Simulink Solver

Mastering Your Simulation Speed & Accuracy: A Deep Dive into Simulink Solvers

1. Fixed-Step Solvers: Predictable & Powerful for Real-Time 
   

   Fixed-step solvers march through your simulation using a constant time interval (the "step size"). This step size never changes, regardless of what's happening in your model.
   
   Model Configuration Setting:
   

   
   Simulink Model for showcasing how the step size is considering for the system / pre-defined for the system.
   
   
   
   
   

   

   
   Exported Result from "To Workspace" Block

   
   Result: 
                 
   Common Fixed-Step Solvers in Simulink:
   
   - ode1 (Euler)
   
   - ode1be (Backward Euler)
    
   - ode2 (Heun)
   
   - ode3 (Bogacki-Shampine)
   
   - ode4 (Runge-Kutta)
   
   - ode5 (Dormand-Prince)
   
   - ode8 (Dormand-Prince)
   
   - ode14x (extrapolation)
   
   - Discrete (for purely discrete-time models)
   
   - FixedStepAuto (Simulink automatically selects an appropriate fixed-step solver and step size based on model characteristics).
   

2. Variable-Step Solvers: Efficient & Accurate for Offline Analysis
   

   Variable-step solvers are smarter; they adapt their step size during the simulation. When your model's dynamics are changing rapidly (e.g., during a sudden surge or a sharp turn), they take smaller steps to maintain accuracy. When things are relatively stable, they take larger steps to speed up the simulation. This adaptation is based on an error tolerance you define.
   
   Model Configuration Setting:
   

   
   
   Simulink Model for showcasing how the step size is considering for the system / pre-defined for the system.
   
   
   
   
   

   
   
   

   Exported Result from "To Workspace" Block
   
   

   Result:
   
   
   
   

   Common Variable-Step Solvers in Simulink:
   
   - ode15s (stiff / NDF): Good for stiff systems (systems with widely separated time scales).
   
   - ode23 (Bogacki-Shampine): Simpler than ode45, less accurate but can be more efficient for crude error tolerances or mild stiffness.
   
   - ode23s (stiff / Mod. Rosenbrock): Also, for stiff systems, often more efficient than ode15s for crude tolerances.
   
   - ode23t (mod. stiff / Trapezoidal): Good for moderately stiff problems and differential algebraic equations (DAEs).
   
   - ode23tb (stiff / TR-BDF2): Also, for stiff systems.
   
   - ode45 (Dormand-Prince): A good first choice for most continuous systems; a general-purpose solver.
   
   - ode113 (Adams)
   
   - odeN (Non-adaptive)
   
   - daessc (DAE solver for Simscape)
   
   - Discrete (no continuous states): For purely discrete-time models, adapts step size to sample time hits.
   
   Conclusion:
   

   "As we've seen, Simulink's fixed-step and variable-step solvers are powerful tools, each with its distinct strengths. Ignoring them means potentially sacrificing accuracy, wasting simulation time, or hitting roadblocks when moving to hardware.

   By deliberately choosing a fixed-step solver when aiming for deterministic real-time code, you align your model directly with your target hardware's execution rhythm. Conversely, by leveraging a variable-step solver like ode45 for initial design and analysis, you unlock rapid iteration and high fidelity, allowing the solver to intelligently manage the computational load.
   
   
   

   ***Happy Learning***