CONTROL SYSTEM (KEC-602)
B.Tech Semester VI – Theory Examination (2021–22)
Control System engineering deals with the analysis and design of systems that regulate themselves automatically by using feedback and control actions. The primary objective of a control system is to ensure that the output of a system follows the desired input with acceptable accuracy, stability, speed of response, and robustness against disturbances. Control systems are widely used in electrical, mechanical, chemical, aerospace, and instrumentation engineering, making this subject a core component of engineering education.
From the uploaded question paper, it is clear that the syllabus and examination focus on open-loop and closed-loop systems, block diagram reduction, state-space modeling, time-domain specifications, stability analysis, root locus, frequency response methods such as Bode, Nyquist and Polar plots, controllability and observability, and classical control system design concepts. To score well, answers must be written in clear, logically connected paragraphs, supported by mathematical expressions, reasoning, and interpretation of results rather than brief bullet points.
SECTION A – BASIC CONTROL SYSTEM CONCEPTS
(Based on Section A, Page-1)
An open loop system is one in which the control action is independent of the output, whereas a closed loop system uses feedback to compare the output with the reference input and generate an error signal. Closed loop systems provide better accuracy, stability, and disturbance rejection compared to open loop systems, though they are more complex and costly.
The elementary block diagram of an open loop system consists of an input, controller, and plant arranged in sequence, while a closed loop system additionally includes a feedback element and summing junction to form a feedback path.
A system is said to be controllable if it is possible to drive the system from any initial state to any desired final state within finite time using a suitable control input. Controllability is essential for effective control system design.
The state-space model has advantages over the transfer function model because it can represent multiple-input multiple-output systems and provides information about internal states, which transfer functions cannot.
Settling time is the time required for the system response to remain within a specified tolerance band around the final value, while maximum peak overshoot represents the maximum deviation of the response above its steady-state value.
Rise time is the time taken by the response to rise from a specified lower percentage to a higher percentage of its final value, whereas peak time is the time at which the maximum overshoot occurs.
The location of system poles directly determines stability. Poles in the left half of the s-plane indicate stability, poles on the imaginary axis indicate marginal stability, and poles in the right half indicate instability.
The angle of departure in root locus analysis indicates the direction in which the locus leaves a complex pole and is determined using angle conditions.
The gain crossover frequency is the frequency at which the magnitude of the open-loop transfer function becomes unity, and it plays a key role in stability analysis using frequency response methods.
The polar plot provides insight into system stability by plotting the magnitude and phase of the open-loop transfer function over a range of frequencies.
SECTION B – SYSTEM MODELING AND STABILITY ANALYSIS
(Based on Section B, Pages 1–2)
Block diagram reduction simplifies complex control systems into a single equivalent transfer function using series, parallel, and feedback combinations. This technique is essential for analyzing overall system behavior.
The state-space representation of a system described by a differential equation involves defining state variables, forming state equations, and expressing the output equation independently of input when required. This approach provides a complete description of system dynamics.
From the given unit step response curve, system parameters such as gain (K) and time constant (T) can be determined by analyzing rise time, peak overshoot, and steady-state behavior.
The Routh–Hurwitz stability criterion is a mathematical technique used to determine system stability without solving the characteristic equation. It provides information about the number of roots in the right half of the s-plane.
The Nyquist plot is a frequency-domain method used to assess stability by mapping the open-loop transfer function and applying the Nyquist stability criterion.
SECTION C – SIGNAL FLOW GRAPH AND STATE ANALYSIS
(Based on Section C, Page-2)
A signal flow graph represents a control system using nodes and branches, and the overall transfer function is obtained using Mason’s Gain Formula, which considers forward paths, loops, and non-touching loops.
For a given transfer function, state equations are derived to represent system dynamics, and the state diagram visually shows the interaction between state variables.
Controllability and observability analysis determines whether a system’s states can be controlled or observed from input and output respectively. These properties are essential for modern control design.
TIME RESPONSE AND ROOT LOCUS ANALYSIS
(Based on Questions 5 & 6, Page-3)
The unit step response of an under-damped second-order system is derived using standard differential equations and is characterized by oscillations, overshoot, and settling time.
In root locus analysis, the system’s stability and performance are studied by plotting the roots of the characteristic equation as the gain varies. The value of gain at which the system becomes stable or unstable is determined from the locus.
FREQUENCY RESPONSE ANALYSIS
(Based on Question 7, Page-3)
The Bode plot represents the frequency response using magnitude and phase plots on a logarithmic scale. From Bode plots, gain margin, phase margin, and stability of the system can be determined.
By sketching Bode plots for different gain values, the effect of gain variation on stability can be clearly understood.
HOW TO WRITE CONTROL SYSTEM ANSWERS IN THE EXAM
In Control System examinations, never write answers in short bullet points. Always start with a definition or principle, followed by mathematical formulation, analysis, and interpretation of results. Numerical problems must include formulas, assumptions, and step-by-step reasoning. Examiners give maximum weightage to conceptual clarity, correct application of theory, and logical explanation.
