Automatic Control (R7003E) Written Exam Vocabulary

Vocabulary and key technical concepts from the R7003E Automatic Control written exam at Luleå Tekniska Universitet, focusing on LTI systems, observers, and feedback robustness.

Diagonalizable Matrix

A square matrix $A$ that can be transformed into a diagonal form; if $A$ is diagonalizable, the system is represented in modal canonical form.

Jordan Canonical Form

An alternative state-space representation used for an LTI system when the system matrix $A$ is not diagonalizable.

Controllability and Observability Indexes

Metrics used to characterize an LTI $(A, B, C, D)$ system's ability to be controlled by inputs and reconstructed from outputs.

Zero Steady-State Error

A control system performance condition where the output $y(\infty)$ equals the constant reference signal $r$.

Robustness

The property determining if a system's steady-state error performance remains valid when parameters change, such as $A$ changing to $A + SA$.

Augmented System

A system modified with an integrator (e.g., $x_{1} = r - y$) and state feedback ($u = -Kx - K_{1}x_{1}$) to achieve robust steady-state error performance.

Linearized Pendulum Equations

The simplified equations of motion for a pendulum given as $\ddot{\theta} + \omega^{2} \theta = u$, where $\omega = 5\,rad/sec$.

Estimator (Observer)

A mathematical component designed to reconstruct state variables (such as $\theta$) from measurements, with specific roots such as $s = -1010j$.

State Feedback Control

A control strategy using the form $u(t) = -Kx(t) + \bar{N}r(t)$, where $\bar{N}$ is a nonzero scalar, to move system poles to specific locations like $-3 \pm 3j$.

Reduced Order Observer

A type of estimator mentioned in Problem 3 whose use is based on specific system requirements.

PID Control

A traditional control method used in comparison with state feedback control architectures.