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Q1 (a) A plant is modelled by the differential equation d²y 3. +2 + y = u dt² dy dt Assume that the initial condition y(0) = 1 and y(0) = 0. Use the Laplace transform to show that Y(s): = U(s) 3s² + 2s +1 3s +2 + 3s² + 2s +1 (b) The transfer function of a digital control system is given by (၁) G(z) = (z z² - 1 0.5)(z+0.2 + 0.6j) (z + 0.2 - 0.6j) where j is the imaginary unit. Find poles and zeros of the system. Then, determine the stability of the digital system. The block diagram of a fluidic speed control system is shown in Figure 1 where the actual speed C(s) is system output and R(s) is reference speed. Show that the closed-loop transfer function is given by Reference Speed R(s) Ka C(s) 100s²+s+K₂ R(s) Valve Amplifier actuator Turbine Actual Speed 1 1 Ка S 1+100s C(s) Figure 1

Q1 (a) A plant is modelled by the differential equation d²y 3. +2 + y = u dt² dy dt Assume that the initial condition y(0) = 1 and y(0) = 0. Use the Laplace transform to show that Y(s): = U(s) 3s² + 2s +1 3s +2 + 3s² + 2s +1 (b) The transfer function of a digital control system is given by (၁) G(z) = (z z² - 1 0.5)(z+0.2 + 0.6j) (z + 0.2 - 0.6j) where j is the imaginary unit. Find poles and zeros of the system. Then, determine the stability of the digital system. The block diagram of a fluidic speed control system is shown in Figure 1 where the actual speed C(s) is system output and R(s) is reference speed. Show that the closed-loop transfer function is given by Reference Speed R(s) Ka C(s) 100s²+s+K₂ R(s) Valve Amplifier actuator Turbine Actual Speed 1 1 Ка S 1+100s C(s) Figure 1

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Q1 (a) A plant is modelled by the differential equation d²y 3. +2 + y = u dt² dy dt Assume that the initial condition y(0) = 1 and y(0) = 0. Use the Laplace transform to show that Y(s): = U(s) 3s² + 2s +1 3s +2 + 3s² + 2s +1 (b) The transfer function of a digital control system is given by (၁) G(z) = (z z² - 1 0.5)(z+0.2 + 0.6j) (z + 0.2 - 0.6j) where j is the imaginary unit. Find poles and zeros of the system. Then, determine the stability of the digital system. The block diagram of a fluidic speed control system is shown in Figure 1 where the actual speed C(s) is system output and R(s) is reference speed. Show that the closed-loop transfer function is given by Reference Speed R(s) Ka C(s) 100s²+s+K₂ R(s) Valve Amplifier actuator Turbine Actual Speed 1 1 Ка S 1+100s C(s) Figure 1
Transcribed Image Text:Q1 (a) A plant is modelled by the differential equation d²y 3. +2 + y = u dt² dy dt Assume that the initial condition y(0) = 1 and y(0) = 0. Use the Laplace transform to show that Y(s): = U(s) 3s² + 2s +1 3s +2 + 3s² + 2s +1 (b) The transfer function of a digital control system is given by (၁) G(z) = (z z² - 1 0.5)(z+0.2 + 0.6j) (z + 0.2 - 0.6j) where j is the imaginary unit. Find poles and zeros of the system. Then, determine the stability of the digital system. The block diagram of a fluidic speed control system is shown in Figure 1 where the actual speed C(s) is system output and R(s) is reference speed. Show that the closed-loop transfer function is given by Reference Speed R(s) Ka C(s) 100s²+s+K₂ R(s) Valve Amplifier actuator Turbine Actual Speed 1 1 Ка S 1+100s C(s) Figure 1
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