Control Systems

Control Systems – Verified PYQ Authority Guide

Control Systems is a sub-subject authority hub. It is designed to expose the important topic/concept clusters represented by verified SRO PYQs and guide students from broad revision into the exact solved questions that support each area. Every factual learning cue below is drawn from the existing verified, published and approved English PYQ corpus or from its Knowledge Graph relationships; the hub does not invent unsupported technical claims.

PYQ evidence snapshot

24 verified PYQs are currently mapped to this Sub Subject hub. The represented years include 2026, 2025. Exam coverage currently includes Deputy Executive Engineer (Electrical), Class-2, Sports Authority of Gujarat / Assistant Engineer (Electrical), Class-2,, Assistant Engineer (Electrical), Class-2, Road and Building Department. Subject context includes Electrical Engineering. These values come from live mappings and can expand automatically when new verified PYQs are added.

Most useful verified PYQs to solve first

Start with the actual questions rather than memorising a generic note. The links below are ranked from the mapped corpus using repeat history and editorial quality, while the complete explanation stays on the individual question page.

1. A system is represented in state-space form with two state variables and stable eigenvalues, then 1. The system order is two. 2. The system is stable since eigenvalues lie in left half-plane.…
   Deputy Executive Engineer (Electrical), Class-2, Sports Authority of Gujarat / Assistant Engineer (Electrical), Class-2, · 2026 · System Order Eigenvalues and Output Equation
   A state-space model represents internal dynamics using a minimal set of state variables. Output generally depends on both state and direct input through y=Cx+Du.…
2. A system has gain crossover frequency at which magnitude is unity and phase is –150 degrees, then 1. The phase margin of the system is 30 degrees. 2. The system is stable…
   Deputy Executive Engineer (Electrical), Class-2, Sports Authority of Gujarat / Assistant Engineer (Electrical), Class-2, · 2026 · Phase Margin and Gain Crossover
   Gain margin and phase margin quantify distance from the critical feedback condition and are widely used as relative-stability measures; pole and zero locations shape…
3. A unity feedback system has open-loop transfer function such that it is a type-1 system and subjected to a unit step input, then 1. The steady-state error for step input is zero.…
   Deputy Executive Engineer (Electrical), Class-2, Sports Authority of Gujarat / Assistant Engineer (Electrical), Class-2, · 2026 · Type-1 Error Constants
   It determines the order of polynomial input that can be tracked with zero/finite/infinite steady-state error, provided the closed loop is stable. Static-error constants directly…
4. A second-order system has damping ratio 0.5 and natural frequency 4 rad/s, then 1. The system is underdamped and exhibits oscillatory response. 2. The damped natural frequency is less than the natural…
   Deputy Executive Engineer (Electrical), Class-2, Sports Authority of Gujarat / Assistant Engineer (Electrical), Class-2, · 2026 · Damped Frequency Overshoot and Settling
   Second-order dynamics are governed by two independent energy-storage states and are described by natural frequency and damping ratio. With ζ=0.5 and ωn=4 rad/s, ωd=ωn√(1−ζ²)≈3.46…
5. A first-order system has a time constant of 2 seconds and is subjected to a unit step input. The system gain is unity, then 1. The output reaches approximately 63 percent of…
   Deputy Executive Engineer (Electrical), Class-2, Sports Authority of Gujarat / Assistant Engineer (Electrical), Class-2, · 2026 · Time Constant and Step Response
   A standard first-order system has one real pole and an exponential step response controlled by a time constant τ. For τ=2 s, y(t)=1−e^(−t/2). At…
6. Consider the following statements regarding Non-linear Control Systems: 1. Superposition principle does not apply. 2. Linearization is used for analysis near operating point. 3. Non-linear systems are always unstable. 4. Phase plane…
   Deputy Executive Engineer (Electrical), Class-2, Sports Authority of Gujarat / Assistant Engineer (Electrical), Class-2, · 2026 · Linearization and Phase-Plane Analysis
   Nonlinear systems do not obey superposition, but they can still be stable or unstable. Linearization around an operating point uses a local first-order approximation…
7. Consider the following statements regarding Stability in State-Space Analysis: 1. Eigenvalues of the system matrix A define the characteristic roots that determine the system's stability. 2. A system is asymptotically stable if…
   Deputy Executive Engineer (Electrical), Class-2, Sports Authority of Gujarat / Assistant Engineer (Electrical), Class-2, · 2026 · Eigenvalue Criterion for Stability
   A state-space model represents internal dynamics using a minimal set of state variables. Stability of a continuous-time LTI model is tied to eigenvalues of…
8. Consider the following statements regarding State Variable Analysis: 1. State variables define system dynamics completely. 2. State-space model can represent MIMO systems. 3. Transfer function can always be uniquely obtained from state…
   Deputy Executive Engineer (Electrical), Class-2, Sports Authority of Gujarat / Assistant Engineer (Electrical), Class-2, · 2026 · State Model MIMO and Initial Conditions
   A state-space model represents internal dynamics using a minimal set of state variables. It naturally handles MIMO systems and incorporates initial conditions. Key relation:…

