## Feedback Control Systems

OBJECTIVES

LEARNING OUTCOMES:
The theory of differential equations is successfully used to gain profound insight into the fundamental mathematical control design techniques for linear and nonlinear dynamical systems.

KNOWLEDGE AND UNDERSTANDING:
Students should be able to deeply understand (and be able to use) the theory of differential equations and of systems theory, along with related mathematical control techniques.

APPLYING KNOWLEDGE AND UNDERSTANDING:
Students should be able to design feedback controllers for linear (and even nonlinear) dynamical systems.

MAKING JUDGEMENTS:
Students should be able to identify the specific design scenario and to apply the most suitable techniques. Students should be able to compare the effectiveness of different controls, while analyzing theoretical/experimental advantages and drawbacks.

COMMUNICATION SKILLS: Students are expected to be able to read and capture the main results of a technical paper concerning the topics of the course, as well as to effectively communicate in a precise and clear way the content of the course. Tutor-guided individual projects (including Maple and Matlab-Simulink computer simulations as well as visits to labs) invite an intensive participation and ideas exchange.

LEARNING SKILLS:
Being enough skilled in the specific field to undertake following studies characterized by a high degree of autonomy.

COURSE SYLLABUS

Linear systems
The matrix exponential; the variation of constants formula. Computation of the matrix exponential via eigenvalues and eigenvectors and via residual matrices. Necessary and sufficient conditions for exponential stability: Routh-Hurwitz criterion. Invariant subspaces. Impulse responses, step responses and steady state responses to sinusoidal inputs. Transient behaviors. Modal analysis: mode excitation by initial conditions and by impulsive inputs; modal observability from output measurements; modes which are both excitable and observable. Popov conditions for modal excitability and observability. Autoregressive moving average (ARMA) models and transfer functions.
Kalman reachability conditions, gramian reachability matrices and the computation of input signals to drive the system between two given states. Kalman observability conditions, gramian observability matrices and the computation of initial conditions given input and output signals. Equivalence between Kalman and Popov conditions. Kalman decomposition for non-reachable and non-observable systems.
Eigenvalues assignment by state feedback for reachable systems. Design of asymptotic observers and Kalman filters for state estimation of observable systems. Design of dynamic compensators to stabilize any reachable and observable system. Design of regulators to reject disturbances generated by linear exosystems.
Introduction to adaptive control. Introduction to tracking control. Minimum phase systems and Proportional Integral Derivative (PID) control.
Bode plots. Static gain, system gain and high-frequency gain. Zero-pole cancellation. Nyquist plot and Nyquist criterion. Root locus analysis. Stability margins. Frequency domain design. Realization theory.

Introduction to nonlinear systems Nonlinear models and nonlinear phenomena. Fundamental properties. Lyapunov stability. Linear systems and linearization. Center manifold theorem. Stabilization by linearization.

## Analogue Electronics

OBJECTIVES

COURSE SYLLABUS

• Classification of electrical systems and requirements.
• Analysis of transitory and frequency behavior.
• Distortion in electronic systems and Bode diagrams.
• Diode semiconductor devices and circuit applications: clipper, clamper, peak detector, etc. Bipolar Junction and Field-Effect Transistors.
• Biasing techniques for Transistors. Amplifiers classification, analysis and circuit design.
• Frequency response of single and cascaded amplifiers.
• Differential amplifiers and Cascode.
• Current mirrors.
• Feedback amplifiers and stability issues. Power amplifiers.
• Operational amplifiers and related applications.
• Oscillator circuits. Integrated circuits and voltage waveform generators.

