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systems analysis and design
Questions and Answers of
Systems Analysis And Design
A system has the characteristic equation q(s) = s3 + 10s2 + 29s + K = 0. Shift the vertical axis to the right by 2 by using s = sn - 2, and determine the value of gain K so that the complex roots are
A system is represented by Equation (6.22) whereFind the range of k where the system is stable.
Consider the system represented in state variable formx = Ax + Buy = Cx + Du,where(a) What is the system transfer function? (b) For what values of k is the system stable?
A closed-loop feedback system is shown in Figure E6.25. For what range of values of the parameters K and p is the system stable?
Consider the closed-loop system in Figure E6.26, values of k is the system stable? WhereG(s) = 10/s - 10 and Gc(s) = 1/2s + K.(a) Determine the characteristic equation associated with the closed-loop
A system has the characteristic equation s4 + 10s3 + 32s2 + 37s + 20 = 0. Using the Routh- Hurwitz criterion, determine if the system is stable.
A control system has the structure shown in Figure E6.4. Determine the gain at which the system will become unstable.Figure E6.4Feedforward system.
A unity feedback system has a loop transfer function L(s) = K / (s + l)(s + 3)(s + 6), where K = 20. Find the roots of the closed-loop system's characteristic equation.
For the feedback system of Exercise E6.5, find the value of K when two roots lie on the imaginary axis. Determine the value of the three roots.
A negative feedback system has a loop transfer function L(s) = K(s + 2) / s(s - 1). (a) Find the value of the gain when the ζ of the closed-loop roots is equal to 0.707. (b) Find the value of the
Designers have developed small, fast, vertical-takeoff fighter aircraft that are invisible to radar (stealth aircraft). This aircraft concept uses quickly turning jet nozzles to steer the airplane
A system has a characteristic equation s3 + 2s2 + (K + 1)s + 8 = 0. Find the range of K for a stable system.
Utilizing the Routh-Hurwitz criterion, determine the stability of the following polynomials: (a) s2 + 5s + 2 (b) s3 + 4s2 + 8s + 4 (c) s3 + 2s2 - 6s + 20 (d) s4 + s3 + 2s2 + 12s + 10 (e) s4 + s3 +
Robots can be used in manufacturing and assembly operations that require accurate, fast, and versatile manipulation [10, 11]. The open-loop transfer function of a direct-drive arm may be approximated
A feedback control system has a characteristic equation s3 + (1 + K)s2 + 10s + (5 + 15K) = 0. The parameter K must be positive. What is the maximum value K can assume before the system becomes
A system has the third-order characteristic equation s3 + as2 + bs + c = 0, where a, b, and c are constant parameters. Determine the necessary and sufficient conditions for the system to be stable.
Consider the system in Figure P6.13. Determine the conditions on K, p, and z that must be satisfied for closed-loop stability. Assume that K > 0, ζ > 0, and Ïn > 0.Figure
A feedback control system has a characteristic equation s6 + 2s5 + 12s4 + 4s3 + 21s2 + 2s + 10 = 0. Determine whether the system is stable, and determine the values of the roots.
