Modelling (II) Model-based design

Why Modelling? Why spend so much time talking about modelling? Model is a imagination/graphical/mathematical representation of a system Models allow imagination, simulation and analysing, and never exact Modelling depends on your goal A single system may have many models Large ‘libraries’ of standard model template exists A conceptually new model can be a big deal (economic, DNA, protein, brain) Main goals of modelling in Engineering Conceptual design, the rest is routine Analysis Simulation Optimization Perceived results

Modelling (Cycle) 1.Analysis and modelling 2.Simulation 3.System development 4.Optimisation (talk later) 5.Validation and verification

1. Analysis and modelling Deterministic models Control model, gravity, thermal Indeterministic and uncertain models Travelling, gambling, stock price Static models Perspectives Dynamic models Newton mechanics, x’ = f(x, t)

Timing: Samples and Continuous Sampled and continuous Continuous time = Physical system + Digital Control

Servo-System Modelling First principle model Electro-mechanical + computer sampling

Finite State Machines Digital control TCP/IP state machines Complexity Implementable

Hybrid Systems Model Combination of continuous-time dynamic and a state-machine Eg. Thermostat Analytical tools are not fully available Using tools for simulation, Matlab, Mathworks

Partial Differential Equation (PDE) Model Include functions of spatial variables electromagnetic fields mass and heat transfer fluid dynamics structural deformations Model reduction is necessary Computational fluid dynamic (CFD) Eg. Fit step response

2. Simulation Examples Dynamic model: x’=f(x,t) Euler integration methods: x(t+d) = x(t) + d*f(x(t), t) Runge-Kutta method: ode45 in Matlab Models Integration State machine + randomness Probabilistic model Challenges Not a complete picture - need to be aware of that Mixture of continuous and sampled time State machine and continuous logic Complex systems (a lot of subsystems) state machines and hybrid logic

3. System Development Model development is an art skills and experiences help White box models Known models, eg. PDE, FSM, Markov models Black box models Date driven, eg. neural network Grey box models Known with some unknown parameters Identification of model parameters Assumption: model structure Collect plant data Tweak model parameters to achieve a good fit

Empirical Models

4. Validation Big pictures Simulation and includes everything

Real-Time Embedded Systems

Modelling Cycle 1.Analysis and modelling 2.Simulation 3.System development 4.Optimization 5.Validation and verification