Automation, electronics,electronical engineering and space technologies
- Measurements – electrical and nonelectrical measurement. Design of measurement channel. A/D and D/A conversion and converters. Synchronization measurement devices in multichannel system. Signal conditioning and channel calibration. Estimation o measurement uncertainties. Measurement technics with vision systems usage. Operating principle of electrical and nonelectrical measurement transducers.
- Signal Analysis and Identification – Fourier, Laplace, Laurent (Z) transformations. Correlation function, power spectral density. Continues, discrete, ergodic and random processes. Power and energy signals. Stochastic analysis problems: distribution, probability density function. Time and frequency domain identification problems. Digital signal processing problems.
- Control systems – Microprocessor systems, Programmable Logic Controllers, FPGA circuits. Real Time Operating systems for automation. Communication protocols used in industry automation. Combinational and sequential logic systems design. The construction and operation of digital industry automation systems.
- Drive systems – the construction, operation and modelling of electric, hydraulic and pneumatic drives and actuators.
- Robotics – the construction and modelling of robots. Forward and inverse kinematics of robot manipulators. Statics and dynamics problems. Control Systems in Robotics.
- Modelling – linear and nonlinear models of objects mechanical and electrical and technological processes. Classical mechanic, fluid mechanics and thermodynamics problems. Static and dynamic characteristics of dynamic objects (time and frequency domain). Structural dynamics, partial differential equations usage for object modelling. Eigenproblem of the multidimensional objects (mode shapes).
- Control systems theory – the object model notations in the form of differential equations, transmittances and state space models. Continuous and discrete models of SISO and MIMO objects. Control systems synthesis of linear SISO, and MIMO objects. Control systems quality indicators. Eigenvalues and eigenvectors of object models. PID control synthesis methods, pole and zero allocation method, phase and stability margin, state controller, LQR, LQG, robust control, adaptive control. Non-linear MIMO objects synthesis methods. Stability, observability and controllability problems. Luenberger and Kalman state observers. Dynamic optimization methods, Bellman's optimality principle, Pontragin's maximum principle.
Mechanical engineering
Mechanics:
- Properties of a force couple.
- Cases of reduction of the spatial force systems.
- Equilibrium conditions of a force system.
- Instant center of rotation and acceleration.
- Velocity and acceleration of a point in complex motion.
- The principles of mechanics used in the dynamics of the system of point particles.
- Dynamic equations in translational, rotational, planar and spherical motion of a solid.
- Kinetic energy of a solid in translational, rotational, planar and spherical motion.
- Lagrange equations of the first and second kind.
Strength of materials:
- Stress-strain curve, the tensile properties of materials.
- Generalized Hooke’s law for normal and shear strain components.
- Components of stress tensor and strain tensor (special cases: plane stress, plane strain, spatial stress state, spatial strain state), definition of principal stresses.
- Pure bending, internal moment and stress relations, differential equation for the elastic curve of a beam.
- Cylindrical shafts in torsion – distribution of the shear stress, equations for maximum shear stress and angle of twist.
- Material effort, strength theories, equivalent stress.
- Stress concentration phenomenon: stress distribution in notched element, stress concentration factor definition and variables it depends on.
- Wöhler curve and its description: Basquin equation, concepts of limited fatigue strength and fatigue limit.
Construction and operation of machines:
- Characteristics of belt drives and their application in machine design.
- Problems of transmission shafts design and calculations.
- Design of bolted joints working under static and varying load conditions.
- Construction of bearing systems with application of rolling-element bearings.
- Factors influencing the fatigue strength of machine elements.
- Characteristics of contemporary permanent joints.
- Strength conditions of statically loaded machine elements.
- Clutches – selection criteria, basic calculations, examples.
- Application and functions of lubricants in machine construction. Characteristics of seals used in machine construction.
Drive systems:
- Selection criteria of drive systems to various mechanical devices.
- Construction, operation and modelling of electric, hydraulic and pneumatic drives.
- Modern IT tools used to design machine parts and model their movement.
Acoustics:
- The properties of the sound and its sources.
- Contemporary applications of acoustics.
- Methods for conditioning of the acoustics of rooms.
- The purpose of audio engineering.
Robotics:
- The construction and modelling of robots.
