Figure 1.1 Simplified description of a control system

Name: Figure 1.1 Simplified description of a control system
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Description: Figure 1.1 Simplified description of a control system

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.

Figure1.5 Elevator input and output

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

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 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

Table 1.1 Test waveforms used in control systems

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. <<<3.12>>> 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. 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
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. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 2.2 Block diagram of a transfer function
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

Table 2.2 Laplace transform theorems

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 sC(s) + 2C(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 – 1/2e-2t 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 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 network Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 2.5 Laplace-transformed network
Find Vc(s)/V(s) (Ls+R+1/Cs) I(s) = V(s) Vc(s) = I(s)/ Cs Vc(s)/V(s) = (1/LC) / (s2+ (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

Figure 2. 6 a. Two-loop electrical network; b
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 G1= 1/R1 and G2= 1/R2 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

Figure 2.9 Three-loop electrical network

Table 2.4 Force-velocity, force-displacement, 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

Figure 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 system8; b. block diagram

Figure 2. 18 a. Forces on M1 due only to motion of M1 b
Figure 2.18 a. Forces on M1 due only to motion of M1 b. forces on M1 due only to motion of M2 c. all forces on M1 Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 2. 19 a. Forces on M2 due only to motion of M2; b
Figure 2.19 a. Forces on M2 due only to motion of M2; b. forces on M2 due only to motion of M1; c. all forces on M2 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

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

Figure 2.25 Three-degrees-of- freedom rotational system

Figure 2.34 NASA flight simulator robot arm with electromechanical control system components
© Debra Lex. Control Systems Engineering, Fourth Edition by Norman S. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.

Figure 2.35 DC motor: a. schematic12; b. block diagram

Figure 2.36 Typical equivalent mechanical loading on a motor

Figure 2.37 DC motor driving a rotational mechanical load

Figure 2. 39 a. DC motor and load; b. torque-speed curve; c
Figure 2.39 a. DC motor and load; b. torque-speed curve; c. 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
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)

Figure 2. 43 Development of parallel analog: a. mechanical system; b
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 2.45 a. Linear system; b. nonlinear system

Figure 2.46 Some physical nonlinearities

Figure 1.1 Simplified description of a control system

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