CPB 410

Prescribed Textbooks

The following textbook is prescribed. This book will be used for the duration of the module and all students should have a copy.

• Luyben, W.L., Process Modelling, Simulation and Control for Chemical Engineers, second edition, McGraw‑Hill 1990.

The following two textbooks are recommended:

• Seborg, D.E., Edgar, T.F., Mellichamp. D.E., Process Dynamics and Control, Wiley, 2nd edition, 2004.
• Stephanopoulos, G., Chemical Process Control: An Introduction to Theory and Practice, Prentice‑Hall 1984 (Unfortunately out of print, but still an excellent text.)

These books cover essentially the same material, but will be useful to broaden the student’s insight. Each study module will refer to the prescribed book as well as the two recommended books.

General Objectives

In this module the student must develop the necessary skills to design controllers and understand the main principles of process control. Feedback control, feedforward control, advanced control, model predictive control, discrete control, and process identification are topics that are addressed. The tools developed in CPD320 are extended to allow for stability and performance analysis of closed loop systems in the time-, Laplace-, frequency- and z-domains. After completing the module the student will be able to:

• Understand the principle of feedback control in the Laplace, Frequency and time domains and be able to design feedback controllers using relevant techniques and to analyse the behaviour of such systems.
• Understand and apply the the major controller tuning techniques.
• Be able to define performance measures and analyse the performance of a feedback controller
• Understand the principle of feedforward control and design and analyse feedforward controllers
• Understand the principle of model predictive control and the internal model control structure.
• Use z-domain analysis to design and understand discrete controllers.
• Apply the basic process identification techniques to obtain a process model.

Study Themes

Conventional feedback control

On completion of this study theme the student should be able to do the following:

• Define the control objective(s) for a certain system
• Identify the controlled variable, the manipulated variable and the disturbance or load variable for a specific system.
• Understand that feedback control is a corrective and not an anticipatory action
• Understand how the hardware of a feedback control loop works ( measuring sensors, transmitters, controllers and final control elements)
• Understand that the hardware elements in the control loop, apart from the process to be controlled, also exhibit time dependent behaviour.
• Represent the feedback control loop in block format and realise that the variables are represented as deviation variables.
• Be able to determine the sign of the proportional gain of the feedback controller and how this affects control action. (ie direct and reverse, or indirect action)
• Understand what is meant with proportional control and that the magnitude of the proportional gain will influence the speed of response of the controller.
• Be fully able to derive the transfer functions relating a setpoint change to the controlled variable (servo problem), and a change in the load variable to the controlled variable (regulatory problem).
• Be able to obtain responses (qualitatively and quantitatively) for setpoint changes and load changes.
• Should understand why proportional control alone can result in an offset.
• Should be very familiar with the three basic types of control (proportional, integral and differential) and should understand why/how each type assists in the controller “decision making”.
• Should understand and be able to show that integral control action will continue until the error is eliminated (or until the final control element reaches a saturation point)
• Should take note off the fact that differential control will accelerate the control action.
• Should be able to use P, PI and PID algorithms in the time, Laplace as well as frequency domains.
• Should be able to show that the denominator of the servo and regulatory transfer functions of a feedback loop are the same (characteristic equation).
• Should clearly understand that the roots of the characteristic equation (like the poles of any transfer function) contain information on the stability and shape of the servo and regulatory responses.
• Should understand that the controller parameters (Kc, I, D) determine what the roots of the characteristic equation will be.
• Should be able to perform the Routh test to determine whether a transfer function is stable.
• Should be able to decide on whether to use a P, PI or PID controller in a particular application..
• Should be able to design a P, PI or PID controller using the following criteria/methods:
  • Overshoot, decay ratio, settling time
  • Time integral performance
  • Cohen and Coon technique (note that the open loop reaction curve does not contain the controller transfer function).
  • Ziegler Nichols technique
• Realise that different controllers (type and parameters) will have different roots of the characteristic equation (poles of the closed loop transfer function).

Study material: Luyben Chap. 7, Chap. 10; Steph. Chap 13 – 16, Seborg et.al. Chap.8-12. Number of lecture periods: 7

Frequency response methods

On completion of this study theme you should be able to do the following:

• Derive and aply the substitution rule.
• Be able to represent frequency responses as Bode, Nyquist or Nichols plots and interpret thevarious curves and interpret them correctly.
• Appreciate the benefit of handling systems in series.
• Apply the Bode- and Nyquist stability criteria
• Design controllers by allowing for phase and gain margins
• Design controllers by using the maximum log modulus of the closedloop frequency response. (In this regard the student should be able to use Nichols charts with closed loop modulus contours).

Study material: Luyben Chap. 12 – 13; Steph. Chap 17 – 18; Seborg et.al. Chap. 13-14 and additional notes Number of lecture periods: 12

Advanced control methods

On completion of this study theme you should be able to do the following:

• Understand the effect of dead-time on a feedback loop and apply methods to compensate for this – the Smith-compensator.
• Understand the effect of inverse response on a feedback loop and apply methods to compensate for this.
• Understand and apply the advantages of cascade control.
• Understand the difference between feedforward and feedback control.
• Design feedforward controllers and understand the physical realisability of such controllers.
• Understand the advantages of the combination of feedforward and feedback control and apply this method.
• Understand and apply ratio control.
• Understand internal model control (IMC) and apply it for designing feedback controllers.
• Be familiar with the concepts adaptive control, inferential control, selective control and split-range control.

Study material: Luyben Chap. 11, Steph. Chap 19 – 22, Seborg et.al. Chap.15-16 and additional notes Number of lecture periods: 7

Discrete methods

On completion of this study theme you should be able to do the following:

• Know the elements of digital control loops.
• Take note of the sampling theorem and the factors which influence the choice of sampling interval.
• Mathematically represent the discretisation of continuous signals.
• Understand the working of hold-elements and represent this mathematically.
• Discretise continuous models.
• Know and apply the definition, properties and inversion of the z-transform.
• Calculate the discrete response of dynamic systems.
• Derive pulse transfer functions. Understand the physical realisability of pulse transfer functions.
• Give the qualitative response of discrete systems.
• Derive the closed loop transfer functions of control loops containing discrete elements.
• Perform stability analysis of discrete systems and understand the role of the sampling interval.
• Apply the bi-linear transform and understand its utility.
• Understand and apply the discretisation of conventional control algorithms (velocity- and position form).
• Design and understand deadbeat controllers for changes in setpoint and load.
• Understand and apply Dahlin’s control algorithm.
• Understand the origin of ringing poles and take the necessary steps to move or remove such poles.

Study material: Luyben Chap. 18-20; Steph. Chap 26 – 30, Seborg et.al. Chap.8.6, 17 and additional notes Number of lecture periods: 12

Process identification

On completion of this study theme you should be able to do the following:

• Determine an approximate transfer function model using a step test.
• Determine a frequency domain model using pulse tests.
• Determine process parameters using the least squares method.

Study material: Luyben Chap. 14; Steph. Chap 31, Seborg et.al. Chap.7 and additional notes Number of lecture periods: 4

State space description of dynamic systems

On completion of this study theme you should be able to do the following:

• Determine state space descriptions for physical systems.
• Understand the relationship between the eigenvalues of the A-matrix and the poles of the system.
• Convert between Laplace- and state space descriptions and back.

Study material: Luyben Chap. 15 (paragraphs 15.3 & 15.4); Seborg et.al. Chap.44 and additional notes. Number of lecture periods: 3