The stability of a motorcycle and rider is an important area for study because many motorcycle designs result in vehicles that are difficult to control [12, 13]. The handling characteristics of a
A system has a closed-loop transfer function T(s) = 1 / s3 + 5s2 + 20s + 6. (a) Determine whether the system is stable. (b) Determine the roots of the characteristic equation. (c) Plot the response
The elevator in Yokohama's 70-story Landmark Tower operates at a peak speed of 45 km/hr. To reach such a speed without inducing discomfort in passengers, the elevator accelerates for longer periods,
Consider the case of rabbits and foxes in Australia. The number of rabbits is x1 and if left alone, it would grow indefinitely (until the food supply was exhausted) so that x1 = kx1. However, with
The goal of vertical takeoff and landing (VTOL) aircraft is to achieve operation from relatively small airports and yet operate as a normal aircraft in level flight [16]. An aircraft taking off in a
An antenna control system was analyzed in Problem P4.5, and it was determined that, to reduce the effect of wind disturbances, the gain of the magnetic amplifier, ka, should be as large as
A personal vertical take-off and landing (VTOL) aircraft is shown in Figure P6.20(a). A possible control system for aircraft altitude is shown in Figure P6.20(b).(a) For K = 6, determine whether the
Consider the system described in state variable form byx(t) = Ax(t) + Bu(t)y(t) = Cx(t)whereand where k1 k2 and both k1 and k2 are real numbers. (a) Compute the state transition matrix
Arc welding is one of the most important areas of application for industrial robots [11]. In most manufacturing welding situations, uncertainties in dimensions of the part, geometry of the joint, and
A feedback control sys tern is shown in Figure P6.4. The controller and process transfer functions are given byGc(s) = K and G(s) = s + 40 / s(s + 10)and the feedback transfer function is H(s) = l/(s
Determine the relative stability of the systems with the following characteristic equations (1) by shifting the axis in the s-plane and using the Routh-Hurwitz criterion, and (2) by determining the
A unity-feedback control system is shown in Figure P6.6. Determine the relative stability of the system with the following transfer functions by locating the complex roots in the s-plane:(a)
The linear model of a phase detector (phase-lock loop) can be represented by Figure P6.7 [9].The phase-lock systems are designed to maintain zero difference in phase between the input carrier signal
A very interesting and useful velocity control system has been designed for a wheelchair control system. We want to enable people paralyzed from the neck down to drive themselves in motorized
A cassette tape storage device has been designed for mass-storage [1]. It is necessary to control the velocity of the tape accurately. The speed control of the tape drive is represented by the system
A teleported control system incorporates both a person (operator) and a remote machine. The normal teleportation system is based on a one-way link to the machine and limited feedback to the operator.
Consider the case of a navy pilot landing an aircraft on an aircraft carrier. The pilot has three basic tasks. The first task is guiding the aircraft's approach to the ship along the extended
A control system is shown in Figure AP6.3. We want the system to be stable and the steady-state error for a unit step input to be less than or equal to 0.05 (5%).(a) Determine the range of
A bottle-filling line uses a feeder screw mechanism, as shown in Figure AP6.4. The tachometer feedback is used to maintain accurate speed control. Determine and plot the range of K and p that permits
Consider the closed-loop system in Figure AP6.5. Suppose that all gains are positive, that is, K1 > 0, K2 > 0, K3 > 0, K4 > 0, and K5 > 0.(a) Determine the closed-loop transfer function T(s) =
A spacecraft with a camera is shown in Figure AP6.6(a).The camera slews about 16° in a canted plane relative to the base. Reaction jets stabilize the base against the reaction torques from the
A human's ability to perform physical tasks is limited not by intellect but by physical strength. If, in an appropriate environment, a machine's mechanical power is closely integrated with a human
The capstan drive system of problem CDP5.1 uses the amplifier as the controller. Determine the maximum value of the gain Ka before the system becomes unstable.
The control of the spark ignition of an automotive engine requires constant performance over a wide range of parameters [15]. The control system is shown in Figure DP6.1, with a controller gain K to
An automatically guided vehicle on Mars is represented by the system in Figure DP6.2. The system has a steerable wheel in both the front and back of the vehicle, and the design requires that H(s) =
A unity negative feedback system withhas two parameters to be selected.(a) Determine and plot the regions of stability for this system.(b) Select Ñ‚ and K so that the steady-state error to a ramp
The attitude control system of a space shuttle rocket is shown in Figure DP6.4 [17].(a) Determine the range of gain K and parameter m so that the system is stable, and plot the region of
A traffic control system is designed to control the distance between vehicles, as shown in Figure DP6.5 [15].(a) Determine the range of gain K for which the system is stable.(b) If Km is the maximum
Consider the single-input, single-output system as described byx(t) = Ax(t) + Bu(t)y(t) = Cx(t)whereAssume that the input is a linear combination of the states, that is, u(t) = -Kx(t) + r(t), where
Consider the feedback control system in Figure DP6.7.The system has an inner loop and an outer loop. The inner loop must be stable and have a quick speed of response.(a) Consider the inner loop
Consider the feedback system shown in Figure DP6.8.The process transfer function is marginally stable. The controller is the proportional-derivative (PD) controllerGc(s) = KP + KDs.Determine if it is
Determine the roots of the following characteristic equations: (a) q(s) = s3 + 3s2 + 10s + 14 = 0. (b) q(s) = s4 + 8s3 + 24s2 + 32s + 16 = 0. (c) q(s) = s4 + 2s2 + 1 = 0.
