Analyze the behaviour of a booster rocket

Assignment Help Other Engineering
Reference no: EM131218714

In this assignment, you will analyze the behaviour of a booster rocket, and design a control system to automatically regulate the heading angle of the booster.

1. Dynamics of a booster rocket

A booster rocket (or engine) is either the first stage of a multi-stage launch vehicle, or a shorter-burning rocket used in parallel with longer-burning sustainer rockets to augment the space vehicle's takeoff thrust and payload capability. Figure 1 is an illustration of the booster rocket and the signals in the system.

1006_Booster rocket.jpg

The heading of the booster rocket, θ(t), following the application of a force, f (t), may be represented by the following transfer function :

G(s) = θ(s)/F (s) = 1/s2 - α   (1)

where θ(s) = L{θ(t)} and F (s) = L{f (t)}. For the purpose of this assignment, set the parameter α to 10+C/1000, where C may be derived by reading the last 2 digits of your student matriculation number. For example, if your matriculation number is A0**1234*, then let C = 34.

i. What are the values of the system poles ? Using the information that system poles provide about system behaviour, describe what happens to the space booster when an input signal is applied.

ii. Sketch the impulse response, θ(t).

2. Analysis of the booster rocket control system

A feedback control system needs to be developed to automatically manipulate the heading angle. Figure 2 on the next page shows the block diagram of the automatic heading control system. The control system uses a navigational sensor to measure the heading angle of the booster rocket, and the output signal, x(t), is determined by the following expression

x(t) = Kpe(t) + Kdde(t)/dt + Ki 0te(τ)dτ      (2)

where e(t) = θr(t) - θ(t), θr(t) is the desired heading of the rocket booster at time t. Kp, Kd and Ki are constants to be designed. In addition to tracking the desired heading angle, the control system should also reject disturbances d(t), such as wind gust, that may influence the behaviour of the booster rocket.

2271_Figure1.jpg

i. Derive the transfer functions Gr(s) = θ(s)/θr(s) and GD(s) = θ(s)/D(s). What is the order of the booster rocket control system?

ii. Which of the three design parameters (Kp, Kd and Ki) should be set to zero for Gr(s) = θ(s)/D(s) to be a second order system? Set the remaining two parameters to zero in turn. For each of the two scenarios, derive the range of values that will yield a bounded output signal.

iii. Design Kp, Kd and Ki such that the automatic heading control system is a second order system with system poles s1,2 = -1 ± 3j.

iv. Sketch the response of the system designed in part iii when the desired heading angle is 30 degrees i.e. θr(t) = 30u(t) where u(t) is the unit step function. The steady-state heading angle should be clearly labeled.

v. Suppose the wind disturbance acting on the booster rocket undergoes a step change i.e. d(t) = u(t), where u(t) is the unit step function. You may assume that θr(t) = 0.

- Derive the trajectory of the heading angle for the system designed in part iii.
- Discuss the effect of a step change in wind disturbance on the heading direction of the booster rocket if Ki is non-zero.

Suggest a value of Ki that will stabilize the booster rocket heading angle (You may use the values of Kp and Kd that were computed in part iii).

Reference no: EM131218714

Questions Cloud

Recursive way instead of an iterative way : 1. Are there problem types that could be better approached in a recursive way instead of an iterative way? How could we identify them?
2 ways of protecting ourselves against mobilesource : How would changes in the discount rate be likely to affect the comparison among these two options?
What level of output should firm produce to maximize profits : What level of output should the firm produce to maximize profits? How does the profit maximization condition for a monopoly differ from that for a perfectly competitive firm? How does this difference impact efficiency under each market structure?
Explain the causes and affects of current consumer culture : Explain the causes and affects of current consumer culture. Your essay should Psycho-social and historical developments that have shaped current consumer behavior
Analyze the behaviour of a booster rocket : Department of Electrical & Computer Engineering - EE2023 Signal & Systems - You will analyze the behaviour of a booster rocket, and design a control system to automatically regulate the heading angle of the booster.
What is the word modern mean : What's the word "modern" mean? (You can look up "modern" in Wikipedia for ideas, but I want you to generate your own explanation of the term, not copy one from the internet). What makes Degas' The Dance Class modern? (this is really your thesis an..
Estimate the social costs of this regulation : In order to protect the quality of its nearby water resources, a community places a restriction on any housing development closer than 100 feet to a wetland. How might you estimate the social costs of this regulation?
The oriental contingent by diana chang : "The Oriental Contingent" by Diana Chang. -  Which character engages your interest? Why? - What purpose does this character serve?
Managerial function in the development of business policy : BM6199/BMN399 Investigative Study. Beardwell (2004) HRM can be viewed as part of the strategic managerial function in the development of business policy, in which it plays both a determining and a contributory role and is particularly so for multi..

Reviews

Write a Review

 

Other Engineering Questions & Answers

  Derive the given two equations in the problem

The Soave-Redlich-Kwong equation is a commonly used cubic equation of state, second in popularity only to the Peng-Robinson Equation of state. In this problem, just derive the two equations (7.66) given in the problem.

  Games of all kinds are the result of a process that

you will explore a game through the lens set up by the weekly material.games of all kinds are the result of a process

  Determine the force on the circular strut

Determine the force on the circular strut that extends across the duct. The upstream and downstream pressures

  What is the purpose of the giant nested statement

How did the ALU need to get modified to implement these instructions? What is the purpose of the giant nested ?: statement inside the updated ALU module

  The test statistic for the hypothesis test

If you randomly select 1 M&M plain candy, what is the probability That the candy will weigh less than 0.8535 g?

  Pair of graphs to show an perfectly competitive industry

Create a pair of graphs to show an perfectly competitive industry and firm in long-run equilibrium. Put the graphs side by side and use the same vertical scale for both graphs.

  Disc profiles in order to get job

Part 1: Write a brief essay describing two ways you would effectively use the DiSC profiles in order to get job.

  Difference between the pvcs and pvtc

If the design speed of the curves is 50 mi/h, what is the common grade between the sag and crest curves (G2 of sag and G1 of crest, from west to east), and what is the elevation difference between the PVCs and PVTc?

  Explain the tradeoff between sensing range and precision

Explain the tradeoff between sensing range and precision (note that this tradeoff is endemic to all sensors, not just accelerometers and gyroscopes)

  Draw the inductor voltage and current waveforms

Problem 1. Calculate the rms value of the following waveforms (1) v(t) =15 sin(2g600

  Problem regarding the downward force

If the pressure inside is 1.0 atm, what downward force must the crew exert on the hatch to open it?

  Small cellular structures

Small cellular structures (ribosomes, mitochondria, & others) that perform specific metabolic functions for the cell as a whole What is the function of the heart, how does it pump blood?

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd