Modern Control Engineering
150 Chapter 4 / Mathematical Modeling of Fluid Systems and Thermal Systems Taking the Laplace transform of Equation (4–44), assu ...
Example Problems and Solutions 151 or Noting that we obtain or Taking the Laplace transforms of both sides of this last equation ...
152 Chapter 4 / Mathematical Modeling of Fluid Systems and Thermal Systems Since thermal resistance Rmay be written as heat flow ...
Problems 153 B–4–2.Consider the liquid-level control system shown in Figure 4–43. The controller is of the proportional type. Th ...
154 Chapter 4 / Mathematical Modeling of Fluid Systems and Thermal Systems B–4–4.Figure 4–45 shows a pneumatic controller. The p ...
Problems 155 Actuating error signal Flapper Nozzle e a b k X + x R Orifice III Ps Pb + pb Pc + pc Figure 4–47 Pneumatic controll ...
156 Chapter 4 / Mathematical Modeling of Fluid Systems and Thermal Systems B–4–8.Figure 4–49 shows a flapper valve. It is placed ...
Problems 157 B–4–10.Consider the liquid-level control system shown in Figure 4–52. The inlet valve is controlled by a hydraulic ...
158 Chapter 4 / Mathematical Modeling of Fluid Systems and Thermal Systems B–4–11.Consider the controller shown in Figure 4–53. ...
5 159 Transient and Steady-State Response Analyses 5–1 Introduction In early chapters it was stated that the first step in analy ...
aa 160 Chapter 5 / Transient and Steady-State Response Analyses Which of these typical input signals to use for analyzing system ...
aa Section 5–2 / First-Order Systems 161 R(s) E(s) C(s) R(s) C(s) (a) (b) 1 Ts 1 +– Ts+ 1 Figure 5–1 (a) Block diagram of a firs ...
aa 162 Chapter 5 / Transient and Steady-State Response Analyses c(t) 1 0 0.632 A B T 2 T 3 T 4 T 5 Tt Slope=^1 T c(t)= 1 – e– (t ...
aa Section 5–2 / First-Order Systems 163 r(t) c(t) 6 T 4 T 2 T 02 T 4 T 6 Tt T T r(t)=t c(t) Steady-state error Figure 5–3 Unit- ...
aa 164 Chapter 5 / Transient and Steady-State Response Analyses An Important Property of Linear Time-Invariant Systems. In the a ...
aa Section 5–3 / Second-Order Systems 165 +– r K 1 s(Js+B) ecT J B (a) + R(s) R(s) C(s) C(s) T(s) (b) K K +– s(Js+B) (c) Fig ...
aa 166 Chapter 5 / Transient and Steady-State Response Analyses R(s) E(s) vn C(s) s(s+ 2 zvn) 2 + Figure 5–6 Second-order sy ...
aa Section 5–3 / Second-Order Systems 167 Hence the inverse Laplace transform of Equation (5–11) is obtained as fort 0 (5–12) F ...
aa 168 Chapter 5 / Transient and Steady-State Response Analyses (3)Overdamped case(z>1): In this case, the two poles of C(s)/ ...
aa Section 5–3 / Second-Order Systems 169 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0 123456789101112 0.8 vnt c(t) z = 0 0.1 0.2 0 ...
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