Advances in PID Control

1. Introduction.- 1.1 Evolution of the PID Controller.- 1.2 Components of the PID Controller.- 1.2.1 The Proportional part.- 1.2.2 The Integral part.- 1.2.3 The Derivative part.- 1.3 Choice of Controller Type.- 1.3.1 On/Off controller.- 1.3.2 P controller.- 1.3.3 PD controller.- 1.3.4 PI controller.- 1.3.5 PID controller.- 1.4 Nomenclature of the PID Controller.- 1.5 Structures of the PID Controller.- 1.5.1 Parallel type.- 1.5.2 Series type.- 1.5.3 Relationship between Parallel and Series types.- 1.5.4 Incremental type.- 2. Classical Designs.- 2.1 Introduction.- 2.2 Design Objectives - Speed Versus Stability.- 2.3 Trial and Error Method.- 2.4 The Ziegler-Nichols Methods.- 2.4.1 The step response method.- 2.4.2 The frequency response method.- 2.4.3 The modified generalized frequency response method.- 2.5 The Stability Limit Method.- 2.6 The Cohen-Coon Method.- 2.7 The Tyreus-Luyben Method.- 3. Modern Designs.- 3.1 Introduction.- 3.2 Constraints of Classical PID Control.- 3.3 Pole Placement Design.- 3.3.1 PI control of first-order systems.- 3.3.2 PID control of second-order systems.- 3.3.3 General case.- 3.4 Dominant Pole Placement.- 3.5 Gain and Phase Margin Design I: PI Controller.- 3.5.1 The design method.- 3.5.2 Simulation study.- 3.6 Gain and Phase Margin Design II: PID Controller.- 3.6.1 Simulation study.- 3.7 Linear Quadratic Control Design.- 3.7.1 LQR solution for time-delay systems.- 3.7.2 PI tuning for first-order modeling.- 3.7.3 Simulation study.- 3.7.4 Extension to second-order modeling.- 3.7.5 Robustness analysis.- 3.8 Composite PI-Adaptive Control Design.- 3.8.1 Problem formulation.- 3.8.2 PI control based on first-order dominant model.- 3.8.3 Nonlinear adaptive control.- 3.8.4 Passivity of dynamical systems.- 3.8.5 Simulation study.- 4. Automatic Tuning.- 4.1 Introduction.- 4.1.1 Methods based on step response analysis.- 4.1.2 Methods based on frequency response analysis.- 4.2 Step Response Approach.- 4.2.1 Modeling from a step test.- 4.2.2 Simulation study.- 4.3 Relay Feedback Approach.- 4.3.1 Basic idea.- 4.3.2 Improved estimation accuracy.- 4.3.3 Estimation of a general point.- 4.3.4 Estimation of multiple points.- 4.4 On-line Relay Tuning.- 4.4.1 Configuration.- 4.4.2 Structure identification.- 4.4.3 Assessment of Control Performance.- 4.4.4 Controller design.- 4.5 FFT on Relay Transients.- 4.5.1 The FFT-Relay Method.- 4.5.2 Simulation study.- 4.6 Frequency Response - Transfer Function Conversion.- 4.6.1 Single and multiple lag processes.- 4.6.2 Second-order modeling.- 4.7 Continuous Self-Tuning of PID Control.- 4.7.1 Process estimation from load disturbance response.- 4.7.2 PID adaptation.- 5. Multi-loop Control.- 5.1 Introduction.- 5.2 The Modified Ziegler-Nichols Method.- 5.3 Review of the BLT (Biggest Log-Modulus Tuning).- 5.4 Modified Ziegler-Nichols Method for Multi-Loop Processes.- 5.5 Derivation of the Design Equations.- 5.6 Simulation study.- 5.7 Extension to Cross-coupled Controllers.- 6. Practical Issues.- 6.1 Introduction.- 6.2 Non-linearities.- 6.2.1 Transducer characteristics.- 6.2.2 Friction.- 6.2.3 Saturation.- 6.2.4 Hysteresis.- 6.2.5 Dead zone.- 6.2.6 Process characteristics.- 6.2.7 Gain scheduling.- 6.3 Disturbances.- 6.3.1 Set point changes.- 6.3.2 Low frequency drift.- 6.3.3 High frequency noise.- 6.4 Operational Aspects.- 6.4.1 Set point weighting.- 6.4.2 Auto-manual bumpless transfer.- 6.5 Digital PID Implementation.- 6.5.1 Selection of sampling interval.- 6.5.2 Discretization.- A. Industrial Controllers.- A.l ABB COMMANDER 351.- A.2 Elsag Bailey Protonic 500/550.- A.3 Foxboro 718PL/PR.- A.4 Honeywell UDC3300.- References.