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 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 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 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 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; 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 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 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 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. 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 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.
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. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.
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) 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 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.
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 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 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 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 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. 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 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 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 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 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 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 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, 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. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.
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; 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 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; 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 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. Nise Copyright © 2004 by John Wiley & Sons. All rights reserved.
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