Master entrance examination of Beihang, 2019-2020

Syllabus of Engineering Science

Part I: Linear Time-Invariant systems

Chapter 1: Modeling of automation systems

I – Forward chain control II – Feedback control

Chapter 2: Hypotheses related to the study of linear time-invariant (LTI) systems

I – Continuity

1°) Definition

2°) Mathematical consequence II – Linearity

1°) Concept of operating point 2°) Local linearization

3°) Mathematical consequence 4°) Main types of nonlinearities

III – Time invariance

1°) Definition

2°) Mathematical consequenceChapter 3: Performances of LTI systems

I – Steady-state performances 1°) Stability

2°) Precision and robustness II – Transient-state performances

1°) Swiftness

2°) Damping

Chapter 4: Mathematical tools for the study of LTI systems

I – Laplace transform of a continuous signal

1°) Determination of the time response by convolution 2°) Definition of the Laplace transform

3°) Convolution product and transfer function 4°) Mathematical properties and main theorems 5°) Laplace transform of basic signals

II – Modeling by a block diagram

Chapter 5: Time response

I – 1st order systems

1°) Differential equation and transfer function 2°) Step response

3°) Impulse response 4°) Response to a ramp

II – 2nd order systems

1°) Differential equation and transfer function 2°) Step response

3°) Impulse response and response to a ramp III – Other systems

1°) Partial fraction decomposition

2°) General methodology and implicationsChapter 6: Frequency response

I – Definition and methods 1°) Definition

2°) Determination of the magnitude and phase shift 3°) Magnitude and phase plots

II – Frequency plots

1°) Bode plots

2°) Nichols plot

3°) Nyquist plot

III – Frequency response of some basic systems 1°) Integrator system

2°) 1st order system 3°) 2nd order system 4°) Pure delay

IV – Frequency response of other systems

1°) General form of a transfer function

2°) General methodology and consequences

Chapter 7: Algebraic methods for the determination of the performances of a LTI system

I – Stability

1°) Analysis of the transfer function

2°) Algebraic determination by means of Routh-Hurwitz’s criterion II – Precision and robustness

1°) Different types of closed-loop transfer function 2°) Precision conditions

3°) Robustness conditions III – Swiftness and damping

1°) Notion of dominant pole 2°) Determination of swiftness 3°) Determination of damping