1) Consider the system below: Vehicle Controller Steering dynamics Desired Actual bearing angle bearing angle 50 K 2+ 10s + 50 s(s + 5) Figure 1: Simplified Block Diagram of a Self-Guiding Vehicle's Bearing Angle Control. • Find a K value that the system has minimum rise time and minimum overshoot. Let us call this proportional gain as Kopt • Show each step while finding Kopt-

1) Consider the system below: Vehicle Controller Steering dynamics Desired Actual bearing angle bearing angle 50 K 2+ 10s + 50 s(s + 5) Figure 1: Simplified Block Diagram of a Self-Guiding Vehicle's Bearing Angle Control. • Find a K value that the system has minimum rise time and minimum overshoot. Let us call this proportional gain as Kopt • Show each step while finding Kopt-

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Weight Ple Figure 4: Schematic of a pile driver f(t) m+bv=f(1) m by 3 X pile Figure 5: First-order model of the pile in soil 5. Figure 4 shows a pile driver that is used to drive piles into soil to provide foundation support for buildings. Two major components of a pile driver are a pile and a weight. The pile is in the form of a long rod going into the soil. The weight is to impact the pile at the top with an impulsive force, thus driving the pile into the soil. Figure 5 shows a first-order model of the pile in the soil. The impulsive force produced by the weight is f(t). The resistance of the soil is modeled via a viscous damping coefficient. b. The weight of the pile is balanced by the normal forces in the soil, so it does not need to be considered. In addition, the elasticity of the soil is ignored. Let z(t) and v(t) be the downward displacement and velocity of the pile, respectively. The equation of motion governing the pile velocity v(t) is dv (5) where m is the mass of the pile.…