1. Model Reference Adaptive Control Survey of Control Systems (MEM 800)
Presented by Keith Sevcik

2. Concept
Controller
Model
Adjustment
Mechanism
Plant
Controller Parameters
ymodel u
yplant uc
Design controller to drive plant response to mimic ideal response (error = yplant-ymodel => 0)
Designer chooses: reference model, controller structure, and tuning gains for adjustment mechanism

3. MIT Rule Tracking error: Form cost function: Update rule:
Change in is proportional to negative gradient of
sensitivity
derivative

4. MIT Rule Can chose different cost functions EX:
From cost function and MIT rule, control law can be formed

5. MIT Rule EX: Adaptation of feedforward gain Π Adjustment Mechanism
ymodel u
yplant uc Π θ
Reference Model
Plant - +

6. MIT Rule For system where is unknown Goal: Make it look like
using plant (note, plant model is scalar multiplied by plant)

7. MIT Rule Choose cost function: Write equation for error:
Calculate sensitivity derivative:
Apply MIT rule:

8. MIT Rule Gives block diagram: considered tuning parameter Π
Adjustment Mechanism
ymodel u
yplant uc Π θ
Reference Model
Plant - +

9. MIT Rule
NOTE: MIT rule does not guarantee error convergence or stability
usually kept small
Tuning crucial to adaptation rate and stability.

10. MRAC of Pendulum
System d2 d1 dc T

11. MRAC of Pendulum Controller will take form: Model Adjustment Mechanism
Controller Parameters
ymodel u
yplant uc

12. MRAC of Pendulum
Following process as before, write equation for error, cost function, and update rule:
sensitivity
derivative

13. MRAC of Pendulum
Assuming controller takes the form:

14. MRAC of Pendulum

15. MRAC of Pendulum
If reference model is close to plant, can approximate:

16. MRAC of Pendulum
From MIT rule, update rules are then:

17. MRAC of Pendulum Block Diagram Π ymodel e yplant uc θ1 Reference Model+ - θ2

18. MRAC of Pendulum
Simulation block diagram (NOTE: Modeled to reflect control of DC motor)

19. MRAC of Pendulum
Simulation with small gamma = UNSTABLE!

20. MRAC of Pendulum
Solution: Add PD feedback

21. MRAC of Pendulum
Simulation results with varying gammas

22. LabVIEW VI Front Panel

23. LabVIEW VI Back Panel

24. Experimental Results

25. Experimental Results PD feedback necessary to stabilize system
Deadzone necessary to prevent updating when plant approached model
Often went unstable (attributed to inherent instability in system i.e. little damping)
Much tuning to get acceptable response

26. Conclusions
Given controller does not perform well enough for practical use
More advanced controllers could be formed from other methods
Modified (normalized) MIT
Lyapunov direct and indirect
Discrete modeling using Euler operator
Modified MRAC methods
Fuzzy-MRAC
Variable Structure MRAC (VS-MRAC)