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Control Systems Fundamentals
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1
Question
What is a control system?
Answer
A control system is an arrangement of components that takes an input (a command or reference), processes it through a mechanism or plant, and produces an output that is managed or regulated to achieve a desired behavior or performance.
2
Question
Define an open-loop control system and give one advantage and one disadvantage.
Answer
An open-loop control system is a system that applies an input to a process and produces an output without monitoring or correcting that output. Advantage: simpler and cheaper because it requires no feedback sensors or comparison logic. Disadvantage: cannot correct for disturbances or model errors, so accuracy can be poor under varying conditions.
3
Question
Define a closed-loop control system and explain how it differs from an open-loop system.
Answer
A closed-loop control system monitors the output, compares it to the desired input (reference), and uses the difference (error) to automatically make corrective adjustments to the process. Unlike an open-loop system, a closed-loop system uses feedback to reduce errors and improve accuracy and robustness to disturbances.
4
Question
What is a disturbance in control systems? Provide two examples.
Answer
A disturbance is any external or internal influence that affects the system output in an undesired way. Examples: (1) A gust of wind acting on a drone’s position control, (2) Load torque variation on an electric motor shaft.
5
Question
What is transient response and why is it important?
Answer
Transient response is the system’s short-term reaction to a change in input, initial condition, or disturbance before it settles to a steady behavior. It is important because it determines how quickly the system responds, the level of overshoot, and the mechanical or electrical stress placed on components during the change.
6
Question
What is steady-state response and how does it relate to accuracy?
Answer
Steady-state response is the long-term behavior of the system after transients have died out. It determines how close the system output remains to the desired reference over time; the difference between the desired value and the actual output in steady state is called steady-state error, which directly measures accuracy.
7
Question
Define steady-state error.
Answer
Steady-state error is the difference between the desired reference input and the actual system output after the transient response has decayed and the system has reached steady behavior.
8
Question
What does system stability mean in control engineering?
Answer
Stability means the system’s ability to return to a bounded, acceptable response after a disturbance or change in input; mathematically, for linear systems, it means all natural response modes decay with time (no unbounded growth).
9
Question
Explain power gain in the context of control systems.
Answer
Power gain refers to the use of a control system to convert a low-power input command into a higher-power output action through the process or actuator, typically by combining control signals with power stages so the plant delivers more power than the control signal alone.
10
Question
What is remote control in control systems?
Answer
Remote control is operating a system from a distance by sending commands (inputs) over a communication link to a controller or actuator that performs actions at the remote location, often requiring feedback and communication reliability considerations.
11
Question
Define input, process (plant), and output in a control system.
Answer
Input: the signal or command given to the control system (reference). Process (plant): the physical system or mechanism that transforms the input into an output. Output: the resulting action or signal produced by the system that we measure or want to control.
12
Question
What is feedback and why is it used in control systems?
Answer
Feedback is information about the actual output sent back to be compared with the reference input. It is used to generate an error signal and enable the controller to correct the process, improving accuracy, disturbance rejection, and robustness.
13
Question
What is an error signal?
Answer
An error signal is the difference between the desired reference input and the measured output (or a processed version of it). The controller uses the error to decide corrective actions.
14
Question
How is accuracy defined for a control system?
Answer
Accuracy is how close the system output is to the desired reference value, typically measured by metrics such as steady-state error or percentage error in steady conditions.
15
Question
What is meant by system speed in control systems? Name two common measures of speed.
Answer
System speed refers to how quickly a system responds to changes in input or disturbances. Two common measures are rise time (time to go from a low to high percentage of the final value) and settling time (time for the output to remain within a specified band around the final value).
16
Question
What is mechanical stress in relation to control transients and why does it matter?
Answer
Mechanical stress refers to physical strain on components caused by rapid or large transient responses (like big accelerations, jerks, or overshoot). It matters because excessive stress can fatigue parts, cause wear, or lead to failure, so transients must be managed for longevity and safety.
17
Question
List five common applications of control systems.
Answer
Homes (thermostats, HVAC), industry (process control, robotics), science (instrumentation and stabilization), transportation (vehicle cruise control, autopilot), and biological/natural systems (homeostasis in organisms, population dynamics modeling).
18
Question
What is a mathematical model in control engineering?
