Transcript 1. Introduction - National Cheng Kung University

CH 1 Introduction
Prof. Ming-Shaung Ju
Dept. of Mechanical Engineering
NCKU
1. Introduction
 What
is adaptive control?
An adaptive controller is a controller with
adjustable parameters and a mechanism
for adjusting the parameters.
 Adaptive control systems have two loops
A
normal feedback with process and
controller
 A parameter adjustment loop (slower
dynamics)
Structure of Adaptive Systems
History of adaptive control theory

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1950s design of autopilots for high performance
aircraft (gain scheduling) speeds & altitude
1960s control theories : state space & stability,
dynamic programming, system identification
1970s different estimation schemes combined
with various design methods
Late 1970s-1980s proofs for stability of
adaptive systems, merge of robust control and
system identification
USA X-15 experimental aircraft
History of adaptive control theory
(cont’d)
1990s robustness of adaptive controllers,
nonlinear system theory help understanding
adaptive control
 2000s related to learning in computer science,
artificial intelligence

Why adaptive control system?
Linear feedback has limited capability to cope
with parameter changes of the process and
variations in disturbance characteristics
 Process variations may due to

 Nonlinear
actuators
 Large deviation of operating point

Examples of variations in disturbance

frequency contents of disturbance
Adaptive Schemes
 Gain
scheduling
 Model-reference adaptive control
 Self-tuning regulator
 Dual control
Gain Scheduling
Speed (Mach no.)
Altitude
Note: command & control signal are not utilized
Model-Reference Adaptive Control
Performance specification
e = ym-y
Self-Tuning Regulator
Indirect adaptive
Desired
System identification
Certainty equivalent principle: estimates are used as if they are true parameters
Dual Control

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Limitation of above schemes: parameter uncertainties not
considered
When Certainty Equivalence Principle is not valid
Augment process state and parameters into a new state and
formulate a nonlinear stochastic control problem
(stochastic optimal control )
Nonlinear estimator: conditional probability distribution
of state p(z｜y, u) (hyper-state)
Feedback controller maps hyperstate to control
Maintain good control and small estimation errors (dual)
Dual Control
Adaptive Control Problem


Process Model

State space model

Transfer function (matrix)

Continuous-time or discrete-time
Controller structure

A controller with adjustable parameters

Direct adaptive control


Parameters tuned without characteristics of the process and its
disturbance
Indirect adaptive control

Process model and disturbance characteristics are estimated then use
these information to design the controller
Design Procedures
1.
2.
3.
4.
Characterize desired behavior of closed-loop
system (stability, performance)
Determine a control law with adjustable
parameters
Find a mechanism for adjusting the parameters
Implement the control law