3.2 Model reference adaptive control (MRAC) structure

Model Reference Adaptive Control (MRAC) is a powerful technique that uses a reference model to guide system behavior. It adapts controller parameters in real-time, making it ideal for systems with unknown or changing dynamics, like aircraft and robots.

MRAC systems have several key components working together. The reference model sets the desired behavior, while the adjustable controller and adaptation mechanism work to make the plant match this ideal. This approach improves performance and handles uncertainties effectively.

Model Reference Adaptive Control (MRAC) Structure

Concept of MRAC

Top images from around the web for Concept of MRAC

• 

  Frontiers | Model Reference Predictive Adaptive Control for Large-Scale Soft Robots View original

  Is this image relevant?

• 

  Frontiers | Model Reference Predictive Adaptive Control for Large-Scale Soft Robots View original

  Is this image relevant?

• 

  Frontiers | Adaptive Control Strategies for Interlimb Coordination in Legged Robots: A Review View original

  Is this image relevant?

• 

  Frontiers | Model Reference Predictive Adaptive Control for Large-Scale Soft Robots View original

  Is this image relevant?

• 

  Frontiers | Model Reference Predictive Adaptive Control for Large-Scale Soft Robots View original

  Is this image relevant?

1 of 3

Top images from around the web for Concept of MRAC

• 

  Frontiers | Model Reference Predictive Adaptive Control for Large-Scale Soft Robots View original

  Is this image relevant?

• 

  Frontiers | Model Reference Predictive Adaptive Control for Large-Scale Soft Robots View original

  Is this image relevant?

• 

  Frontiers | Adaptive Control Strategies for Interlimb Coordination in Legged Robots: A Review View original

  Is this image relevant?

• 

  Frontiers | Model Reference Predictive Adaptive Control for Large-Scale Soft Robots View original

  Is this image relevant?

• 

  Frontiers | Model Reference Predictive Adaptive Control for Large-Scale Soft Robots View original

  Is this image relevant?

1 of 3

• Adaptive control technique employs reference model to specify desired closed-loop performance
• Forces plant output to track reference model output adapting controller parameters in real-time
• Compensates for uncertainties in plant dynamics handling nonlinearities and disturbances
• Improves performance for systems with unknown or varying parameters (aircraft control, robotics)

Components of MRAC systems

• Reference model specifies desired closed-loop behavior as stable, linear time-invariant system
• Adjustable controller contains tunable parameters generating control input to plant
• Adaptation mechanism updates controller parameters using error between plant and reference model outputs
• Plant represents system to be controlled with potentially unknown or varying parameters
• Error signal measures difference between plant and reference model outputs
• Control input generated by adjustable controller manipulates plant behavior

Adaptation laws for controllers

• Error equation: $e(t) = y_p(t) - y_m(t)$ where $y_p(t)$ is plant output and $y_m(t)$ is reference model output
• Gradient descent method minimizes cost function based on error
• MIT rule adaptation law: $\frac{d\theta}{dt} = -\gamma e \frac{\partial e}{\partial \theta}$ where $\theta$ is controller parameter and $\gamma$ is adaptation gain
• Lyapunov-based adaptation laws ensure stability and convergence
• Parameter projection constrains parameter estimates within known bounds

Stability analysis of MRAC

• Lyapunov stability theory constructs function $V(e, \tilde{\theta})$ where $e$ is tracking error and $\tilde{\theta}$ is parameter estimation error
• Stability analysis proves $\dot{V} \leq 0$ for asymptotic stability
• Barbalat's lemma proves convergence when $\dot{V} \leq 0$
• Persistence of excitation ensures parameter convergence
• Robustness analysis employs $\sigma$-modification and $e$-modification techniques
• Transient performance analyzes overshoot and settling time
• Steady-state error evaluates asymptotic tracking performance