Control Systems interview questions

1. A.network with pole nearer the origin than its zero placed well below crossover, raising low-frequency gain to cut steady-state error without disturbing transient response
2. B.Kp, Kv and Ka are the low-frequency limits of G(s), sG(s) and s²G(s); a type-1 system has zero step error and ramp error 1/Kv
3. C.network with zero nearer the origin than its pole that adds phase near gain crossover, improving phase margin and speed at the cost of wider bandwidth and noise
4. D.path traced by closed-loop poles as gain varies from zero to infinity, starting at open-loop poles and ending at open-loop zeros or along asymptotes to infinity

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1. A.Lead compensator
2. B.Ziegler-Nichols closed-loop tuning
3. C.Static error constants
4. D.Peak overshoot

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1. A.Static error constants — network with pole nearer the origin than its zero placed well below crossover, raising low-frequency gain to cut steady-state error without disturbing transient response
2. B.Static error constants — Kp, Kv and Ka are the low-frequency limits of G(s), sG(s) and s²G(s); a type-1 system has zero step error and ramp error 1/Kv
3. C.Static error constants — time for the response to enter and stay within a ±2% band of its final value, approximately 4/(ζωn) for a second-order system
4. D.Static error constants — maximum excursion beyond the final value, e^(−πζ/√(1−ζ²)) for a second-order system, depending only on damping ratio and about 16% at ζ = 0.5

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1. A.maximum excursion beyond the final value, e^(−πζ/√(1−ζ²)) for a second-order system, depending only on damping ratio and about 16% at ζ = 0.5
2. B.Kp, Kv and Ka are the low-frequency limits of G(s), sG(s) and s²G(s); a type-1 system has zero step error and ramp error 1/Kv
3. C.state-space property that the initial state can be reconstructed from output measurements, holding when [C; CA; …; CA^(n−1)] has full rank n
4. D.path traced by closed-loop poles as gain varies from zero to infinity, starting at open-loop poles and ending at open-loop zeros or along asymptotes to infinity

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1. A.Peak overshoot
2. B.Static error constants
3. C.Lead compensator
4. D.Root locus

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1. A.Peak overshoot — path traced by closed-loop poles as gain varies from zero to infinity, starting at open-loop poles and ending at open-loop zeros or along asymptotes to infinity
2. B.Peak overshoot — network with pole nearer the origin than its zero placed well below crossover, raising low-frequency gain to cut steady-state error without disturbing transient response
3. C.Peak overshoot — maximum excursion beyond the final value, e^(−πζ/√(1−ζ²)) for a second-order system, depending only on damping ratio and about 16% at ζ = 0.5
4. D.Peak overshoot — network with zero nearer the origin than its pole that adds phase near gain crossover, improving phase margin and speed at the cost of wider bandwidth and noise

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1. A.Kp, Kv and Ka are the low-frequency limits of G(s), sG(s) and s²G(s); a type-1 system has zero step error and ramp error 1/Kv
2. B.network with pole nearer the origin than its zero placed well below crossover, raising low-frequency gain to cut steady-state error without disturbing transient response
3. C.state-space property that the initial state can be reconstructed from output measurements, holding when [C; CA; …; CA^(n−1)] has full rank n
4. D.time for the response to enter and stay within a ±2% band of its final value, approximately 4/(ζωn) for a second-order system

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1. A.Ziegler-Nichols closed-loop tuning
2. B.Settling time
3. C.Static error constants
4. D.Root locus

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1. A.Settling time — time for the response to enter and stay within a ±2% band of its final value, approximately 4/(ζωn) for a second-order system
2. B.Settling time — network with zero nearer the origin than its pole that adds phase near gain crossover, improving phase margin and speed at the cost of wider bandwidth and noise
3. C.Settling time — magnitude in dB and phase against log frequency, where each real pole contributes −20 dB/decade and −90° asymptotically, letting gain and phase margins be read directly
4. D.Settling time — Kp, Kv and Ka are the low-frequency limits of G(s), sG(s) and s²G(s); a type-1 system has zero step error and ramp error 1/Kv

