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Contents
Contents
Course on Dynamics of multidisplicinary and controlled Systems
Christian Schmid
Contents
Introduction into System Control
Control objectives
Open loop vs closed loop
The basic structure of closed-loop systems
The Laplace transform
Definition
Correspondences of the Laplace transform
Main theorems of the Laplace transform
The inverse Laplace transform
Solving linear differential equations using the Laplace transform
Laplace transform of the impulse δ(t) and step σ(t)
Transfer functions
Definition
Interpretation of the transfer function
Realisability and properness of transfer functions
Transfer functions with dead time
Poles and zeros of the transfer function
Using transfer functions for calculations
Frequency Response
Definitions
Nyquist plot of a frequency response
Bode plot
Some important transfer function elements
The proportional element (P element)
The integrator (I element)
The derivative element (D element)
The 1st-order lag element (PT
1
element)
The proportional plus derivative element (PD element)
The derivative lag element (DT
1
element)
The 2nd-order lag element (PT
2
element and PT
2
S element)
Bandwidth of a system
Example for the construction of a Bode plot
Systems with minimum and non-minimum phase behaviour
Systems with dead time
Stability of linear control systems
Stable and unstable systems
Definition of stability and stability conditions
Algebraic stability criteria
The Hurwitz criterion
Routh criterion
Nyquist criterion
Nyquist criterion using Nyquist plots
Simplified forms of the Nyquist criterion
The Nyquist criterion using Bode plots
The root-locus method
Introduction and basic ideas
General rules for constructing root loci
Example of an application of the root-locus method
Behaviour of linear continuous-time control systems
Dynamical behaviour of a closed loop system
Static properties of the closed loop
Transfer function G
0
(s) with delayed P behaviour
Transfer function G
0
(s) with delayed I behaviour
Transfer function G
0
(s) with delayed I
2
behaviour
Performance indices
Time-response specifications
Integral performance indices
Determination of quadratic performance indices
PID control and associated controller types
The classical three-term PID controller
Optimal tuning of PID controllers
Advantages and disadvantages of the different types of controllers
Empirical tuning rules according to Ziegler and Nichols
Design of controllers using pole-zero compensators
Characteristics in frequency and time domain
Controller design using frequency domain characteristics
Application of the design using frequency domain characteristics
Controller design using the root-locus method
Compensator design methods
Basic ideas of compensator design
Design by specifying the closed-loop transfer function
The method of Truxal and Guillemin
Generalised compensator design method
The basic idea
Zeros of the closed loop
The synthesis equations
Application of the method
Compensator design for reference and disturbances
Structure of the closed loop
The design procedure
Design of the pre-filter
Application of the design method
Improving the control behaviour by more complex loop structures
Problem
Disturbance feed-forward control
Disturbance feed-forward on the controller
Disturbance feed-forward on the manipulated variable
Control systems with an auxiliary manipulated variable
Cascade control systems
Control system with auxiliary manipulated variable
Control system with anti-windup measure
State-space representation
State-space representation of single-input-single-output systems
State-space representation of multi-input-multi-output systems
The relationship between transfer functions and the state-space representation
State-space vs transfer function approach
Uniqueness of the state variables
Controllability and observability
Design of state-feedback control systems
Structures and properties of state-feedback control systems
State-feedback control with integrator
Design of state-feedback controllers by pole placement
Design of a system in controller canonical form
Design using Ackermann's formula
State reconstruction using observers
Structure of an observer
Design of observers
Combined observer-controllers
Example of a state-feedback control system
Introduction to fuzzy techniques
Crisp and fuzzy logic
Why use fuzzy logic for control ?
Ideas of the fuzzy control methodology
Basics of fuzzy sets
Fuzzy sets
Membership functions
Elementary operators for fuzzy sets
Fuzzy relations
Fuzzy composition
Fuzzy systems
Fuzzification
Fuzzy inference machine
Defuzzification
Centre of gravity method (COG)
Centre of singleton method (COS)
Maximum methods
Margin properties of the centroid methods
The Takagi-Sugeno fuzzy system
The components of a fuzzy system
Fuzzy control
Basic structure of a fuzzy controller
Transfer behaviour of fuzzy controllers
Representation using 2D characteristics
Influence of the membership functions and rule base on the characteristic
Representation using 3D characteristics
Example of a fuzzy control system
Loading crane plant model
Fuzzy control system design
Contribution of fuzzy control
Mathematical and table appendix
The Laplace transform
Convergence
The inverse Laplace transform
Main theorems of the Laplace transform
The complex G-plane
Detailed analysis of 2nd-order lag elements
Determining resonances of 2nd-order lag elements
Poles and step responses of 2nd-order lag elements
The law of Bode and the Hilbert transformation
Stability considerations using the weighting function
Equivalence of the Hurwitz and Routh criteria
Determination of J
ISE
using determinants
Tables
Christian Schmid 2005-05-09
