An Overview of Emerging Trends in Nonlinear Control

Outline

• Linearization
• State Transition Matrix, Eigenvalues and Eigenvectors
• Controllability and Observability
• State Variable and Output Feedback, Pole-Placement Design, General Eigenstructure Assignment problem
• Full-Order Observers and Reduced-Order Observers
• An Introduction to the Calculus of Variations
• The Minimum Principle
• Linear-Quadratic Optimal Control. Optimal Regulators and Observers.
• References
  

Control System Design

Fig. 1. Categories of Control Systems

Steps in Control System Design

Linear State Variable Feedback Regulator:

Given the System:

,

The linear state feedback regulator control law (Control Logic or Controller) is defined as:

Design Problem: Find the Gain Matrix K such that the closed loop system is:

a) Stable

b) Has the Desired Time Response Characteristics

Pole-Placement Design Technique:

(i) Select n Desired Pole Locations, Form the Desired Characteristic Polynomial

(ii) Closed-Loop Characteristic Polynomial of the State Feedback Regulator is given by:

(iii) Compute the Elements of K by Equating the Coefficients of Like Powers of in (I) and (ii). [Click Here for a Flow Chart of the Pole Placement Method]

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