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1. A.network with pole nearer the origin than its zero placed well below crossover, raising low-frequency gain to cut steady-state error without disturbing transient response
2. B.maximum excursion beyond the final value, e^(−πζ/√(1−ζ²)) for a second-order system, depending only on damping ratio and about 16% at ζ = 0.5
3. C.path traced by closed-loop poles as gain varies from zero to infinity, starting at open-loop poles and ending at open-loop zeros or along asymptotes to infinity
4. D.PID rules from ultimate gain Ku and period Pu: Kp = 0.6Ku, Ti = 0.5Pu, Td = 0.125Pu, giving roughly quarter-amplitude decay

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1. A.Peak overshoot
2. B.Lead compensator
3. C.Ziegler-Nichols closed-loop tuning
4. D.Root locus

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1. A.Root locus — path traced by closed-loop poles as gain varies from zero to infinity, starting at open-loop poles and ending at open-loop zeros or along asymptotes to infinity
2. B.Root locus — state-space property that the initial state can be reconstructed from output measurements, holding when [C; CA; …; CA^(n−1)] has full rank n
3. C.Root locus — time for the response to enter and stay within a ±2% band of its final value, approximately 4/(ζωn) for a second-order system
4. D.Root locus — PID rules from ultimate gain Ku and period Pu: Kp = 0.6Ku, Ti = 0.5Pu, Td = 0.125Pu, giving roughly quarter-amplitude decay

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1. A.magnitude in dB and phase against log frequency, where each real pole contributes −20 dB/decade and −90° asymptotically, letting gain and phase margins be read directly
2. B.maximum excursion beyond the final value, e^(−πζ/√(1−ζ²)) for a second-order system, depending only on damping ratio and about 16% at ζ = 0.5
3. C.path traced by closed-loop poles as gain varies from zero to infinity, starting at open-loop poles and ending at open-loop zeros or along asymptotes to infinity
4. D.network with pole nearer the origin than its zero placed well below crossover, raising low-frequency gain to cut steady-state error without disturbing transient response

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1. A.Bode plot
2. B.Lag compensator
3. C.Ziegler-Nichols closed-loop tuning
4. D.Root locus

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1. A.Bode plot — time for the response to enter and stay within a ±2% band of its final value, approximately 4/(ζωn) for a second-order system
2. B.Bode plot — state-space property that the initial state can be reconstructed from output measurements, holding when [C; CA; …; CA^(n−1)] has full rank n
3. C.Bode plot — maximum excursion beyond the final value, e^(−πζ/√(1−ζ²)) for a second-order system, depending only on damping ratio and about 16% at ζ = 0.5
4. D.Bode plot — magnitude in dB and phase against log frequency, where each real pole contributes −20 dB/decade and −90° asymptotically, letting gain and phase margins be read directly

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1. A.maximum excursion beyond the final value, e^(−πζ/√(1−ζ²)) for a second-order system, depending only on damping ratio and about 16% at ζ = 0.5
2. B.Kp, Kv and Ka are the low-frequency limits of G(s), sG(s) and s²G(s); a type-1 system has zero step error and ramp error 1/Kv
3. C.network with zero nearer the origin than its pole that adds phase near gain crossover, improving phase margin and speed at the cost of wider bandwidth and noise
4. D.magnitude in dB and phase against log frequency, where each real pole contributes −20 dB/decade and −90° asymptotically, letting gain and phase margins be read directly

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1. A.Lead compensator
2. B.Observability
3. C.Peak overshoot
4. D.Static error constants

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1. A.Lead compensator — path traced by closed-loop poles as gain varies from zero to infinity, starting at open-loop poles and ending at open-loop zeros or along asymptotes to infinity
2. B.Lead compensator — time for the response to enter and stay within a ±2% band of its final value, approximately 4/(ζωn) for a second-order system
3. C.Lead compensator — network with zero nearer the origin than its pole that adds phase near gain crossover, improving phase margin and speed at the cost of wider bandwidth and noise
4. D.Lead compensator — state-space property that the initial state can be reconstructed from output measurements, holding when [C; CA; …; CA^(n−1)] has full rank n

