Control Systems

Introductory about control systems. Feedback. Examples of applications. Differential equations and transfer functions, linear SISO systems. Linearisation of nonlinear systems. Responses for some basic systems. Poles and zeros. The dilemma between fast response and oscillations/instability. Proportional (P-)control. Integral (I-) control explained in the time domain. Time delays in a feedback loop. Frequency response, Bode diagram. Feedback processes, Nichols diagram. Stability of feedback systems, Nyquist diagram. Stability via Bode diagram. Synthesis of control systemms with Bode diagrams. Control to cancel disturbances, control to follow references (servo control). Standard controllers: P, PI, PID, PD. Experimental tuning (Ziegler-Nichols' and Skogestad's SIMC method). Phase lift through derivative (D-) effect, for increased stability. Time delays in the frequency domain, Cascade control. Feedforward. Control of 2 x 2 MIMO system. Computer control of systems (discrete control).

Knowledge: Basic knowledge about linear differential equation models of dynamic systems, impulse- and step responses, frequency response models. Knowledge of stability issues in linear systems, and tools for analysis of this in feedback systems. Knowledge of the basic standard controllers in use. Knowledge of systematic methods for the design of simple controllers based on known process models, and experimental tuning applied to physical processes. Have the foundation for advanced courses in control systems.Skill: To independently design simple real-world control solutions, and contribute in a team doing more complex projects. To independently be able to analyse system characteristics. Be able to design and tune basic controllers.General competence: Be able to communicate with colleagues about control system solutions for processes, both with colleagues in the field and laypersons. Be aware of the role and potential of the discipline of control systems in production, infrastructure and society.

Lectures, computer exercises and calculation exercises. Compulsory computer exercises in two-student groups, using MATLAB, also a compulsory laboratory exercise.