BME Control Systems 3

Question 1

In a PID controller, which term is responsible for eliminating steady-state error?

Accepted Answer

Integral (I) term

Answer

The integral term continuously accumulates error over time and generates an output that drives steady-state error to zero by adding an effective open-loop integrator.

Question 2

In state-space representation ẋ = Ax + Bu, y = Cx + Du, the matrix A is called the:

Accepted Answer

System (state) matrix

Answer

Matrix A is the system (state) matrix; its eigenvalues are the natural frequencies of the system, and it governs how state variables evolve without external input.

Question 3

What is the primary practical drawback of applying pure derivative (D-only) control action?

Accepted Answer

It amplifies high-frequency measurement noise

Answer

Differentiation magnifies rapid signal changes, so a pure derivative controller greatly amplifies high-frequency noise present in measured outputs, making stand-alone D control impractical.

Question 4

The Nyquist stability criterion determines closed-loop stability based on:

Accepted Answer

Net encirclements of the −1 + j0 point by the Nyquist plot

Answer

Using Cauchy's argument principle, the Nyquist criterion counts net clockwise encirclements of −1 + j0 by the open-loop Nyquist plot to determine the number of unstable closed-loop poles.

Question 5

A system is completely controllable if:

Accepted Answer

Any initial state can be driven to any desired state in finite time via an appropriate input

Answer

Complete controllability requires that for any initial state x₀ and desired final state xf, there exists an input u(t) that transfers the system from x₀ to xf in finite time; this is verified by the rank of the controllability matrix.

BME - Bachelor of Mechanical Engineering Practice Test

BME - Bachelor of Mechanical Engineering Practice Test

BME Control Systems 3