Answer
A mathematical model is an equation-based representation of a physical system (the plant) that captures its dynamic behavior, typically using differential equations, transfer functions, or state-space models to predict outputs for given inputs.
19
Question
Define the transfer function and write its basic formula.
Answer
The transfer function is the ratio of the Laplace transform of the output to the Laplace transform of the input for a linear time-invariant (LTI) system under zero initial conditions. It is written as: $G(s)=\dfrac{C(s)}{R(s)}$, where $C(s)$ is the output transform and $R(s)$ is the input transform.
20
Question
What is a Linear Time-Invariant (LTI) system?
Answer
An LTI system is a system whose parameters do not change with time (time-invariant) and that satisfies the principles of superposition (linearity). For such systems, methods like transfer functions and convolution apply.
21
Question
Give the definition of the Laplace transform and its integral expression.
Answer
The Laplace transform of a time-domain function $f(t)$ (for $t\ge 0$) is defined as $F(s)=\mathcal{L}\{f(t)\}=\displaystyle\int_0^{\infty} e^{-st} f(t)\,dt$, where $s$ is a complex variable.
22
Question
State the closed-loop transfer function for a forward path $G(s)$ and feedback path $H(s)$ and explain the significance of the denominator.
Answer
The closed-loop transfer function with negative feedback is $T(s)=\dfrac{G(s)}{1+G(s)H(s)}$. The denominator $1+G(s)H(s)$ determines closed-loop poles; its roots (values of $s$ making the denominator zero) govern stability and transient behavior.
23
Question
How do you determine closed-loop stability from the closed-loop transfer function?
Answer
Closed-loop stability is determined by the locations of the poles of the closed-loop transfer function (the roots of $1+G(s)H(s)=0$). For continuous-time LTI systems, stability requires all poles to have negative real parts (i.e., lie in the left half of the complex $s$-plane).
24
Question
What is the Final Value Theorem and what's its formula for a Laplace transform $F(s)$?
Answer
The Final Value Theorem gives the steady-state (long-time) value of a time function when it exists: $\displaystyle\lim_{t\to\infty} f(t)=\lim_{s\to 0} sF(s)$, provided all poles of $sF(s)$ have negative real parts (i.e., the limit exists for a stable system).
25
Question
Describe how to compute steady-state error for a unity-feedback system using the transfer function $G(s)$.
Answer
For a unity-feedback system (feedback path = 1), the steady-state error to a reference is determined by static error constants. For a unit-step input, the position error constant $K_p=\lim_{s\to 0} G(s)$ and the steady-state error is $e_{ss}=\dfrac{1}{1+K_p}$. This assumes the closed-loop system is stable so the final value exists.
26
Question
What are common transient-response specifications used in controller design? Briefly define each.
Answer
Common specifications: Rise time (time for output to go from a low to high percentage, e.g., 10% to 90% of final value); Peak time (time to first maximum peak); Overshoot (amount the peak exceeds final value, often as a percentage); Settling time (time for output to stay within a specified band, e.g., ±2% of final value). These quantify speed and damping.
27
Question
What is the difference between negative and positive feedback?
Answer
Negative feedback subtracts a portion of the output from the reference to reduce error and stabilize/linearize the system; it is the common form used in control. Positive feedback adds a portion of the output to the reference, which can increase gain but may lead to instability or oscillation if uncontrolled.
28
Question
Explain how feedback improves disturbance rejection.
Answer
Feedback measures the output and corrects deviations from the desired reference, so when a disturbance alters the output, the control action driven by the error works to counteract the disturbance and restore the output toward the setpoint. The loop gain magnitude and controller design determine how effectively disturbances are rejected.
29
Question
What is loop gain and why does it matter?
Answer
Loop gain is the product of forward-path and feedback-path gains around the feedback loop, typically $L(s)=G(s)H(s)$. It matters because its magnitude and phase determine closed-loop sensitivity, disturbance rejection, bandwidth, and potential for instability (via Nyquist/Bode criteria).
30
Question
How does increasing controller gain typically affect steady-state error and transient response?
Answer
Increasing controller (or loop) gain usually reduces steady-state error and improves tracking, but it can also speed up the response and increase overshoot and oscillatory behavior, possibly degrading stability or increasing mechanical stress in actuators.