Figure 1 1 Simplified description of a control

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Figure 1. 1 Simplified description of a control system Control Systems Engineering, Fourth Edition

Figure 1. 1 Simplified description of a control system Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 1. 5 Elevator input and output Control Systems Engineering, Fourth Edition by Norman

Figure 1. 5 Elevator input and output Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 1. 6 Block diagrams of control systems: a. open-loop system; b. closed-loop system

Figure 1. 6 Block diagrams of control systems: a. open-loop system; b. closed-loop system Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 1. 11 The control system design process Control Systems Engineering, Fourth Edition by

Figure 1. 11 The control system design process Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 1. 9 Antenna azimuth position control system: a. system concept; b. detailed layout;

Figure 1. 9 Antenna azimuth position control system: a. system concept; b. detailed layout; c. schematic; d. functional block diagram Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 1. 10 Response of a position control system showing effect of high and

Figure 1. 10 Response of a position control system showing effect of high and low controller gain on the output response Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 1. 12 Equivalent block diagram for the antenna azimuth position control system Control

Figure 1. 12 Equivalent block diagram for the antenna azimuth position control system Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Table 1. 1 Test waveforms used in control systems Control Systems Engineering, Fourth Edition

Table 1. 1 Test waveforms used in control systems Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Modeling In order to systematically design a controller for a particular system, one needs

Modeling In order to systematically design a controller for a particular system, one needs a formal - though possibly simple - description of the system. Such a description is called a model. A model is a set of mathematical equations that are intended to capture the effect of certain system variables on certain other system variables. Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Modeling Models are classified according to properties of the equation they are based on.

Modeling Models are classified according to properties of the equation they are based on. Examples of classification include: In many situations nonlinear models can be linearized around a user defined operating point. Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 2. 1 a. Block diagram representation of a system; b. block diagram representation

Figure 2. 1 a. Block diagram representation of a system; b. block diagram representation of an interconnection of subsystems Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Modeling in Frequency Domain Transfer Function Control Systems Engineering, Fourth Edition by Norman S.

Modeling in Frequency Domain Transfer Function Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Transfer Function is the ratio of output to input in frequency domain G(s) =

Transfer Function is the ratio of output to input in frequency domain G(s) = C(s)/R(s) Figure 2. 2 Block diagram of a transfer function Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Table 2. 1 Laplace transform table Control Systems Engineering, Fourth Edition by Norman S.

Table 2. 1 Laplace transform table Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Table 2. 2 Laplace transform theorems Control Systems Engineering, Fourth Edition by Norman S.

Table 2. 2 Laplace transform theorems Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Examples 1) Find the transfer function represented by dc(t)/dt + 2 c(t) = r(t)

Examples 1) Find the transfer function represented by dc(t)/dt + 2 c(t) = r(t) Sol’n Taking Laplace transform of both sides s. C(s) + 2 C(s) = R(s) G(s) = C(s)/R(s) = 1/(s+2) 2) Find the response c(t) to an input r(t) = u(t) a unit step. Sol’n C(s) = R(s)G(s) = 1/s(s+2) = 0. 5/s – 0. 5/(s+2) Inverse Laplace c(t) = 1/2 – 1/2 e-2 t Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Table 2. 3 Voltage-current, voltage-charge, and impedance relationships for capacitors, resistors, and inductors Component

Table 2. 3 Voltage-current, voltage-charge, and impedance relationships for capacitors, resistors, and inductors Component V-I I-V V-Q Impedence Admittance Z(s)=V/I Y(s) = I/V Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

L di(t)/dt + Ri(t) + 1/C ∫i(τ) dτ = v(t) Figure 2. 3 RLC

L di(t)/dt + Ri(t) + 1/C ∫i(τ) dτ = v(t) Figure 2. 3 RLC network Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Find Vc(s)/V(s) (Ls+R+1/Cs) I(s) = V(s) Vc(s) = I(s)/ Cs Vc(s)/V(s) = (1/LC) /