Consider a unity negative feedback system with Gc(s) = K and G(s) = s2 - s + 2 / s2 + 2s + 1. Develop an m-file to compute the roots of the closed-loop transfer function characteristic polynomial for
A unity negative feedback system has the loop transfer function Gc(s)G(s) = s + 1 / s3 + 4s2 + 6s + 10. Develop an m-file to determine the closed-loop transfer function and show that the roots of the
Consider the closed-loop transfer functionT(s) = 1 / s5 + 2s4 + 2s3 + 4s2 + s + 2.(a) Using the Routh-Hurwitz method, determine whether the system is stable. If it is not stable, how many poles are
A "paper-pilot" model is sometimes utilized in aircraft control design and analysis to represent the pilot in the loop. A block diagram of an aircraft with a pilot "in the loop" is shown in Figure
Consider the feedback control system in Figure CP6.6. Using the for function, develop an m-file script to compute the closed-loop transfer function poles for 0 ¤ K ¤ 5 and
Consider a system in state variable form:(a) Compute the characteristic equation using the poly function. (b) Compute the roots of the characteristic equation, and determine whether the system is
Consider the feedback control system in Figure CP6.8.(a) Using the Routh-Hurwitz method, determine the range of K1 resulting in closed-loop stability.(b) Develop an m-file to plot the pole locations
Consider a system represented in state variable formx = Ax + Buy = Cx + Du,where(a) For what values of k is the system stable? (b) Develop an m-file to plot the pole locations as a function of 0
Let us consider a device that consists of a ball rolling on the inside rim of a hoop [11]. This model is similar to the problem of liquid fuel sloshing in a rocket. The hoop is free to rotate about
A unity feedback system has the loop transfer function L(s) = KG(s) = K(s + 2) / s(s + 1). (a) Find the breakaway and entry points on the real axis. (b) Find the gain and the roots when the real part
A robot force control system with unity feedback has a loop transfer function [6](a) Find the gain K that results in dominant roots with a damping ratio of 0.707. Sketch the root locus. (b) Find the
A unity feedback system has a loop transfer function(a) Sketch the root locus for K > 0.(b) Find the roots when K = 10 and 20.(c) Compute the rise time, percent overshoot, and settling time (with
A unity feedback system has a loop transfer function(a) Draw the root locus as z varies from 0 to 100. (b) Using the root locus, estimate the percent overshoot and settling time (with a 2% criterion)
A unity feedback system has the loop transfer function(a) Determine the breakaway and entry points of the root locus and sketch the root locus for K > 0. (b) Determine the gain K when the two
(a) Plot the root locus for a unity feedback system with loop transfer function(b) Calculate the range of K for which the system is stable. (c) Predict the steady-state error of the system for a ramp
A negative unity feedback system has a loop transfer functionwhere T = 0.1 s. Show that an approximation for the time delay is Using obtain the root locus for the system for K > 0. Determine the
A control system, as shown in Figure E7.17, has a processG(s) = 1 / s(s - 1).(a) When Gc(s) = K, show that the system is always unstable by sketching the root locus. (b) When Gc(s) K(s + 2) / s +
A closed-loop negative unity feedback system is used to control the yaw of the A-6 Intruder attack jet. When the loop transfer function isdetermine (a) the root locus breakaway point and (b) the
A unity feedback system has a loop transfer function(a) Determine the angle of departure of the root locus at the complex poles. (b) Sketch the root locus. (c) Determine the gain K when the roots are
A tape recorder has a speed control system so that H(s) = 1 with negative feedback and L(s) = Gc(s)G(s) = K / s(s + 2)(s2 + 4s + 5). (a) Sketch a root locus for K, and show that the dominant roots
A unity feedback system has a loop transfer function(a) Determine the range of K for stability. (b) Sketch the root locus. (c) Determine the maximum ζ of the stable complex roots.
A unity feedback system has a loop transfer functionSketch the root locus. Determine the gain K when the complex roots of the characteristic equation have a ζ approximately equal to 0.66.
