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**Q1:**5 6 7 8 9 The longitudinal equations of motion of an airplane may be approximated by the following differential equations: (a) Rewrite these equations in state-space form. (b) Fid the eigenvalues of the uncontrolled system. (c) Determine a state feedback control law so that the augmented system has a damping ratio of 0.5 and an undamped natural frequency of 20 rad/s. w = -2w + 1798 – 278e Ö = -0.25w - 150 - 458 An airplane is found to have poor lateral/directional handling qualities. Use state feedback to provide stability augmentation. The lateral/directional equations of motion are as follows: = [ABT Ap Ar Lag] The desired lateral eigenvalues are: -0.05 -0.003 -0.98 0.21 [AB] -1 -0.75 Ap 16 Ar 0.3 0 -0.3 1 1 -0.15 0 0 0 Aroll = -1.5 s-1 Aspiral = 0.05 s-1 0 = Aroll = -0.35±j1.5 rad/s Assume the relative authority of the ailerons and rudder are: 9₁ = Q= [ΔΦ] R= Assume the states in problem 4 are unavailable for state feedback. Design a state observer to estimate the states. Assume the state observer eigenvalues are three times as fast as the desired closed-loop eigenvalues. i.e., A[state observer] =32[state feedback] C=[10] + Assume the states in problem 5 are unavailable for state feedback. Design a state observer to estimate the states. Assume the state observer eigenvalues are twice as fast as the desired closed-loop eigenvalues. i.e., A[state observer] =22[state feedback], where 21,2 = -10 +j17.3. A0max=+10° = ±0.175 rad Ademax = ±15° = ±0.26 rad 0 1.7 0.3 0 Design an optimal control law for problem 4. Use the following constraints and weighting functions: 1 A0max 1 Δδ?, 0 -0.2 [Ada] -0.6A8] [As a ] 0 max. 1.0 and 92 = 8/8a = 0.33.See Answer**Q2:**5 6 7 8 9 The longitudinal equations of motion of an airplane may be approximated by the following differential equations: (a) Rewrite these equations in state-space form. (b) Fid the eigenvalues of the uncontrolled system. (c) Determine a state feedback control law so that the augmented system has a damping ratio of 0.5 and an undamped natural frequency of 20 rad/s. w = -2w + 1798 – 278e Ö = -0.25w - 150 - 458 An airplane is found to have poor lateral/directional handling qualities. Use state feedback to provide stability augmentation. The lateral/directional equations of motion are as follows: = [ABT Ap Ar Lag] The desired lateral eigenvalues are: -0.05 -0.003 -0.98 0.21 [AB] -1 -0.75 Ap 16 Ar 0.3 0 -0.3 1 1 -0.15 0 0 0 Aroll = -1.5 s-1 Aspiral = 0.05 s-1 0 = Aroll = -0.35±j1.5 rad/s Assume the relative authority of the ailerons and rudder are: 9₁ = Q= [ΔΦ] R= Assume the states in problem 4 are unavailable for state feedback. Design a state observer to estimate the states. Assume the state observer eigenvalues are three times as fast as the desired closed-loop eigenvalues. i.e., A[state observer] =32[state feedback] C=[10] + Assume the states in problem 5 are unavailable for state feedback. Design a state observer to estimate the states. Assume the state observer eigenvalues are twice as fast as the desired closed-loop eigenvalues. i.e., A[state observer] =22[state feedback], where 21,2 = -10 +j17.3. A0max=+10° = ±0.175 rad Ademax = ±15° = ±0.26 rad 0 1.7 0.3 0 Design an optimal control law for problem 4. Use the following constraints and weighting functions: 1 A0max 1 Δδ?, 0 -0.2 [Ada] -0.6A8] [As a ] 0 max. 1.0 and 92 = 8/8a = 0.33.See Answer**Q3:**project. Topic: *Technological Innovations in Aviation Promoting Aircraft Safety: The Invention of the Automatic Flight Control System and its impact on aviation safety (1912-2022)". General The final submission is a short research proposal. The suggested word count is 2,500-3,000 words (around ten pages, double spaced, font size 12). Abstract, list of references, tables with numerical results (if any), and figures (including their captions and titles) are not included into the word count. All submissions must be made via the dedicated Dropbox set up on Bright space platform. Report Structure and Key Points I suggest that the final report have the following structure: - Abstract-200 words maximum. Note that abstract does not count towards the word limit for the report. - Introduction, where the topic of the report is introduced and motivated. Suggested volume-up to 400 words. - Literature Review. Minimum number of references: 15. Suggested number of references: 25-30. At least a third of the references should be scholarly journal papers or working papers. Suggested volume- up to 800-1000 words. - Methodology. In this section, you need to identify at least one qualitative and at least one quantitative research questions pertaining to the topic of your report. Identify variables, making sure to specify the independent and key dependent variables. You are also to describe how you would set up and carry out your work to address the research questions you have identified. Suggested volume-up to 400 words. - Discussion. Discuss expected results of your study, based on theory, available evidence, your educated guesses. Make sure you link your discussion to the research questions you have identified in the previous section. Suggested volume-up to 400 words./n- Methodology. In this section, you need to identify at least one qualitative and at least one quantitative research questions pertaining to the topic of your report. Identify variables, making sure to specify the independent and key dependent variables. You are also to describe how you would set up and carry out your work to address the research questions you have identified. Suggested volume-up to 400 words. - Discussion. Discuss expected results of your study, based on theory, available evidence, your educated guesses. Make sure you link your discussion to the research questions you have identified in the previous section. Suggested volume-up to 400 words. - Concluding Comments. In this section, in addition to discussing the importance of your work, provide a discussion of weaknesses of your study, and also give some suggestions for follow-up work. Suggested volume-up to 300 words. - List of references, which are to be organized alphabetically by the lead author's last name. Only use those references that are in the text. For this assignment, there is no minimum or maximum number of references to be used this only related to the literature review. List of references is not included into the word count. - Appendices are not allowed. Plagiarism Plagiarism is the representation of another author's language, thoughts, ideas, or expressions as one's own original work. Plagiarism is considered a serious form of academic dishonesty, and attracts severe penalties, up to and including a failing grade for the course, with the possibility of additional administrative actions taken by the University. Please check with the instructor if you have any questions, concerns, or doubts.See Answer**Q4:**Consider the Piper-Dakota small airplane shown in Figure 1 below. The transfer function betweenSee Answer

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