Problem 3. (17 points) A control system is shown in the figure, where a circular

Question

Problem 3. (17 points) A control system is shown in the figure, where a circular disk of moment of inertia lo is constrained by a spring (k) and a damper (c), and is subject ac.d to an external torque Mo(t) and a control force F(). In the control system, y,() is a reference input; et) is an error signal; the sensor measures the angular position 0(0) of the disk, with the output44 y() g,0); the controller output ut) is described by a PD-control law Disk C I ely de(t) dt and the actuator applies force F.(t) to the disk, which is governed by dF (t) In the above description, g, k" k, , and all are constant parameters. (a) Write down all the equations for the control system. (7 points) (b) Draw a block diagram of the control system in the Laplace transform domain, with y,() being the input and 06) being the output. To earn full credit, you must show all the variables, including Y, (5), Mo(s), r(s), (s), E(s), U(s) and F: (s). ( 10 points)

Explanation / Answer

a)All equation

1.circular system equation

Equation in laplace domain(s)

(X(s)=teta(s))

w=angular velocity

M=1/2(Isquare* W)

X(s)=[(1/M)/(s(s square2+C/M s+K/M)]*F(s)......1

2.e(s)=yr-y(t)

PD controller

3.u(s)=(Kpe(s)+skde(s)) ........3

4.Actuator Transfer Function(TF) (a=alpha)

(output) F(s)=[B/(s+a)]*u(s) (input)......4

b) control flow diagram

error signal --->PD Controller(place the equation 3)-->Actuator TF(equation 4)--->circluar disk TF(equation 1)--->output X(s)(teta) take output in give to sensor negative feedback i am assume sensor TF is Unity

                                  All the best

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.