MY-ASSIGNMENTEXPERT™可以为您提供 cehd MATH683 Optimization Theory最优化的代写代考和辅导服务！
这是乔治梅森大学最优化的代写成功案例。
MATH683课程简介
Introduces basic mathematical ideas and methods for solving linear and nonlinear programming problems, with emphasis on mathematical aspects of optimization theory. Reviews classical topics of linear programming, and covers recent developments in linear programming, including interior point method. Considers basic results in nonlinear programming, including very recent developments in this field. Offered by Mathematics. May not be repeated for credit.
Prerequisites
Enrollment limited to students with a class of Advanced to Candidacy, Graduate, Junior Plus, Non-Degree or Senior Plus.
Enrollment is limited to Graduate, Non-Degree or Undergraduate level students.
Students in a Non-Degree Undergraduate degree may not enroll.
Schedule Type: Lecture
Grading:
This course is graded on the Graduate Regular scale.
MATH683 Optimization Theory HELP（EXAM HELP， ONLINE TUTOR）
Write a set of state equations for the electromechanical system shown in Fig. 1-P7. The amplifier gain is $K_a$, and the developed torque is $\lambda(t)=K_t i_f(t)$, where $K_a$ and $K_t$ are known constants.
$d i_f(t) / d t=-R_f i_f(t) / L_f+K_a e(t) / L_f ; d \omega(t) / d t=K_t i_f(t) / I-B \omega(t) / I$
Draw a block diagram, or signal flow graph, and write state and output equations that correspond to the transfer functions:
(a) $\frac{Y(s)}{U(s)}=\frac{5}{s[s+1]}$
(b) $\frac{Y(s)}{U(s)}=\frac{1}{s^2}$
(c) $\frac{Y(s)}{U(s)}=\frac{10}{s^3+5 s^2+6 s+3}$
(d) $\frac{Y(s)}{U(s)}=\frac{8}{2 s^4+6 s^3+14 s^2+7 s+1}$
(e) $\frac{Y(s)}{U(s)}=\frac{5[s+2]}{s[s+1]}$
(f) $\frac{Y(s)}{U(s)}=\frac{[s+1][s+2]}{s^2}$
(g) $\frac{Y(s)}{U(s)}=\frac{10\left[s^2+2 s+3\right]}{s^3+5 s^2+6 s+3}$
(h) $\frac{Y(s)}{U(s)}=\frac{4}{[s+1][s+2]}$
(i) $\frac{Y(s)}{U(s)}=\frac{\left[s^2+7 s+12\right]}{s[s+1][s+2]}$
(j) $\frac{Y(s)}{U(s)}=\frac{8\left[s^3+s+2\right]}{2 s^4+6 s^3+14 s^2+7 s+1}$
(a) $\dot{x}_1(t)=x_2(t) ; \dot{x}_2(t)=-x_2(t)+5 u(t) ; y(t)=x_1(t)$
(c)
$$
\begin{aligned}
& \dot{x}_1(t)=x_2(t) ; \dot{x}_2(t)=x_3(t) ; \dot{x}_3(t)=-3 x_1(t)-6 x_2(t)-5 x_3(t)+10 u(t) \
& y(t)=x_1(t)
\end{aligned}
$$
(e) $\dot{x}_1(t)=x_2(t) ; \dot{x}_2(t)=-x_2(t)+5 u(t) ; y(t)=2 x_1(t)+x_2(t)$
(g)
$$
\begin{aligned}
& \dot{x}_1(t)=x_2(t) ; \dot{x}_2(t)=x_3(t) ; \dot{x}_3(t)=-3 x_1(t)-6 x_2(t)-5 x_3(t)+10 u(t) \
& y(t)=3 x_1(t)+2 x_2(t)+x_3(t)
\end{aligned}
$$
(i)
$$
\begin{aligned}
& \dot{x}_1(t)=u(t) ; \quad \dot{x}_2(t)=-x_2(t)+u(t) ; \quad \dot{x}_3(t)=-2 x_3(t)+u(t) ; \quad y(t)= \
& 6 x_1(t)-6 x_2(t)+x_3(t) .
\end{aligned}
$$
For each of the following systems determine:
(i) If the system is controllable.
(ii) If the system is observable.
