ELI2300 Dynamic Systems Course description

Knowledge of linear dynamic systems is important in many applications, including control systems, robotics, electronics, signal processing, communications and biomedical engineering.

The course covers the analysis of linear dynamic systems in the time domain. The course addresses the modelling of dynamic systems with differential equations and the solving of ODEs by applying the Laplace transform. Systems are further analysed by their transfer functions.

The course further introduces the fundamentals of feedback control in dynamic systems. Students learn how to represent a process, sensor, actuator, and controller in block diagrams, to derive open-loop and closed-loop transfer functions, and to assess stability by using pole locations. Emphasis is placed on understanding and comparing P, PI, PD, and PID controllers, selecting an appropriate controller structure for a given system, and tuning controller parameters by using the plant transfer function.

Throughout the course, numerical simulation tools are used to study time responses, explore design trade-offs, and support the modelling and control of simple mechanical, electrical, thermal, and fluid systems.

Language of instruction: English

Builds on ELPE1300 Electric Circuits, MEK1400 Physics, MEK1000 Mathematics1000.

No requirements other than the admission requirements.

After completing the course, the student is expected to have achieved the following learning outcomes defined in terms of knowledge, skills, and general competence.

Knowledge

The student has knowledge of:

• modelling first and second order physical systems (e.g., mechanical, electrical, thermal, and fluid systems) as ordinary differential equations,
• laplace transformation, partial fractions, and transfer functions,
• inverse Laplace transform and time responses,
• transforming a flow sheet of a system to a block diagram (including the plant, controller, sensor, actuator, and feedback loop),
• deriving the open-loop and closed-loop transfer functions by using block diagrams,
• stability analysis for open-loop and closed-loop systems using pole plots,
• characteristics of first order and second order functions (including gain, time constant, damping ratio, rise-time, overshoot, and settling time),
• basic understanding of P, PI, PD, and PID controllers in a feedback loop,
• PID controller tuning using the plant transfer function.

Skills

The student is capable of:

• setting up mathematical models of first and second order physical systems,
• solving ordinary differential equations by using Laplace transforms,
• finding the time response of first and second order systems to an input such as impulse, step, ramp, pulse,
• ability to transform between flow sheets, block diagrams, and ordinary differential equations by using transfer functions,
• evaluating stability of open-loop and closed-loop systems,
• characterising first-order and second-order system parameters based on their time-response,
• analysing a system and choosing an appropriate controller type (e.g., P, PI, PD or PID),
• deriving PID controller parameters using the plant transfer function,
• simulation of dynamic systems with a feedback controller by using a numerical simulation software.

General competence

The student:

• has the ability to analyse a simple physical system and formulate an appropriate dynamic model to solve a control problem,
• is able to apply transfer function models to design a simple feedback controller for a simple physical system,
• is able to discuss and justify dynamic modelling and control design choices and their associated trade-offs for a simple physical system.

The teaching consists of lectures combined with 4 individual exercises and 2 instructor-led lab demonstrations. Students will be asked to complete ‘individual’ exercises individually, not as a group. After each lab demo, the students will be asked to write a lab report as a group.

The following coursework is compulsory and must be approved before the student can sit in the exam:

• 2 lab reports in groups of 2-4 students,
• 4 individual exercises.

The approval requires an average of 60% (360/600 available points) from all 6 coursework assignments in total. (I.e., students can choose to not submit an assignment if they already have 360/600.)

The exam consists of two parts.

Part 1: Individual exam under supervision, 3 hours. This part counts 60 %.

Part 2: A project report in groups of 2-4 students. This part counts 40 %.

Both parts of the exam must be passed in order to pass the course.

The exam results can be appealed.

In the event of a resit or rescheduled exam, an oral examination may be used instead. In the case of an oral exam being used, examination results cannot be appealed.

An offline handheld calculator.

If the calculator’s internal memory can store data, the memory must be deleted before the exam.

Graded scale A-F.

One internal examiner. The course may be selected for grading by external examiners.