Control Engineering

ANTONIO PIETRABISSA

General objectives

The course aims at providing basic concepts and methodologies related to the most widely used control methodologies in the framework of process automation and at applying them in the industrial contexts, suitably modeled as complex and heterogeneous processes that are interconnected through appropriate material transport and communication infrastructures.

Specific objectives

Knowledge and understanding:
The students will learn methodologies for the robust control of linear time-delay systems, Internal Model Control and Model Predictive Control with specific reference to process control problems.

Apply knowledge and understanding:
Students will be able to design robust controllers for process automation equipment, e.g., to achieve robust tuning of PID controllers, and to apply industrial Model Predictive Control algorithms.

Critical and judgment skills:
The student will be able to choose the most suitable control methodology for a specific process control problem starting from its state-space model or from its transfer-function model.

Communication skills:
The course activities allow the student to be able to communicate and discuss the main problems concerning process control and the possible design choices for their solutions in terms of control laws.

Learning ability:
The aim of the course is to make the students aware on how to deal with control problems in the context of process automation.

General objectives

The course aims at providing basic concepts and methodologies related to the most widely used control methodologies in the framework of process automation and at applying them in the industrial contexts, suitably modeled as complex and heterogeneous processes that are interconnected through appropriate material transport and communication infrastructures.

Specific objectives

Knowledge and understanding:
The students will learn methodologies for the robust control of linear time-delay systems, Internal Model Control and Model Predictive Control with specific reference to process control problems.

Apply knowledge and understanding:
Students will be able to design robust controllers for process automation equipment, e.g., to achieve robust tuning of PID controllers, and to apply industrial Model Predictive Control algorithms.

Critical and judgment skills:
The student will be able to choose the most suitable control methodology for a specific process control problem starting from its state-space model or from its transfer-function model.

Communication skills:
The course activities allow the student to be able to communicate and discuss the main problems concerning process control and the possible design choices for their solutions in terms of control laws.

Learning ability:
The aim of the course is to make the students aware on how to deal with control problems in the context of process automation.

Prerequisites:
Basic knowledge of systems theory.
Basic knowledge of control theory.

There are no prerequisite exams.

Introduction to process control. (10h)
Process Control Overview. Significance of process control. Objectives. Levels of Process Control. Process Dynamics and Mathematical Models. Regulatory Control. Control System Design. Multivariable Control. Batch Process Automation. Automation and Process Safety.

Classic process control. (25h)
Internal Model Control (IMC). Robust control. Robust PID tuning with IMC. Time-delay systems. Time margin. Smith Predictor. Robustness to time delay mismatches. Robust PID tuning in presence of delays with IMC.

Model Predictive Control. (25h)
Introduction to Model Predictive Control. The Model Predictive Control (MPC) principle. Relevance of MPC in current industrial process automation. Basic notions about Quadratic Programming. Model Predictive Controllers. MPC elements: prediction model, objective function, control law. MPC algorithms: Dynamic Matrix Control, Model Algorithmic Control, Predictive Functional Control. State space formulation. MPC and Optimal Control.

Eduardo F. Camacho, Carlos Bordons Alba, “Model Predictive Control”, Series: Advanced Textbooks in Control and Signal Processing, XXII, 2nd ed. 2004, 405 p., ISBN 978-0-85729-398-5.

Slides and lecture notes by A. Pietrabissa available via the website.

Reference bibliography:

Process control
T. F. Edgar, J. Hahn, “Process Automation”, in Handbook of Automation, 2009
D.E. Seborg et al., Process Dynamics and Control (3rd ed.), 2009

Classic process control
Braatz, R. D. (1995). Internal model control. In The Control Handbook (W. S. Levine, ed.) CRC Press, pp. 215-224
Rivera, Daniel E. "Internal model control: a comprehensive view." Arizona State University (1999).
Morari, M. & Zafiriou, E. (1989). Robust Process Control. Prentice Hall, Englewood Cliffs, New Jersey

Model Predictive Control
Eduardo F. Camacho, Carlos Bordons Alba, “Model Predictive Control”, Series: Advanced Textbooks in Control and Signal Processing, XXII, 2nd ed. 2004, 405 p., ISBN 978-0-85729-398-5.
K. Basil and M. Cannon, "Model predictive control", Switzerland: Springer International Publishing, 2016

The course is taught by using the blackboard and/or slides depending on the topic.
The slides are distributed before each lecture and are later updated, and redistributed, with the annotations made during the lecture.

