LPV and LTV Models
Create, manipulate, analyze, and simulate linear parameter-varying (LPV) and linear time-varying models (LTV). These models can approximate nonlinear systems and allow you to efficiently apply linear design techniques to nonlinear models.
With the available functionality, you can:
Create LPV or LTV models from mathematical expressions.
Create LPV or LTV models that interpolate linearization results over a grid of operating conditions.
Simulate time response.
Specify signal-based connections between varying models and with LTI models.
Sample dynamics over a grid of parameters to obtain local LTI approximations.
Discretize and resample LPV or LTV models.
|Linear parameter-varying state-space model (depuis R2023a)|
|Linear time-varying state-space model (depuis R2023a)|
|Access test values for validating data function (depuis R2023a)|
|Modify test values for validating data function (depuis R2023a)|
|Compute operating condition from specifications (depuis R2023b)|
Sampling and Interpolation
Time Response Simulation
|Step response of dynamic system|
|Impulse response plot of dynamic system; impulse response data|
|Plot simulated time response of dynamic system to arbitrary inputs; simulated response data|
|System response to initial states of state-space model|
|Options for step or impulse responses (depuis R2023a)|
Continuous-Time Varying Systems
|Varying Lowpass Filter||Butterworth filter with varying coefficients|
|Varying Notch Filter||Notch filter with varying coefficients|
|PID Controller||Continuous-time or discrete-time PID controller|
|PID Controller (2DOF)||Continuous-time or discrete-time two-degree-of-freedom PID controller|
|Varying Transfer Function||Transfer function with varying coefficients|
|Varying State Space||State-space model with varying matrix values|
|Varying Observer Form||Observer-form state-space model with varying matrix values|
Discrete-Time Varying Systems
|Discrete Varying Lowpass||Discrete Butterworth filter with varying coefficients|
|Discrete Varying Notch||Discrete-time notch filter with varying coefficients|
|Discrete PID Controller (2DOF)||Discrete-time or continuous-time two-degree-of-freedom PID controller|
|Discrete PID Controller||Discrete-time or continuous-time PID controller|
|Discrete Varying Transfer Function||Discrete-time transfer function with varying coefficients|
|Discrete Varying State Space||Discrete-time state-space model with varying matrix values|
|Discrete Varying Observer Form||Discrete-time observer-form state-space model with varying matrix values|
LTV and LPV Model Basics
Using Analytic LTV and LPV Models
- LPV Model of Bouncing Ball
Construct an LPV representation of a system that exhibits multi-mode dynamics.
- LPV Model of Engine Throttle
Model engine throttle behavior as a linear parameter-varying system.
- Analysis of Gain-Scheduled PI Controller
Analyze gain-scheduled PI control of an LPV system.
- LPV Model of Magnetic Levitation System
Create analytic LPV model from linearized equations of magnetic levitation system.
- Gain-Scheduled LQG Controller
Demonstrate instability in gain-scheduled control when parameters vary too quickly.
Using Gridded LTV and LPV Models
- LPV Approximation of Boost Converter Model
Obtain linear parameter-varying approximation of a nonlinear Simscape™ Electrical™ model.
- Design and Validate Gain-Scheduled Controller for Nonlinear Aircraft Pitch Dynamics
Approximate nonlinear behavior of airframe pitch axis dynamics using linear parameter-varying model.
- LPV Model of Magnetic Levitation Model from Batch Linearization Results
Create a gridded LPV model from batch linearization results of a magnetic levitation model.
- Reduced Order Modeling of a Nonlinear Dynamical System as an Identified Linear Parameter Varying Model (System Identification Toolbox)
Identify a linear parameter varying reduced order model of a cascade of nonlinear mass-spring-damper systems.