model reference adaptive control survey of control systems mem 800 l.
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Model Reference Adaptive Control Survey of Control Systems (MEM 800). Presented by Keith Sevcik. Model. y model. Adjustment Mechanism. Controller Parameters. u c. Controller. Plant. u. y plant. Concept.

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Presentation Transcript
concept

Model

ymodel

Adjustment

Mechanism

Controller Parameters

uc

Controller

Plant

u

yplant

Concept
  • 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
mit rule
MIT Rule
  • Tracking error:
  • Form cost function:
  • Update rule:
    • Change in is proportional to negative gradient of

sensitivity

derivative

mit rule4
MIT Rule
  • Can chose different cost functions
  • EX:
  • From cost function and MIT rule, control law can be formed
mit rule5

Reference Model

ymodel

Adjustment Mechanism

-

+

θ

Π

Plant

uc

Π

u

yplant

MIT Rule
  • EX: Adaptation of feedforward gain
mit rule6
MIT Rule
  • For system where is unknown
  • Goal: Make it look like

using plant (note, plant model is scalar multiplied by plant)

mit rule7
MIT Rule
  • Choose cost function:
  • Write equation for error:
  • Calculate sensitivity derivative:
  • Apply MIT rule:
mit rule8

Reference Model

ymodel

Adjustment Mechanism

-

+

θ

Π

Plant

uc

Π

u

yplant

MIT Rule
  • Gives block diagram:
  • considered tuning parameter
mit rule9
MIT Rule
  • NOTE: MIT rule does not guarantee error convergence or stability
  • usually kept small
  • Tuning crucial to adaptation rate and stability.
mrac of pendulum11

Model

ymodel

Adjustment

Mechanism

Controller Parameters

uc

Controller

u

yplant

MRAC of Pendulum
  • Controller will take form:
mrac of pendulum12
MRAC of Pendulum
  • Following process as before, write equation for error, cost function, and update rule:

sensitivity

derivative

mrac of pendulum13
MRAC of Pendulum
  • Assuming controller takes the form:
mrac of pendulum15
MRAC of Pendulum
  • If reference model is close to plant, can approximate:
mrac of pendulum16
MRAC of Pendulum
  • From MIT rule, update rules are then:
mrac of pendulum17

Reference Model

ymodel

-

+

Π

+

-

uc

yplant

θ1

e

Plant

Π

θ2

Π

Π

MRAC of Pendulum
  • Block Diagram
mrac of pendulum18
MRAC of Pendulum
  • Simulation block diagram (NOTE: Modeled to reflect control of DC motor)
mrac of pendulum19
MRAC of Pendulum
  • Simulation with small gamma = UNSTABLE!
mrac of pendulum20
MRAC of Pendulum
  • Solution: Add PD feedback
mrac of pendulum21
MRAC of Pendulum
  • Simulation results with varying gammas
experimental results25
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
conclusions
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)