## Physics I

OBJECTIVES

LEARNING OUTCOMES
1 – Analyze and interpret motion of particles, systems and rigid bodies and perform calculations relative to the different types of motion (rectilinear, curvilinear, rotational, etc.)
2 – Analyze and interpret the above types of motion in relatively moving inertial refernce frames and perform calculations to switch from one reference frame to another.
3 – Analyze and interpret oscillatory motion, simple, forced and damped harmonic motion, and perform calculations of the: i) horizontal and vertical mass-spring systems, ii) simple pendulum, iii) compound pendulum.
4 – Analyze and interpret wave motion, transverse and longitudinal waves, and wave equations, and perform calculations of transverse waves along a stretched string and of longitudinal waves inside pressurized gases.
5 – Formulate the concepts of superposition and interference; analyze standing waves, sound waves, and the Doppler effect.
6 – Analyze and interpret elementary concept of fluid statics and fluid dynamics, and perform calculations of bouyant forces and of motion of fluids in constricted pipes.
7 – Interpret the concepts of temperature, heat, and phase change, and perform calculations with temperature scales, heat capacity, and specific heat.
8 – Conceptualize the model of the ideal gas, perform calculations using the ideal gas law, and analyze and interpret the kinetic theory of ideal gases.
9 – Interpret the first law of thermodynamics, and calculate and predict work, heat, and internal energy change for various thermodynamic processes.
10 – Interpret the concepts of reversibility, second law of thermodynamics, and entropy, and analyze heat engines, heat pumps and refrigerators.

KNOWLEDGE AND UNDERSTANDING
Students acquire understanding and knowledge of the most important phenomena and physical laws concerning the world around us, at the level in which they operated (Physics 1). The teaching approach provides the foundation for this understanding, based on the use of mathematical methods and on the presentation / explanation of historical and recent experiments and examples taken from everyday life. The most important physical topics are learned in terms of logical and mathematical structure, and experimental evidence. At the end of the course students have assimilated a complete knowledge of the basic themes of classical physics. The methods by which these skills are provided include lectures, tutoring, exercises and knowledge are assessed during exercises, tutoring and final exams.

APPLYING KNOWLEDGE AND UNDERSTANDING
Physics 1 students are capable to create, describe, refine and use representations and models (both conceptual and mathematical) to communicate scientific phenomena and solve scientific problems. Basically, to make a good model, they have to be able to identify a set of the most important characteristics of a phenomenon or system that may simplify analysis. Since the use of representations is fundamental to model introductory physics, they must know how to realize pictures, motion diagrams, force diagrams, graphs, diagrams, and mathematical representations such as equations, and recognize that representations help in analyzing phenomena, making predictions, and communicating ideas.

MAKING JUDGEMENTS
The training provided for students in Physics is hallmarked by the acquisition of a flexible mentality that helps them to extend the knowledge learned to new concepts, enabling them to introduce elements of innovation. They are capable of assessing orders of size for the physical quantities relevant to the system under study. These activities encourage students to develop their independence of judgement. They become capable to pose, refine and evaluate scientific questions, being an important instructional and cognitive goal. Even within a simple physics topic, posing a scientific question is mandatory.

COMMUNICATION SKILLS
Students develop the ability to present what they have learnt during the course with clarity, and likewise additional knowledge acquired from textbooks. They are expected to present their knowledge effectively. This skill, which concerns both oral and written presentations, should be based on the capability for analysis and integration of areas of knowledge developed during the course. They necessarily develop a positive attitude to group work.
Assessment of the attainment of written and oral communication skills is performed during classroom exercises, tutoring and through written and oral exams at the end of the course.

LEARNING SKILLS
Physics 1 students learn how to work with scientific explanation and theories, justify claims with evidence, articulate the reasons that scientific explanations and theories are refined or replaced, evaluate scientific explanations.
On these bases they connect and relate knowledge across various scales, concepts, and representations “in” and “across” domains. For example, after learning the concepts of conservation law in the context of mechanics, students will describe what the concept of conservation means in physics and extend the idea to other context.
This will be assessed by exercises, during tutoring time and exams at the end of the course.

