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Definition of Systems • aggregation of things so combined to form an integral or complex whole [Encyclopedia Americana] • interdependent group of items forming a unified whole [Webster] • combination of components that act together to perform a function not possible with any of the individual parts [IEEE: Electronic Terms] Systems Engineering • General systems can be : physical, human made objects as well as ``population dynamics’’ ``economic mechanisms’’ • SE is the art of designing and optimising systems, starting from the desired or identified need (for a system) to the specifications for all the system elements SE applied to Product Development • SE provides a structured and logical framework to develop a customised method of product development • Life cycle of product Development: – Need Analysis, Product Planning and Analysis, Evolution from System Research to System Design, Production, Evaluation, Customer Support Product Planning • Extracting the system specifications from the objectives of the project definition • "design/develop/manufacture" something (=system) that will produce a product/service (=outputs) which satisfies certain needs (=requirements) • the system needs information, knowledge, and intelligence, human and/or other resources (=inputs) to produce outputs • the system transfers (=functionality) inputs to outputs Product (System) Analysis • Analysis begins with partitioning the functionality into components (interfacing different functions) • components must be complete and unambiguous and implementable (as software, mechanical/electronic hardware) • interaction between components should be simple Product Analysis (Cont..) • main outcome is the system specification that may also contain High level decisions: – choice of technology for each component – basic (e.g. control) structure: centralised/decentralised – assignment of responsibilities • examples of Mechatronic products that passed this stage: automated highways and smart cars. Other Steps in SE • Evolution from Research to Design – Design and Research (e.g. Smart Cars) • conceptual design considering financial and other restrictions • Production or implementation – Rapid-prototypes (Smart Bolts) • Evaluation and verification • Customer Support Customisation of SE • Mechatronic Systems Engineering considers the specific elements of integration or fusion of component disciplines in the systems Engineering context. Examples: – concurrency known from Manufacturing processes – inherent parallelism to be exploited in implementing an embedded system with an intelligent neural network algorithm. Mechatronic Systems • traditional Electronics+Mechanical systems (sequential design method) • Mechatronic systems (concurrent design and synergistic integration) • General System Theory applicable to Mechatronic Systems • Goals of GST :) Modeling and Analysis, Design and Synthesis, Control, Performance Evaluation, Optimization System Behavior • can be defined by state equations • The state of a system at t0 is the information required at t0 such that – output y(t), for all t greater or equal to t0, is uniquely determined from this information and from input u(t) for t greater or equal to t0. • State Space X of a system is the set of all possible values state can take General State Equations • State equations are the set of equations required to specify the state x(t) for all t greater or equal to t0 given x(t0) and u(t) for t greater or equal to t0 – x(t) = f(x(t),u(t),t) x(t0)=x0 – y(t) = g(x(t),u(t),t) Behavioral Classification of Systems • static (independent of past values) or dynamic • dynamic systems are dependent of past values and therefore differential/difference equations are often used to describe the behavior. Dynamic systems can be: – time varying (behavior does change with time) or time invariant Discrete Event Systems (Intro) • time-invariant systems can be linear or nonlinear. Nonlinear systems can be: – continuous (state variable can take any value) or discrete state (state variable є discrete set), • discrete state systems can be time driven (state changes with the time)or event driven (state changes or transitions are forced by asynchronously generated discrete events) • event driven systems can be deterministic or stochastic (at least one output is random) DES (Intro, Cont...) • DES are discrete state and event driven processes (obviously they are nonlinear, dynamic and time-invariant processes): • State space X is a discrete set, state transitions driven by the events are of the form: IF action AND the current state is S1 THEN next state become S2. – g(a1U1+ a2U2 ) NOT = a1 g( U1 ) + a2 g( U2 ) – Output depends on past values of input – behavior when a specific input is applied does not change with time Examples of DES • Queueing Systems containing entities, resources, and the queue (e.g. ATM) • Computer Systems with jobs/tasks competing for resources (CPU, memory, ..) • Manufacturing Systems with production parts and pieces competing for machines and robots... • Interactive multimedia introduction at http://vita.bu.edu/cgc/MIDEDS/ Mathematical Models for DES • untimed models: sample paths represent a sequence of states; S1->e1->S2->e2->S3 • timed models: sample paths also have time instants at which state transitions take place; S1->(e1,t1)->S2->(e2,t2)->S3 • language is the ``universal set’’ of all possible orderings of events that could happen in a system (for untimed models). Mathematical Models (Cont..) • Languages, timed-languages, stochastic timed languages represent three levels of abstractions at which DES are modeled. Automata and Petrinets are the modeling formalisms discussed in the lecture. • E= Set of all possible events => alphabet of the language. Event sequences => words • Can we build a system that represent a given language ? Can we develop the language represented by an existing system ? Do two systems ``speak’’ identical languages ? Language of a DES • language over an event set E is a set of finite-length strings (or words) formed from events in E – eg. E ={start, print-status-report, done} = {s,p,d} – L= {ε, s, sp, spd, sppd, spppd, sd} and ε = empty string – Concatenation(s,p) = > sp, Concatenation(sp,d) = > spd – Concatenation(s, ε) = Concatenation(ε ,s) = s Terminology and Operations • E* is the set of all finite strings of elements of E including ε • E* = {ε,s,ss,sss….,sp,spp,….} is an infinite set • all languages L possible with the event set E are subsets of E* • * is called the Kleene closure operator: Terminology and Operations (Cont...) • Set operations (intersection,union…) can be applied to languages L1,L2... over the event set E (all L1,L2… are subsets of E*) • Concatenation: LaLb :={s ε E*: (S=sa,sb) and (sa ε La) and (sb ε Lb)} • Prefix-closure of L: (L is a subset of E*) L = {s ε E*: for all t ε E* (st ε L)} • L is usually subset or equals to L, if L = L then L is prefix-closed Automata • A language which specifies all possible sequences of events is a formal way of describing the behavior of a DES. • An automata represents a language according to defined set of rules. – nodes of automata represents the states of DES – labeled arcs represent transitions between the states – the set of transition labels is the event set – initial state and marked states need to be defined Deterministic Automata • G = (set of states, set of Events associated with transitions in G, transition_function, active_event_set, initial_state,marked_states) • Fig 2.1 : – f(x,ε) = x – f(x,se) = f(f(x,s),e) for s ε E* and e ε Ε – f(x,gba) = y,f(x,aagb)=z, f(z,b^) = z (n greater/equals 0) Blocking • Language generated by G: L(G)= {s ε E*: f(x_initial,s) defined} • Language marked by G : Lm(G) = {s ε L(G): f(x_initial,s) ε Xm} (fig. 2.2) • Automata G1 and G2 are equivalent if they generate and mark the same language (fig 2.3) • Lm(G) subset/equals Lm(G) subset/equals L(G) • blocking if G reach x : Active event set at x = 0 and x NOT ε Xm • Automation G is blocking if deadlock or livelock happens, when Lm(G) subset (ONLY) of L(G). Nonblocking is the case if Lm(G) = of L(G). Petri Nets (instead of automata) • PN graph is weighted bipartite graph (P,T,A,w) – P is the finite set of places (one type of nodes) – T is the finite set of transitions (another type of nodes) – A is a set of arcs from P --> T and T -->P – w: A ---> {1,2,3,...} is the weight function on the arcs • Marked Petri Net is a five-tuple (P,T,A,w,x): where x is a marking of the set of places P; x=[x(p1), x(p2),...] • row vector x is also considered as the state of the petri net • a transition is enabled if x(pi) greater-equals w(pi,tj)

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posted: | 12/6/2012 |

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