Automatic Control Systems II

This course is intended as a sequel to “Automatic Control Systems I”, which introduced the basics of System Theory for open-loop systems. Here, emphasis is given to the analysis of systems control in closed-loop control circuits. Initially, the concept of system stability is presented. We specifically explain how stability is linked to the operational behavior of the system. Then, we focus on the stability and performance characteristics of systems under control in a closed loop circuit. The closed-loop stability is studied by means of the Routh algebraic criterion. The performance characteristics are analyzed by means of the transient parameters (overshoot, settling time etc) of the closed loop system response to typical inputs and the associated steady state error. Next, we introduce the concept of relative stability, which essentially explains how the closed loop stability is affected by the choice and tuning of the controller. Tools for studying the relative closed loop stability include the Root Locus theory and the Nyquist (and Bode) plots. These are used in a controller design context, with essentially materializes in choosing the suitable controller and tuning it on a basis of obtaining the desired closed loop response to typical inputs. Finally, we introduce the concept of inner system state by focusing on State-Space representation of systems. The State-Space equations are solved using either Laplace transform of the system eigenvalues, the system response is computed and the trajectories of state-space variables are presented.

Objectives

• Obtaining a solid background for studying the operational behavior and stability of systems in closed-loop control circuits. • Be capable of designing controllers for closed-loop system operation using the root locus theory or the Nyquist or Bode plots of the open loop system. • Understanding the State-Space representation of systems and using it for obtaining the state-space variables and, consequently, the system response.

Prerequisites

Automatic Control Systems I, Mathematics I, II and III.

Syllabus

Qualitative characteristics of closed-loop systems. Qualitative characteristics of closed-loop systems – Steady state errors. The concept of system stability – Routh algebraic stability criterion. Relative stability of closed-loop systems using the Root Locus method. Controller design using the Root Locus method. Controller design problem formulated as a set of performance equations. Relative stability of closed-loop system using Nyquist and BODE plots. State-Space representation: Variables, Equations, Controller and Observer Canonical Forms. Solving the State-Space equations using the Laplace transform. Solving the State-Space equations using the system eigenvalues.