Algebra 2. Consider the system 91 +92 сos (лq1)+q2 = U₁+U₂ 92-cosq2 + e¹-q1 = 12, where 91, 92 are generalized coordinates and u₁, u2 are the control inputs. (a) Define a state vector x and a control input u, and rewrite these equations in state-space form (i.e., derive the state equation). Then, find an equilibrium (xe, ue) where ue = 0. (b) Suppose that the output of interest is = [₁₁ [9+39192+1₂ 91 +92 Linearize the state and output equations about the equilibrium (xe, ue). y =
Algebra 2. Consider the system 91 +92 сos (лq1)+q2 = U₁+U₂ 92-cosq2 + e¹-q1 = 12, where 91, 92 are generalized coordinates and u₁, u2 are the control inputs. (a) Define a state vector x and a control input u, and rewrite these equations in state-space form (i.e., derive the state equation). Then, find an equilibrium (xe, ue) where ue = 0. (b) Suppose that the output of interest is = [₁₁ [9+39192+1₂ 91 +92 Linearize the state and output equations about the equilibrium (xe, ue). y =
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Q 5
![Algebra
2. Consider the system
91 +92 сos (лq1) +92=U₁+U₂
92-cosq2+e¹-91 = 1₂,
where 91, 92 are generalized coordinates and u₁, u2 are the control inputs.
(a) Define a state vector x and a control input u, and rewrite these equations in state-space
form (i.e., derive the state equation). Then, find an equilibrium (xe, ue) where ue = 0.
(b) Suppose that the output of interest is
= [9₁ +31
[9+39192+1₂]
91 +92
Linearize the state and output equations about the equilibrium (xe, ue).
y =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd7a714a4-ebd8-4877-b945-31460b45f9c3%2F6a9ef50e-c6f3-44fa-b977-37747ab15b73%2Fi3zudnh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Algebra
2. Consider the system
91 +92 сos (лq1) +92=U₁+U₂
92-cosq2+e¹-91 = 1₂,
where 91, 92 are generalized coordinates and u₁, u2 are the control inputs.
(a) Define a state vector x and a control input u, and rewrite these equations in state-space
form (i.e., derive the state equation). Then, find an equilibrium (xe, ue) where ue = 0.
(b) Suppose that the output of interest is
= [9₁ +31
[9+39192+1₂]
91 +92
Linearize the state and output equations about the equilibrium (xe, ue).
y =
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