Formula & key-relationship bank from verified solutions

• ẋ=Ax+Bu; y=Cx+Du.
• At gain crossover ω_gc: PM=180°+∠G(jω_gc).
• Type 1: Kp=lim_{s→0}GH=∞ → ess,step=1/(1+Kp)=0; Kv=lim_{s→0}sGH finite → ess,ramp=1/Kv.
• Characteristic form: s²+2ζω_n s+ω_n²=0.
• G(s)=1/(τs+1); y(t)=1−e^(−t/τ).
• Local linearization uses the Jacobian evaluated at the operating point.

Use these as revision triggers and open the linked PYQ before applying a formula numerically; variable definitions and assumptions belong to the exact solved question.

Core ideas repeatedly reinforced by the solved corpus

• A state-space model represents internal dynamics using a minimal set of state variables. Output generally depends on both state and direct input through y=Cx+Du. Key relation: ẋ=Ax+Bu; y=Cx+Du. Exam focus: Eigenvalues of A are the state-model characteristic roots.…
• Gain margin and phase margin quantify distance from the critical feedback condition and are widely used as relative-stability measures; pole and zero locations shape the frequency response. At gain crossover, phase=−150°, so PM=180−150=30°. Gain margin must be evaluated…
• It determines the order of polynomial input that can be tracked with zero/finite/infinite steady-state error, provided the closed loop is stable. Static-error constants directly produce the truth set {1,2,3}. Key relation: Type 1: Kp=lim_{s→0}GH=∞ → ess,step=1/(1+Kp)=0; Kv=lim_{s→0}sGH finite…
• Second-order dynamics are governed by two independent energy-storage states and are described by natural frequency and damping ratio. With ζ=0.5 and ωn=4 rad/s, ωd=ωn√(1−ζ²)≈3.46 rad/s, so the response is underdamped and has nonzero overshoot. Key relation: Characteristic form:…
• A standard first-order system has one real pole and an exponential step response controlled by a time constant τ. For τ=2 s, y(t)=1−e^(−t/2). At t=2 s, y≈0.632. Key relation: G(s)=1/(τs+1); y(t)=1−e^(−t/τ). Exam focus: 63% at τ, ~95% at…

Exam tips already validated in SRO solutions

• Eigenvalues of A are the state-model characteristic roots.
• Positive phase margin usually indicates a stable negative-feedback loop with normal assumptions.
• Type-1 mnemonic: step → zero error; ramp → finite error; parabolic → infinite error.
• ζ1 overdamped.
• 63% at τ, ~95% at 3τ, ~99% at 5τ.

Common mistakes to avoid

• Output is not generally independent of state variables.
• Frequency response is not independent of poles and zeros.
• Ignoring the closed-loop stability condition when applying steady-state error formulas.
• Overdamped responses do not sustain oscillations.
• Do not confuse one time constant with 95% settling.

Topic and concept coverage

Mapped topic labels include Time Response, Controllers, State-Space Analysis, Frequency Response, Root Locus, Steady-State Analysis, Nonlinear Control. The concept trail includes Autocorrelation of Rectangular Pulse, Branches Poles Zeros and Breakaway Points, Control Signal Modification, Critically Damped Step Response, Damped Frequency Overshoot and Settling, Damping Ratio and Response Type, Direct Lyapunov Method, Effect of PI Control. Use these labels as a revision map: move from the broad area to the narrow concept, solve a verified PYQ, inspect the detailed reasoning, and then attempt another question from the same cluster.

Knowledge Graph navigation

Continue with Electrical Engineering, Controllers, Feedback, Feedback Systems, Frequency Response, Nonlinear Control, Time Response, State-Space Analysis, State Variables. These are canonical SRO entity links based on the Knowledge Graph and shared question mappings, not keyword-stuffed tag pages.

How to revise this authority page efficiently

1. Solve before reading: answer a mapped PYQ first.
2. Read the exact explanation: verify the correct principle, formula, distractor logic and common mistake on that question page.
3. Move one level in the graph: use the closest concept/sub-topic/topic link rather than opening unrelated content.
4. Reattempt: solve another verified PYQ from this hub and check whether the same error repeats.

Quality scope: this page is automatically maintained from SRO’s verified mapped corpus. It enriches one canonical authority URL instead of generating multiple near-duplicate pages for keyword variants. Manual authority articles are never overwritten by the automated engine.