姚斌机电控制技术考试试卷及答案解析.docx

第 1 页
Mechatronic Control Systems
Spring 2021
Dr. Bin Yao
FINAL EXAM
April 30, 2021
Problem
Point Value
Points the plant has an unstable pole at 1, to avoid excessive overshoot due to this unstable pole, the CL bandwidth should be higher than the break frequency of this unstable pole, which can be roughly met by imposing the following conditions on dominant CL poles:
(4)
As the plant has a stable zero at -3 which tends to increase the overshoot significantly when it is slower comparing to the CL bandwidth, to avoid excessive overshoot, the following condition on dominant CL poles should be imposed normally:
(5)
Thus we can place the dominant CL poles around 2 to make a compromise between the conflicting requirements of (4) and (5). Note that as this zero is stable, you can also cancel this zero in the controller design (by placing one CL pole at -3) to remove its effect on the CL response with respect to the reference input as well. In that case, its effect still appears in the CLTF from the disturbance input to the output.
c). With a second-order controller of the form (1),
(6)
we have four controller parameters free to choose and the resulting CL system has four poles. Thus we can arbitrarily place all four CL poles with the controller form of (6). For simplicity, let all CL poles at -2, which leads to the following desired CL characteristic polynomial (CLCP):
第 5 页
(7)
From (2), the actual CLCP with the controller (6) is
(8)
Comparing (7) and (8), we obtain
(9)
Thus,
(10)
PROBLEM 2
第 6 页
(20 Points)
Consider the following two-DOF feedback system:
Sensor
Reference
Value
Noises
-
Controller
Plant
where
and the system has the following characteristics:
The input disturbance has significant energy in the frequency band [0, 1] rad/s.
The measurement noise has significant energy in the frequency band [5, 100]rad/s.
The reference signal has significant energy in the frequency band [