
Course unit
MODERN CONTROL FOR ENERGY SYSTEMS
INP7080037, A.A. 2018/19
Information concerning the students who enrolled in A.Y. 2017/18
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Educational activities in elective or integrative disciplines 
INGINF/04 
Automatics 
6.0 
Course unit organization
Period 
First semester 
Year 
2nd Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
6.0 
48 
102.0 
No turn 
Start of activities 
01/10/2018 
End of activities 
18/01/2019 
Prerequisites:

No specific requirements. Familiarity with fundamentals of linear algebra (matrix operations, eigenvalues and eigenvectors, base transformation, trace, determinant, inversion, exponential of matrix,..) and complex numbers (rectangular and polar representations, operations with complex numbers, Eulerâ€™s formula,..) 
Target skills and knowledge:

Ability to derive a mathematical model of a physical system in terms of continuoustime differential equations, in particular for thermal, energy and hydraulic systems.
Ability to understand the characteristics in time and frequency domains of general dynamic systems. Ability to determine operating equilibrium conditions. Linearization about equilibrium conditions. Ability to design a PID controller for linear dynamic systems SISO that meets the desired performance requirements. Particular emphasis will be placed on application of the mathematical tools to realistic energy systems and the use of simulative software tools such as Matlab and Simulink. 
Examination methods:

Written exam (3 hours)
Oral exam (optional upon request of the student) 
Assessment criteria:

The assessment of the preparation of the student will be based ' on his/her understanding of the topics, on the acquisition of concepts and methodologies proposed and the ability to apply them in an autonomous and knowledgeable way. 
Course unit contents:

 Modeling: Descriptions and derivation of mathematical models for thermal, energy and hydraulic systems using differential equations with concrete examples: heat exchangers, hydraulic pumps and valves, temperature control, fluid level control in tanks.
 Introduction to MATLAB and SIMULINK for Control Systems
 Statespace representation of dynamical systems: linear and nonlinear, modal analysis, forced and natural responses, transient and steadystate behaviour
 Stability of dynamical systems: equilibrium points, Lypunov functions
 Linearization about equilibrium points
 Laplace transform and its properties'. Transfer function. Inverse Laplace Transform.
 Representation SISO LTI systems: differential equations, transfer function, impulse response.
 Timedomain analysis of LTI systems: raising time, overshoot, and connections with Bode diagrams
 Bode plot: definition of resonance frequency, the resonance peak, bandwidth.
 Nyquist plot: open loop and closed loop. Nyquist criterion to establish stability, vector error, phase margin, gain margin.
PID controllers: considerations on the choice of actions, design of controllers P, PI, PD, PID using frequency domain approach
 Application of the previous mathematical tools for the design of control systems for energy systems and validation using Matlab/SImulink 
Planned learning activities and teaching methods:

Lectures on the black board which alternate between theory and examples and exercises in line with those required in the witten and oral exams. Few MATLAB/Simulink laboratories for numerical analysis of dynamical systems 
Additional notes about suggested reading:

The main material is based on the lecture notes, PDF notes provided by the instructor and textbook. 
Textbooks (and optional supplementary readings) 

Karl A. Astrom, Richard Murray, Feedback systems: an introduction for scientists and engineers Control of Dynamic Systems. : Prentice Hall, 2016. Available on line: http://www.cds.caltech.edu/~murray/mlswiki/?title=First_edition


