ). Many complex systems have a hierarchy similar structure: the closer ( temporally and / or spatially ) one approaches, the more details are visible. It can always go back the same structures occur regardless of the scale. In this case, there is no hierarchy before, but self-similarity. Self-similarity is in biology at less structures (but see cauliflower) as found in basic principles, such as the rules of evolution are ( over-production - Variation - selection ) on all structural and temporal levels.
Dynamics
It is characterized by the time response of the system. Static systems show without outside influences both the macro level and at the micro level, no changes (example: pendulum at rest ). Dynamic systems are subject at the micro level lasting changes, but can at least temporarily, at the macro level, a steady state take (examples: chemical equilibrium reaction, the forest ecosystem ). If a system is considered as static or dynamic, depending on the time scale and the length of time of observation of the system. This is evident in systems in equilibrium, but fluctuate around their equilibrium position: If the observation period is too short, can not be determined whether they are fluctuations around a mean or whether the rising or sinking trend exists (example: climate fluctuations since the beginning of direct measurements). Where a large scale chosen, the fluctuations are not detected; the system behaves seemingly static.
Interaction
Systems and elements are linked by relationships. These relationships can be energy, material and information flows.
Possibilities on the macro level:
- Isolated systems have neither a substance nor an exchange of energy with the environment.
- Although (Ab) closed systems can exchange energy with the environment, but not substances.
- Open systems exchange with the environment both materials and energy.
Depending on the defined system boundaries, a system can be considered isolated, completed or considered open since it directly impacts depends on the distinction between system and environment.
Isolated and closed systems are in reality practically non-existent, their modeling is however necessary in the investigation of very complex systems.
Determinacy
The determinism is the degree of " predetermined nature " of the system: A system moves from one state to the state Z1 Z2 on: Z1 → Z2. For deterministic systems, this transition is determined ( mandatory), in stochastic likely.
Deterministic systems do not allow in principle the derivation of their behavior from a previous state, stochastic systems. Classical deterministic systems allow an unambiguous determination of their condition at any time in the past and the future with reasonable accuracy (for example, planetary motion ). Sufficiently here is based on human manageable, or relevant time periods and scales. The development of chaotic systems is not always clear, since all parameters with theoretically infinitely high accuracy must be known, they are sensitive to the initial conditions. With appropriate (mathematical) models can be relevant statements about the past and future of deterministic and stochastic systems make. The complexity of a system is not an indicator of predictability can take: There are simple deterministic systems that are chaotic (eg double pendulum) and complex deterministic systems ( chloroplasts during photosynthesis ).
Stability
Considerations of the response of a system at the macro level in the steady state to external disturbances
Consideration of the elements at the micro level
In stable systems, the structure of the system does not change. The number, nature and interaction of the elements remains constant. In unstable systems satisfy slight changes in the system conditions to cause a change in the structure brought about. This may be caused by both the outside and inside by its own momentum.
With increasing complexity of the interchangeability of the elements and therefore the structural stability will be lost. If in highly complex systems one element against another exchange, which no longer has the same properties, the overall behavior of the system can change. (Example: organ transplantation ).
What stability of a system is determined depends on the specified time scale and the observation period, from the definition of the disorder: Some stable systems go at sufficiently strong disturbances in unstable conditions over (example: activation of chemical reactions). All systems can be destroyed by strong interference.
Depending on the allocation of system boundaries
The assignment to one of stability categories also depends on the definition of the system boundaries from:
Example system ball / bowl
In case of failure, ie bumping the ball, the ball rolls back into its original position. Too strong a shock promoted the ball out of the bowl, the ball falls to the ground. Thus, the original system is destroyed. But the system will ball / bowl / bottom considered, the ball is in the bowl only in a metastable state, as it assumes a more stable condition on the ground.
If the ball lands on an inverted bowl ( unstable system ), any distortion also leads to destruction. However, if the system reverse bowl / ball / ground considered, any disturbance leads to a new state.
Example bar pendulum
Here, the system can vary depending on the positional relationship focus to take fulcrum three different states which behave differently to perturbations: eccentric arrangement: There is exactly one stable state, all other states are unstable. ( Fall pivot point and focus together) for another pendulum system with centric storage there are endless possibilities of orientation of the bar, but all are unstable.
Time variance
Time variance describes the dependence of the system performance of the time of observation. A time-varying system behaves differently at different times. In technical systems, the reason usually is time-dependent parameter values , in biological systems, for example, in different environmental conditions. Time-invariant systems, however, behave the same at any time. A mechanical clock is time-invariant, for example, if one neglects wear. A shuttle, wherein the length of the suspension varies with the time, time-variant.
EN 61069-1
The European Standard EN 61069-1 proposes as the basis of self-assessment of a system in the control system, the system properties shown in the table before. The standard is published in Germany as DIN standard DIN EN 61069-1.
- Customization configurability
- Programmability
- Extensibility
- Accuracy precision
- Repeatability
- Availability maintainability
- Reliability
- Representation
- Procedure hierarchy
- Access
- Staff applicable regulations
- Intrinsic Safety
- Explosion protection
- Support user
- Supplier
- Documentation
- Training
- Software
- Extension
- Communication
- Spare Parts
- Loss of heat radiation
- Supply requirements
Other properties
- Discrete ( time - or condition- discrete) - continuously
- Linear - nonlinear
- Purpose or goal-oriented
- Adaptive ( adapting )
- Autonomous ( independent of external control)
- Autopoietic (self- propagating )
- Thinking
- Learning
- Controlling
- Regulating, self-regulating
- Trivial - not trivial
- Distributed / concentrated parametrically
- Systems theory