• Flow and speed variations
– – – – Concentration control Steel rolling mills Paper machines Rotary kilns
• Wide operating range with a nonlinear system
Lecture One Class Introduction
Instructor: Dr. ZHENG Yi（郑毅）
Nov. 9, 2016 E-mail: yizheng@ Webpage:
Today’s Agenda
• • • • What is Adaptive Control? Why Adaptive Control? Class Logistics Questions?
Standard Adaptive Controller
Fixed-Gain Control
• Requires accurate system modelling
– Trade-off performance with uncertainty (May fail under high level of uncertainty) – Tuned to worst case rather than real physical system
• According to the Webster’s dictionary, adaptation means:
– adjustment to environmental conditions – alteration or change in form or structure to better fit the environment
2Байду номын сангаас
What is “adaptive”?
• According to the Webster’s dictionary, to adapt means:
– to adjust oneself to particular conditions – to bring oneself in harmony with a particular environment – to bring one’s acts, behavior in harmony with a particular environment
• Environmental changes • Change in dynamics • Structural damage
Adaptive Control
• Achieves a given system performance asymptotically
– Does not excessively rely on models – Does not trade performance for modeling accuracy – Improves itself under unforeseen, adverse conditions
• Deal with uncertainties
– plant change: component-to-component variation, aging, wearing, etc. – operating environment change: disturbances – unmodeled dynamics: ignored slow dynamics
– Flight control
• Variations in Disturbance Dynamics
– Wave characteristics in ship steering – Raw materials in process industries
A Brief History
• 1950s: Heuristic design of adaptive control for autopilot • 1960s: MIT rules, model reference adaptive control (with stability guarantee) • 1970s: real breakthrough in the development of rigorous theory: Lyapunov design, stability analysis. • 1980s: instability of adaptive systems was brought to focus. Robust adaptive control became a very hot topic. • 1990s: Nonlinear adaptive control design methodology development dominated. • 2000s: Focus on applications
• Effect depends on the desired closed-loop bandwidth • Better to use frequency responses
Effect of Process Variations
Example 1.1: Consider the system given by for a=-0.01, 0, 0.01 Feedback control law u=uc-y
Where is adaptive control used?
• • • • • • Aerospace Automotive Process control Communication Web search ….
Application
• Case study one: Patriot air defense missile & Scud missiles
Effect of Process Variations
• Example 1.2: Consider the system for T=0,0.015,0.03
Feedback control law u=uc-y
Figure: Open-loop responses
Figure: Unit Step closed-loop responses
Adaptive Schemes
• Dual Control
Types of AC systems
• Parametric adaptive control: Controller structure is fixed, the parameters are updated on-line.
And Many others…
Adaptive Schemes
• Gain Scheduling
Adaptive Schemes
• Model Reference Adaptive Systems (MRAS)
Adaptive Schemes
• Self-Tuning Regulators (STR)
What is Adaptive Control?
• Adaptive Control:
– A controller with adjustable parameters and a mechanism for adjusting the parameters (Adaptive Control, Astrom and Wittenmark) – A control system that can modify its behavior in response to changes in the dynamics of the process and the disturbances. – A control method used by a controller which must adapt to a controlled system with parameters which vary, or are initially uncertain. (Wikipedia)
Constraints: min t max Hit accuracy
Application (cont.)
• Case study two: Fighter attack Trajectory unknown Constraints：
• Tracking trajectory • Hit accuracy • Min t
Effect of Process Variations
Figure: Open-loop Bode plots
Figure: Closed-loop Bode plots
Effect of Process Variations
• Nonlinear actuators or sensors
– Nonlinear valves
Judging the severity of process variations
• Difficult to judge impact of process variations on closed-loop behavior from open-loop time responses
– Significant changes in open-loop responses may have little effect on closed-loop response – Small changes in open-loop responses may have significant effect on closed-loop response
• Achieve high performance • Take advantage of available on-line computation resources • …