Find Vc(s)/V(s) (Ls+R+1/Cs) I(s) = V(s) Vc(s) = I(s)/ Cs Vc(s)/V(s) = (1/LC) / (s 2+ (R/L)s+ 1/LC) Figure 2. 5 Laplace-transformed network Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 2. 4 Block diagram of series RLC electrical network Control Systems Engineering, Fourth

Figure 2. 4 Block diagram of series RLC electrical network Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 2. 6 a. Two-loop electrical network; b. transformed two-loop electrical network; c. block

Figure 2. 6 a. Two-loop electrical network; b. transformed two-loop electrical network; c. block diagram Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 2. 7 Block diagram of the network of Figure 2. 6 Let G

Figure 2. 7 Block diagram of the network of Figure 2. 6 Let G 1= 1/R 1 and G 2= 1/R 2 Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 2. 8 Transformed network ready for nodal analysis Control Systems Engineering, Fourth Edition

Figure 2. 8 Transformed network ready for nodal analysis Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 2. 9 Three-loop electrical network Control Systems Engineering, Fourth Edition by Norman S.

Figure 2. 9 Three-loop electrical network Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Table 2. 4 Force-velocity, forcedisplacement, and impedance translational relationships for springs, viscous dampers, and

Table 2. 4 Force-velocity, forcedisplacement, and impedance translational relationships for springs, viscous dampers, and mass Translational Mechanical Systems Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 2. 15 a. Mass, spring, and damper system; b. block diagram Control Systems

Figure 2. 15 a. Mass, spring, and damper system; b. block diagram Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 2. 16 a. Free-body diagram of mass, spring, and damper system; b. transformed

Figure 2. 16 a. Free-body diagram of mass, spring, and damper system; b. transformed free-body diagram Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 2. 17 a. Two-degrees-of-freedom translational mechanical system 8; b. block diagram Control Systems

Figure 2. 17 a. Two-degrees-of-freedom translational mechanical system 8; b. block diagram Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 2. 20 Three-degrees-of-freedom translational mechanical system Control Systems Engineering, Fourth Edition by Norman

Figure 2. 20 Three-degrees-of-freedom translational mechanical system Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Table 2. 5 Torque-angular velocity, torque-angular displacement, and impedance rotational relationships for springs, viscous

Table 2. 5 Torque-angular velocity, torque-angular displacement, and impedance rotational relationships for springs, viscous dampers, and inertia Rotational Mechanical Systems Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 2. 22 a. Physical system; b. schematic; c. block diagram Control Systems Engineering,

Figure 2. 22 a. Physical system; b. schematic; c. block diagram Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 2. 25 Three-degrees-offreedom rotational system Control Systems Engineering, Fourth Edition by Norman S.

Figure 2. 25 Three-degrees-offreedom rotational system Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 2. 35 DC motor: a. schematic 12; b. block diagram Control Systems Engineering,

Figure 2. 35 DC motor: a. schematic 12; b. block diagram Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 2. 41 Development of series analog: a. mechanical system; b. desired electrical representation;

Figure 2. 41 Development of series analog: a. mechanical system; b. desired electrical representation; c. series analog; d. parameters for series analog Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 2. 42 Series analog of mechanical system of Figure 2. 17(a) Control Systems

Figure 2. 42 Series analog of mechanical system of Figure 2. 17(a) Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 2. 43 Development of parallel analog: a. mechanical system; b. desired electrical representation;

Figure 2. 43 Development of parallel analog: a. mechanical system; b. desired electrical representation; c. parallel analog; d. parameters for parallel analog Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 2. 44 Parallel analog of mechanical system of Figure 2. 17(a)

Figure 2. 44 Parallel analog of mechanical system of Figure 2. 17(a)

Figure 2. 45 a. Linear system; b. nonlinear system Control Systems Engineering, Fourth Edition

Figure 2. 45 a. Linear system; b. nonlinear system Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 2. 46 Some physical nonlinearities Control Systems Engineering, Fourth Edition by Norman S.

Figure 2. 46 Some physical nonlinearities Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.