Attendance of the course is optional.

The written test consists of one exercise on Internal Model Control, one on Model Predictive Control and in some open-ended questions on the course programme.
Indicatively, each exercise accounts for one third of the evaluation; the other third depends on the questions.
The oral test consists of the written test discussion with possible insights. The final grade will take into account the written grade and the evaluation of the answers to the questions of the oral exam.

Discuss why the Model Predictive Control (MPC) methodology may improve the safety of plants.
How is the error signal defined in IMC and what does it represent?
Which are the main differences between IMC and classical control?
Why a feedback delay may render a controlled system unstable?
What is the Padé approximation?
Show the effect of the delay block on Bode and Nyquist diagrams
What is the robust control problem?
Define the uncertainty models and their differences
Why is an upperbound needed for the robust control problem?
Why is the robust stability theorem conservative?
Which is the idea behind the SP?
Why MPC may improve safety in process control?
Compare the PFC computational efficiency vs. MAC/DMC
Which are the PFC drawback vs. MAC/DMC?
Under which conditions the MPC can solve the constrained infinite-horizon optimal control problem?
Why do we introduce a final cost and what does it represent?
Why do we need a minimum amount of time-steps for the prediction horizon?

Examples of exam exercises:

Exercise 1
Let the process be described by the transfer function: P(s)=0.01*(s-10)/(s+0.1)^2 e^(-θs), with θ∈(1.9,2.05)s.
Considering that the nominal delay is θ'=2s and by following the IMC design, tune the parameters of a Smith-Predictor controller in such a way that:
- the controlled system has 0 steady-state error for step inputs;
- the factorization is optimal under the IAE cost function;
- the controlled system is robustly stable against the uncertainties of the parameter θ.

Exercise 2
Consider a process whose step-response model is given by the following coefficients:
g_1=0,g_2=0.2,g_3=0.4,g_4≈0.5,g_5≈0.5,… .
Compute the control action of a DMC algorithm at time t=5 considering the following data:
- control horizon m=2;
- reference signal r(t)=0.1t;
- cost function J=e^T e, where e is the vector of predicted future errors and u is the vector of future control action variations;
- control actions and measured output available at time t=5:
- u(1)=0.2,u(2)=0.25,u(3)=0.28,u(4)=0.31; y_m (5)= 0.49.
Would the control action u(5) be larger or smaller if the cost function were J=e^T e+0.1u^T u?

• Process Control Overview. Significance of process control. Objectives. Levels of Process Control. Process Dynamics and Mathematical Models. Automation and Process Safety.Dynamic models for process control. 
  • Books: Slide sets 1-4


• Classic process control. Internal Model Control (IMC). PID tuning with IMC. Time-delay systems. Delay margin. Smith Predictor. Robustness to time delay mismatches.
  • Books: Slide sets 5-9


• Introduction to Model Predictive Control. The Model Predictive Control (MPC) principle. Relevance of MPC in current industrial process automation.  Basic notions about Linear Programming and Dynamic Programming.Model Predictive Controllers. MPC elements: prediction model, objective function, control law. MPC algorithms: Dynamic Matrix Control, Model Algorithmic Control, Predictive Functional Control. 
  • Books: Slide sets 10-11


• MPC: State space formulation.Stability of MPC. 
  • Books: Slide set 12


• Exercises on robust Internal Model Control and robust Smith's predictor
  • Books: Slide set E1


• Exercises on MPC
  • Books: Slide set E2