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1. A.path traced by closed-loop poles as gain varies from zero to infinity, starting at open-loop poles and ending at open-loop zeros or along asymptotes to infinity
2. B.network with pole nearer the origin than its zero placed well below crossover, raising low-frequency gain to cut steady-state error without disturbing transient response
3. C.magnitude in dB and phase against log frequency, where each real pole contributes −20 dB/decade and −90° asymptotically, letting gain and phase margins be read directly
4. D.state-space property that the initial state can be reconstructed from output measurements, holding when [C; CA; …; CA^(n−1)] has full rank n

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1. A.Ziegler-Nichols closed-loop tuning
2. B.Lead compensator
3. C.Lag compensator
4. D.Static error constants

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1. A.Lag compensator — time for the response to enter and stay within a ±2% band of its final value, approximately 4/(ζωn) for a second-order system
2. B.Lag compensator — network with pole nearer the origin than its zero placed well below crossover, raising low-frequency gain to cut steady-state error without disturbing transient response
3. C.Lag compensator — magnitude in dB and phase against log frequency, where each real pole contributes −20 dB/decade and −90° asymptotically, letting gain and phase margins be read directly
4. D.Lag compensator — maximum excursion beyond the final value, e^(−πζ/√(1−ζ²)) for a second-order system, depending only on damping ratio and about 16% at ζ = 0.5

Answer + AI explanation with Pro

1. A.network with zero nearer the origin than its pole that adds phase near gain crossover, improving phase margin and speed at the cost of wider bandwidth and noise
2. B.state-space property that the initial state can be reconstructed from output measurements, holding when [C; CA; …; CA^(n−1)] has full rank n
3. C.magnitude in dB and phase against log frequency, where each real pole contributes −20 dB/decade and −90° asymptotically, letting gain and phase margins be read directly
4. D.PID rules from ultimate gain Ku and period Pu: Kp = 0.6Ku, Ti = 0.5Pu, Td = 0.125Pu, giving roughly quarter-amplitude decay

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1. A.Ziegler-Nichols closed-loop tuning
2. B.Settling time
3. C.Observability
4. D.Static error constants

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1. A.Observability — state-space property that the initial state can be reconstructed from output measurements, holding when [C; CA; …; CA^(n−1)] has full rank n
2. B.Observability — PID rules from ultimate gain Ku and period Pu: Kp = 0.6Ku, Ti = 0.5Pu, Td = 0.125Pu, giving roughly quarter-amplitude decay
3. C.Observability — Kp, Kv and Ka are the low-frequency limits of G(s), sG(s) and s²G(s); a type-1 system has zero step error and ramp error 1/Kv
4. D.Observability — network with pole nearer the origin than its zero placed well below crossover, raising low-frequency gain to cut steady-state error without disturbing transient response

Answer + AI explanation with Pro

1. A.PID rules from ultimate gain Ku and period Pu: Kp = 0.6Ku, Ti = 0.5Pu, Td = 0.125Pu, giving roughly quarter-amplitude decay
2. B.time for the response to enter and stay within a ±2% band of its final value, approximately 4/(ζωn) for a second-order system
3. C.state-space property that the initial state can be reconstructed from output measurements, holding when [C; CA; …; CA^(n−1)] has full rank n
4. D.path traced by closed-loop poles as gain varies from zero to infinity, starting at open-loop poles and ending at open-loop zeros or along asymptotes to infinity

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1. A.Lead compensator
2. B.Root locus
3. C.Observability
4. D.Ziegler-Nichols closed-loop tuning

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1. A.Ziegler-Nichols closed-loop tuning — state-space property that the initial state can be reconstructed from output measurements, holding when [C; CA; …; CA^(n−1)] has full rank n
2. B.Ziegler-Nichols closed-loop tuning — Kp, Kv and Ka are the low-frequency limits of G(s), sG(s) and s²G(s); a type-1 system has zero step error and ramp error 1/Kv
3. C.Ziegler-Nichols closed-loop tuning — magnitude in dB and phase against log frequency, where each real pole contributes −20 dB/decade and −90° asymptotically, letting gain and phase margins be read directly
4. D.Ziegler-Nichols closed-loop tuning — PID rules from ultimate gain Ku and period Pu: Kp = 0.6Ku, Ti = 0.5Pu, Td = 0.125Pu, giving roughly quarter-amplitude decay

Answer + AI explanation with Pro