COURSE SYLLABUS

• INTRODUCTION – Measurement. Fundamental quantities and units. Plane angle. Solid angle. Direction. Scalars and vectors. Components. Scalar and vector products. Vector representation of the area. Forces. Composition of concurrent forces. Torque. Torque of concurrent forces. Coplanar forces. Parallel forces.
• KINEMATICS – Rectilinear motion: velocity, acceleration. Curvilinear motion: velocity, acceleration. Motion under constant acceleration (tangential and normal components). Circular motion: angular velocity, angular acceleration. General curvilinear motion.
• RELATIVE MOTION – Relative velocity. Uniform relative translational motion. Uniform relative rotational motion. Motion relative to the earth. Transformation of velocities.
• DYNAMICS OF A PARTICLE – Introduction. The law of inertia. Linear momentum. Principle of conservation of momentum. Dynamic definition of mass. Newton’s second and third laws: the concept of force. Unit of force. Frictional force. Frictional force in fluids. System with variable mass. Curvilinear motion. Angular momentum. Central forces. Equilibrium and rest.
• WORK AND ENERGY – Work. Power. Units of work and power. Kinetic energy. Work of a force constant in magnitude and direction. Potential energy. Conservation of energy of a particle. Rectilinear motion under conservative forces. Motion under conservative central forces. Discussion of potential energy curves. Non-conservative forces.
• DYNAMICS OF A SYSTEM OF PARTICLES – Motion of the centre of mass. Reduced mass. Angular momentum of a system of particles. Kinetic energy of a system of particles. Conservation of energy of a system of particles. Collisions.
• DYNAMIC OF A RIGID BODY – Angular momentum of a rigid body. Moment of inertia. Equation of motion for rotation of a rigid body. Kinetic energy of rotation.
• OSCILLATORY MOTION – Kinematics of simple harmonic motion. Force and energy in simple harmonic motion. Dynamics of simple harmonic motion. The simple pendulum. Compound pendulum. Superposition of two simple harmonic motions. Coupled oscillators. Anharmonic oscillations. Damped oscillations. Forced oscillations.
• MECHANICS OF FLUIDS – Pressure. Variation of pressure with depth. Pressure measurements. Buoyant forces and Archimedes’ Principle. Fluid dynamics: Bernoulli’s Equation. Applications of fluid dynamics.
• MECHANICAL WAVES – Propagation of disturbance. Sinusoidal waves. The speed of waves on strings. Reflection and transmission. Rate of energy transfer. The linear wave equation. The speed of sound. Periodic sound waves. Intensity. The Doppler Effect. Superposition and interference. Standing waves in strings. Resonance. Standing waves in air column. Beats.
• THERMODYNAMICS – Temperature and the Zeroth Law of thermodynamics. Thermometer. Celsius Scale. Gas thermometer. Absolute temperature scale. Macroscopic description od ideal gases. Heat and internal energy. Specific heat. Latent heat. Work and heat. The First Law of thermodynamics. Applications of the First Law. Energy transfer mechanism. The kinetic theory of gases: molecular model Molar specific heat. Adiabatic processes. Equipartition of energy. The Boltzmann Distribution Law. The Second Law of thermodynamics. Heat engines. Pumps and refrigerators. Reversible and irreversible processes. The Carnot engine. Entropy. Entropy changes in irreversible processes. Entropy on macroscopic scale.

## Linear Algebra and Geometry

OBJECTIVES

LEARNING OUTCOMES: The course provides an introduction to linear algebra and euclidean geoemetry.

KNOWLEDGE AND UNDERSTANDING: The student will learn to solve simple geometric and algebraic problems using the tools provided by the course.

APPLYING KNOWLEDGE AND UNDERSTANDING: Ability to apply knowledge and understanding to concrete problems.

MAKING JUDGEMENTS: The student will learn how to interpret the data of an algebraic or geometric problem without following standard schemes.

COMMUNICATION SKILLS: The student will show, esapecially during the oral exam, her/his ability to describe the logical process that yields the theorems studied in the course.

