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 (PT1 element)
    • The proportional plus derivative element (PD element)
    • The derivative lag element (DT1 element)
    • The 2nd-order lag element (PT2 element and PT2 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 G0(s) with delayed P behaviour
    • Transfer function G0(s) with delayed I behaviour
    • Transfer function G0(s) with delayed I2 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 in the frequency domain
    • Steady state of the closed-loop system
  • State-feedback control with integrator
  • Design of state-feedback controllers by pole placement
    • Design of a system in controller canonical form
      • Design of a system not in a 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
      • Derivative theorem
      • Integral theorem
      • Convolution in the time domain
      • Convolution in the frequency domain
      • Initial value theorem
      • Final value theorem
  • 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 JISE using determinants
  • Tables