CH 1 Introduction Prof. Ming-Shaung Ju Dept. of Mechanical Engineering NCKU

1. Introduction What is adaptive control? 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 Adaptive control systems have two loops A normal feedback with process and controller A normal feedback with process and controller A parameter adjustment loop (slower dynamics) A parameter adjustment loop (slower dynamics)

Structure of Adaptive Systems

History of adaptive control theory 1950s design of autopilots for high performance aircraft (gain scheduling) speeds & altitude 1950s design of autopilots for high performance aircraft (gain scheduling) speeds & altitude 1960s control theories : state space & stability, dynamic programming, system identification 1960s control theories : state space & stability, dynamic programming, system identification 1970s different estimation schemes combined with various design methods 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 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 1990s robustness of adaptive controllers, nonlinear system theory help understanding adaptive control 2000s related to learning in computer science, artificial intelligence 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 Linear feedback has limited capability to cope with parameter changes of the process and variations in disturbance characteristics Process variations may due to Process variations may due to Nonlinear actuators Nonlinear actuators Large deviation of operating point Large deviation of operating point Examples of variations in disturbance Examples of variations in disturbance frequency contents of disturbance frequency contents of disturbance

Adaptive Schemes Gain scheduling Gain scheduling Model-reference adaptive control Model-reference adaptive control Self-tuning regulator Self-tuning regulator Dual control Dual control

Gain Scheduling Speed (Mach no.) Altitude Note: command & control signal are not utilized

Model-Reference Adaptive Control Performance specification e = y m -y

Self-Tuning Regulator System identification Desired Indirect adaptive Certainty equivalent principle: estimates are used as if they are true parameters

Dual Control Limitation of above schemes: parameter uncertainties not considered Limitation of above schemes: parameter uncertainties not considered When Certainty Equivalence Principle is not valid 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 ) 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) Nonlinear estimator: conditional probability distribution of state p(z ｜ y, u) (hyper-state) Feedback controller maps hyperstate to control Feedback controller maps hyperstate to control Maintain good control and small estimation errors (dual) Maintain good control and small estimation errors (dual)

Dual Control

Adaptive Control Problem Process Model Process Model State space model State space model Transfer function (matrix) Transfer function (matrix) Continuous-time or discrete-time Continuous-time or discrete-time Controller structure Controller structure A controller with adjustable parameters A controller with adjustable parameters Direct adaptive control Direct adaptive control Parameters tuned without characteristics of the process and its disturbance Parameters tuned without characteristics of the process and its disturbance Indirect adaptive control Indirect adaptive control Process model and disturbance characteristics are estimated then use these information to design the controller Process model and disturbance characteristics are estimated then use these information to design the controller

Design Procedures 1. Characterize desired behavior of closed-loop system (stability, performance) 2. Determine a control law with adjustable parameters 3. Find a mechanism for adjusting the parameters 4. Implement the control law