LEARNING SKILLS: The student will learn to understand the exercises of the written exams, and to develop a method to solve them.

COURSE SYLLABUS

Linear equations and linear systems. Solutions. Consistency of a system. Basic and free variables. Matrix of coefficients. Augmented matrix. Row reduction to echelon matrix. Exercises on linear systems. Numerical vectors. Addition and multiplication by scalars. Linear combinations. Linear systems and vectors. Linearly independent vectors. Finding subsets of linearly independent vectors. Linear systems in matrix form. Exercises on linear systems in vector form. Canonical basis. Linear space. Basis and coordinates of vectors. Steinitz lemma. Dimension of linear spaces. Rank of a matrix. Linear spaces of rows and columns of a matrix. Null space of a matrix. Matrix transformations. Injectivity, surjectivity and rank. Linear transformations and matrices. Multiplication and addition of matrices and their linear transformations. Invertible matrices. Computing the inverse via row reduction Change of coordinates and matrices Vector (linear) spaces. Examples of polynomials and matrices. Linear subspaces. Intersection of linear subspaces. Sum of linear subspaces. Grassmann formula. Basis for intersections and sums of linear spaces. Determinants: definition, properties, computation. Computation of the rank using determinants. Computation of the inverse matrix using determinants. Determinant of a product. Cramer’s formula. Linear transformation between vector spaces. Image and kernel. Matrix of a linear transformation with respect to basis of the domain and of the range. Lines in the plane and in 3-dim. space. Planes in the 3-dim. space. Cartesian and parametric equations. Lines through 2 points. Plane through 3 non collinear points. Relative position of two planes. Relative position of two lines in 3-dimensional space. Inner product. Norm. Distances. Orthogonal vectors, lines, planes. Angles. Cross product in 3-dim. space. Mixed product. Area of parallelogram. Volume of parallelepiped. Eigenvalues and eigenvectors. Characteristic polynomial. Algebraic and geometric multiplicities. Diagonalization of endomorphisms and matrices. Orthogonal subspaces, orthonormal basis, orthogonal matrices.
Gram-Schmidt orthonormalization. Formula for the orthogonal projection. Matrix of orthogonal projections. Spectral theorem for symmetric matrices. Quadratic forms and their classification.Conic curves: classification Rotations and translations that put a conic in normal form.

## Fundamentals of Computing

OBJECTIVES

LEARNING OUTCOMES:
The course aims to provide students with knowledge and skills for an effective use of computer methodologies and tools in the field of engineering, expecially for the development of algorithms.

KNOWLEDGE AND UNDERSTANDING:
Acquire knowledge of the internals of computer architectures.
Acquire knowledge on data structures and algorithms.
Acquire knowledge on the principles of programming languages, including the object-oriented paradigm, and on tools and techniques for software development.

APPLYING KNOWLEDGE AND UNDERSTANDING:
Acquire ability to analyze problems and produce a design and implementation of software artifacts addressing them.
Acquire capability of group working on software development and documentation.

MAKING JUDGEMENTS:
Being able to choose appropriate languages and tools for software development.
Being able to evaluate the correctness and efficiency of a software implementation.

COMMUNICATION SKILLS:
Be able to describe and document software artifacts correctly and effectively.

LEARNING SKILLS:
Being able to use effectively the technical documentation and the reference manuals of systems, products and languages.

COURSE SYLLABUS

• Introduction to Computer Science; Von Neumann architecture; Computer Architectures; CPU and GPU; Programming Paradigms; Functional and Object Oriented Approaches; Principles of Software Engineering and Modeling; Basic concepts and comparison of Programming Languages; Variables; Control structures (Loops, Conditional Selection), Data structures and algorithms; Computational Complexity; Functions and parameters; Recursion; Sorting algorithms; Input/Output; Concurrency and Parallelism; Networking and Distributed Applications; Version Control; The Art of Documentation; Introduction to Safety, Security and Reliability concepts.
• The programming languages taught are C, Java and Rust