(iii) The block diagram or signal flow graph of the system.
(a) $\dot{\mathbf{x}}(t)=\left[\begin{array}{cc}0 & 1 \ 0 & 0\end{array}\right] \mathbf{x}(t)+\left[\begin{array}{l}0 \ 1\end{array}\right] u(t) ; \quad y(t)=x_1(t)$
(b) $\dot{\mathbf{x}}(t)=\left[\begin{array}{ll}0 & 1 \ 0 & 0\end{array}\right] \mathbf{x}(t)+\left[\begin{array}{l}0 \ 1\end{array}\right] u(t) ; \quad y(t)=x_2(t)$
(c) The coupled circuit in Problem 1-9 with $M=0, \mathbf{y}(t)=\left[\begin{array}{l}v_c(t) \ i_{L_2}(t)\end{array}\right]$.
(d) The coupled circuit in Problem 1-9 with $M=0.5 \mathrm{H}, L_1=1.0 \mathrm{H}, L_2=$ $0.5 \mathrm{H}, R_1=2.0 \Omega, R_2=1.0 \Omega, C=0.5 \mathrm{~F}$, and $y(t)=v_c(t)$.
(e)
$\dot{\mathbf{x}}(t)=\left[\begin{array}{rrr}-2 & 0 & 1 \ 0 & -1 & 0 \ -3 & -4 & -2\end{array}\right] \mathbf{x}(t)+\left[\begin{array}{ll}0 & 1 \ 0 & 0 \ 1 & 0\end{array}\right] \mathbf{u}(t) ; \quad y(t)=x_1(t)$
(f)
$\dot{\mathbf{x}}(t)=\left[\begin{array}{rrr}-2 & 0 & 1 \ 0 & -1 & 1 \ -3 & 0 & -2\end{array}\right] \mathbf{x}(t)+\left[\begin{array}{ll}0 & 1 \ 0 & 0 \ 1 & 0\end{array}\right] \mathbf{u}(t) ; \quad y(t)=x_1(t)$
(g)
$$
\begin{gathered}
\dot{\mathbf{x}}(t)=\left[\begin{array}{cccc}
0 & 1 & 0 & 0 \
0 & 0 & 1 & 0 \
0 & 0 & 0 & 1 \
-a_0 & -a_1 & -a_2 & -a_3
\end{array}\right] \mathbf{x}(t)+\left[\begin{array}{l}
0 \
0 \
0 \
1
\end{array}\right] u(t) \
y(t)=x_1(t) ; a_i \neq 0, i=0,1,2,3
\end{gathered}
$$
Key: $\mathrm{C} \triangleq$ controllable, $\mathrm{NC} \triangleq$ not controllable, $\mathrm{O} \triangleq$ observable, $\mathrm{NO} \triangleq$ not observable
(a) $\mathrm{C}, \mathrm{O}$;
(b) $\mathrm{C}, \mathrm{NO}$;
(c) $\mathrm{NC}, \mathrm{O}$;
(d) $\mathrm{C}, \mathrm{O}$;
(e) NC, O;
(f) $\mathrm{C}, \mathrm{NO}$;
(g) C, O.
What are the requirements for the system
$$
\begin{aligned}
& \dot{\mathbf{x}}(t)=\left[\begin{array}{cccc}
\lambda_1 & 0 & 0 & 0 \
0 & \lambda_2 & 0 & 0 \
0 & 0 & \lambda_3 & 0 \
0 & 0 & 0 & \lambda_4
\end{array}\right] \mathbf{x}(t)+\left[\begin{array}{l}
b_1 \
b_2 \
b_3 \
b_4
\end{array}\right] u(t) ; \
& y(t)=\left[\begin{array}{llll}
c_1 & c_2 & c_3 & c_4
\end{array}\right] \mathbf{x}(t)
\end{aligned}
$$
to be:
(i) Controllable?
(ii) Observable?
Assume that $\lambda_i, i=1, \ldots, 4$ are real and distinct.
$\mathrm{C}$ if $b_i \neq 0, i=1,2,3,4$; O if $c_i \neq 0, i=1,2,3,4$.
MY-ASSIGNMENTEXPERT™可以为您提供 cehd MATH683 Optimization Theory最优化的代写代考和辅导服务！