- Simple and inverse kinematics task. Statics and dynamics problems.
- Control Systems in Robotics.
- What is the accuracy and repeatability of the manipulator.
- What are the Euler angels and what are the advantages of using them to describe the orientation of the effector of the robot.
- What is the number of degrees of freedom of manipulator.
- What are the holonomic constraints and whether the mobile robot can be a holonomic object.
Modelling:
- Linear and nonlinear models of objects mechanical and electrical and technological processes.
- Classical mechanic, fluid mechanics and thermodynamics problems.
- Static and dynamic characteristics of dynamic objects (time and frequency domain).
- Structural dynamics, partial differential equations usage for object modelling.
- Eigenproblem of the multidimensional objects (mode shapes).
Biomedical engineering
Knowledge expected from all candidates
The domain range of "biomedical engineering". Concepts of: biocybernetic model, simulation of biological system and examples of their application to selected problems of biology and medicine. The role of biocybernetics and biomedical engineering in progress of technology, biology and medical sciences as well as civilization achievements.
Knowledge representation methods. Concepts of incomplete and tentative knowledge. Expert systems. Inference rules in systems with rule-based representation of knowledge. Fuzzy logic, evolutionary algorithms. Biomedical engineering systems and applications for diagnostics, therapy, rehabilitation and prosthetics of various organs and body parts – examples and general design rules.
Domain range I: electronics and computers in medicine
Backgrounds of theoretical neurocybernetics, goals and methods of brain modeling, various types of artificial neural networks with applications, basics of cognition sciences. Models of biological and technical perception systems (auditory and visual systems in human), regulatory systems (the concept of homeostasis and structure of management systems), and control systems (control and coordination of motor system, control with the gamma loop, cooperation of synergic and antagonist muscles). Population models.
Computer methods for biomedical signal processing and methods for automated analysis and image recognition. Selected issues of artificial intelligence in biomedical applications.
Methods applied in biological and physiological measurements, monitoring of blood circulation, muscle stress, fetal wellbeing, brain function, visual and auditory perception. Examples of digital supportive tools for signal and image-based diagnostics. Multidimensional and multimodal signals. Computer methods for feature extraction and objects / events classification. Methods of surveillance of human in daily living activities (assisted living), ordination and particular characteristics of sensors. Sensor networks. Data security and privacy-related problems in physiological measurement and data transmission. Hospital information systems, therapy planning automatic and telematic triage. Problems of telemedicine: data secyrity and reliability, seamless data access, aspects of mobility and energetic efficiency of equipment. Brain-Computer Interfaces: paradigms and particular characteristics of BCIs.
Domain range II: biomaterials engineering
Basic concepts and definitions: biomaterial, biocompatibility, bioactivity, medical device, implant, transplant, artificial organ, hybrid organ. The relationship between the structure, properties and manufacturing methods of different types of biomaterials: metallic, polymeric, ceramic and composite. Classification of biomaterials by: material type (metals and alloys, ceramics, polymers, carbons, composites, hybrids) and behavior in the biological environment (biostable, degradable, resorbable). Application of metals, polymers, carbons, composites, calcium phosphate bioceramics, bioactive glasses in medicine, e.g. in surgery, orthopedics, cardiac surgery, dentistry. Surface engineering and surface modification techniques. Methods of analysis: structure, microstructure and properties of biomaterials. Biological response to the implant. Biomaterials testing in vitro and in vivo. Tissue engineering and regenerative medicine.
Domain range III: biomechanics
Basic concepts and definitions: Biomechanics and mechanobiology. Fields and directions of research in biomechanics. Structure – function relationship of tissues. Research fields in biomechanics, Division of joints due to type of movement, Biotribiology and issues related to the exploitation of joints and tissues, Bones – structure and mechanical properties, Models of mechanical properties of bones, Functions and properties of articular cartilage, Models of articular cartilage, Structure and properties of connective tissues based on tendon example, Models describing tendon properties, Structure and functions of the spine, Natural and synthetic biomaterials, Modeling of biomaterials as a viscoelastic elements, Experimental methods in tissue biomechanics (including measurements of stress, strain, displacement etc.). Basics of mechanics of tissue and other biological materials – ultimate tensile, compression, bending and torsional strength.