23.2 Simulink for system modeling and simulation

Simulink is a powerful tool for modeling and simulating dynamic systems. It uses block diagrams to represent mathematical models, making it easy to visualize and analyze complex systems. With its extensive library of blocks, you can quickly build and test various designs.

Simulink supports both continuous-time and discrete-time systems, as well as state-space models and transfer functions. By setting simulation parameters and choosing appropriate solvers, you can fine-tune your simulations for accuracy and speed. Subsystems help organize large models into manageable chunks.

Simulink Basics

Introduction to Simulink

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• Simulink is a graphical programming environment for modeling, simulating, and analyzing multidomain dynamical systems
• Provides an interactive graphical environment and a customizable set of block libraries for designing, simulating, implementing, and testing various time-varying systems
• Integrates seamlessly with MATLAB, enabling the incorporation of MATLAB algorithms into models and exporting simulation results to MATLAB for further analysis

Block Diagrams and Model-Based Design

• Simulink uses block diagrams to represent mathematical models of dynamic systems
• Block diagrams consist of blocks interconnected by lines, representing the flow of signals and data between system components
• Blocks can represent mathematical operations, input/output relationships, or complex subsystems (Gain block, Integrator block, Scope block)
• Model-Based Design is a development methodology that uses Simulink to create a system model, which serves as the basis for simulation, verification, and code generation
• Enables rapid iteration and refinement of designs, reducing development time and improving system quality (V-model development process)

Simulink Library Blocks

• Simulink provides an extensive library of predefined blocks for building models
• Library blocks are organized into categories based on their functionality (Math Operations, Continuous, Discrete, Sources, Sinks)
• Users can customize existing blocks or create their own custom blocks using MATLAB functions or S-functions
• Library blocks can be dragged and dropped into the Simulink editor to create models
• Blocks can be parameterized to specify their behavior and characteristics (Sample time, Initial conditions, Block parameters)

System Modeling

Continuous-time and Discrete-time Systems

• Continuous-time systems are characterized by variables that change continuously over time
• Represented by differential equations in Simulink (Integrator block, Transfer Function block)
• Discrete-time systems are characterized by variables that change at discrete time intervals
• Represented by difference equations in Simulink (Unit Delay block, Discrete Transfer Function block)
• Simulink supports the modeling and simulation of both continuous-time and discrete-time systems

State-space Models and Transfer Functions

• State-space models describe a system using a set of first-order differential equations
• Consist of state variables, inputs, outputs, and a set of matrices (A, B, C, D) that define the relationships between them
• Simulink provides blocks for creating and simulating state-space models (State-Space block)
• Transfer functions describe the input-output relationship of a linear time-invariant (LTI) system in the frequency domain
• Represented by a ratio of polynomials in the Laplace domain (s) for continuous-time systems or the Z-domain (z) for discrete-time systems
• Simulink provides blocks for creating and simulating transfer function models (Transfer Function block)

Simulation Setup

Simulation Parameters

• Simulation parameters control the behavior of the simulation, such as the simulation time, step size, and solver type
• Start and stop times define the duration of the simulation (seconds, minutes, hours)
• Step size determines the time interval between simulation steps (Fixed-step, Variable-step)
• Simulink provides a Simulation Parameters dialog box for configuring these settings

Solvers and Simulation Modes

• Solvers are numerical methods used to compute the system's behavior over time
• Simulink offers a variety of solvers for different types of systems (ode45, ode23, ode15s)
• Solvers can be fixed-step or variable-step, depending on the system's characteristics and the desired trade-off between accuracy and simulation speed
• Simulation modes determine how Simulink executes the simulation (Normal mode, Accelerator mode, Rapid Accelerator mode)
• Normal mode is the default mode, suitable for most simulations
• Accelerator and Rapid Accelerator modes can significantly speed up simulations by compiling the model into an executable

Subsystems and Model Organization

• Subsystems are used to organize large models into hierarchical, modular structures
• Subsystems encapsulate a portion of the model, making it easier to understand, maintain, and reuse
• Simulink provides virtual and non-virtual subsystems (Virtual subsystems do not have separate execution contexts)
• Subsystems can be masked, allowing users to create custom interfaces and parameterize the subsystem (Mask Editor)
• Model organization techniques, such as subsystems and model referencing, help manage complexity and facilitate collaboration among team members