A high-performance missile for launching a satellite has a unity feedback system with a loop transfer functionSketch the root locus as K varies from 0
A unity feedback system has a loop transfer functionSketch the root locus for 0 ¤ a
Consider the system represented in state variable formx = Ax + Buy = Cx + Du,whereDetermine the characteristic equation and then sketch the root locus as 0
A closed-loop feedback system is shown in Figure E7.25. For what range of values of the parameters K is the system stable? Sketch the root locus as 0 FIGURE E7.25Non unity feedback system with
Consider the single-input, single-output system is described byx(t) = Ax(t) + Bu(t)y(t) = Cx(t)whereCompute the characteristic polynomial and plot the root locus as 0 ¤ K
Consider the unity feedback system in Figure E7.27. Sketch the root locus as 0 ¤ p Figure E7.27Unity feedback system with parameter p.
Consider the feedback system in Figure E7.28. Obtain the negative gain root locus as - Figure E7.28Feedback system for negative gain root locus.
A control system for an automobile suspension tester has negative unity feedback and a process [12] L(s) = Gc(s)G(s) = K(s2 + 4s + 8) / s2(s + 4) We desire the dominant roots to have a ζ equal to
Consider a unity feedback system with L(s) = Gc(s)G(s) = K(s + 1) / s2 + 4s + 5 (a) Find the angle of departure of the root locus from the complex poles. (b) Find the entry point for the root locus
Consider a unity feedback system with a loop transfer function(a) Find the breakaway points on the real axis. (b) Find the asymptote centroid. (c) Find the values of K at the breakaway points.
One version of a space station is shown in Figure E7.6 [28]. It is critical to keep this station in the proper orientation toward the Sun and the Earth for generating power and communications. The
The elevator in a modern office building travels at a top speed of 25 feet per second and is still able to stop within one-eighth of an inch of the floor outside. The loop transfer function of the
Sketch the root locus for a unity feedback system with(a) Find the gain when all three roots are real and equal. (b) Find the roots when all the roots are equal as in part (a).
The world's largest telescope is located in Hawaii. The primary mirror has a diameter of 10 m and consists of a mosaic of 36 hexagonal segments with the orientation of each segment actively
Sketch the root locus for the following loop transfer functions of the system shown in Figure P7.1 when 0 (a)(b) (c) (d) Figure P7.1
New concepts in passenger airliner design will have the range to cross the Pacific in a single flight and the efficiency to make it economical [16. 29]. These new designs will require the use of
A computer system requires a high-performance magnetic tape transport system [17]. The environmental conditions imposed on the system result in a severe test of control engineering design. A
A precision speed control system (Figure P7.12) is required for a platform used in gyroscope and inertial system testing where a variety of closely controlled speeds is necessary. A direct-drive DC
A unity feedback system has the loop transfer function(a) Find the breakaway point on the real axis and the gain for this point. (b) Find the gain to provide two complex roots nearest the
The loop transfer function of a single-loop negative feedback system isThis system is called conditionally stable because it is stable only for a range of the gain K such that k1
Let us again consider the stability and ride of a rider and high performance motorcycle as outlined in Problem P6.13. The dynamics of the motorcycle and rider can be represented by the loop transfer
Control systems for maintaining constant tension on strip steel in a hot strip finishing mill are called "loopers." A typical system is shown in Figure P7.16. The looper is an arm 2 to 3 feet long
Consider again the vibration absorber discussed in Problems 2.2 and 2.10 as a design problem. Using the root locus method, determine the effect of the parameters M2 and k12. Determine the specific
A feedback control system is shown in Figure P7.18. The filter Gc(s) is often called a compensator, and the design problem involves selecting the parameters α and β. Using
In recent years, many automatic control systems for guided vehicles in factories have been installed. One system uses a magnetic tape applied to the floor to guide the vehicle along the desired lane
The linear model of a phase detector was presented in Problem P6.7. Sketch the root locus as a function of the gain Kv = KaK. Determine the value of Kv attained if the complex roots have a damping
Determine the root sensitivity for the dominant roots of the design for Problem P7.18 for the gain K = 4α/β and the pole s = -2.
Determine the root sensitivity of the dominant roots of the power system of Problem P7.7. Evaluate the sensitivity for variations of (a) The poles at s = -4, and (b) The feedback gain, 1/R.
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