机械臂的自动控制系统
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Jacobian Matrix：
2) The dynamics equation of mechanical arm:
M(θ) G(θ) M(θ)
:
The total driving moment vector
:
The angle of rotation vector
:
Coriolis Centrifugal torqueInertia
. 2.5 1 1 x 2.2 3.1 X 0U
Y
1 0
0 1
பைடு நூலகம்
X
Solution:
2.5
RankQ C
A CA
2.2 2.5
2.2
1
3.1 2 1 3.1
RankQ B 0
AB
2.5 2.2
1 3.1
2.5 2.2 2
k k sI A BK
s 2.5
1
21
2.2 s 3.1
2) The relative order of computing system(计算系统相对阶)
After the two column is 0,
The first two lines of all 0,
And:
• On the output for
, Non singular, The system in the neighborhood of a in x, ，The relative order of the
system is 2.
3) Coordinate transformation
4) System is converted into standard type: The output
5) State feedback matrix,
,The system
become a completely controllable linear system
To the automatic control system accurately, it is necessary to get the accurate values of all status system. However, with the increase of system complexity, rely on the state of sensors to measure information will increase the complexity of hardware, may even lead to system instability. And some state information be restricted conditions, through physical measurement. At this point, the state observer provides a new train of thought: if the analytical model of controlled object is known, can through the design of state observer, then based on the system of external variables (input and output variables) of the actual measured values, the estimate of state variables.
2 2s 3
k k 1 7.6, 2 9.55
k 7.6 9.55
3.Design a observer (full‐orde
r or reduced‐order)
The flexible mechanical arm vibration force analysis
The observer design and analysis
(7)
The form of state transformation matrix: ]^T
Hypothesis and the assumption that the variables:
4) Mechanical arm model equation of state:
State equation:
The output of the system equations:
2.The mechanical arm odel linearization
1) The value of the parameter
• Assignment for(4) (5) (6):
a1=3.77 a2= 2.12 a3= 0.70 a4=80.32 a5=24.07
Group 4: single‐link flexible robot arm
1.The dynamics equation of mechanical arm:
（m2 l2）
（m1 l1）
1) Position equation of manipulator operation end：
State transformation:
:
The gravity vector
:
Inertia matrix
The mathematical expression: Simultaneous : (1) (2) (3)
The mathematical expression and The quantitative value:
3) Defined state variables:
2.State feedback control
The constitution of the state feedback
state feedback u=- Kx+ v
..
xx Ax BU y Cx
State description of close‐loopsystem
.
x =(A-BK)x+Bv
single‐link flexible robot arm
wangyuan
Arrangement：
M1: Build this system in Simulinkwith D/A and A/D converte rs M2: Design a state‐feedback controller (any form are OK) M3: Design a observer (full‐order or reduced‐order) M4: Design output‐feedback controller directly (e.g. PID)
s k k k 2 s( 5.6) 5.55 3.1 2.2
1
1
2
Because the system can be control completely, so all its poles can be arbitrary configuration.
s s
(1
2i)
*
s
(1
2i)
2) The dynamics equation of mechanical arm:
M(θ) G(θ) M(θ)
:
The total driving moment vector
:
The angle of rotation vector
:
Coriolis Centrifugal torqueInertia
. 2.5 1 1 x 2.2 3.1 X 0U
Y
1 0
0 1
பைடு நூலகம்
X
Solution:
2.5
RankQ C
A CA
2.2 2.5
2.2
1
3.1 2 1 3.1
RankQ B 0
AB
2.5 2.2
1 3.1
2.5 2.2 2
k k sI A BK
s 2.5
1
21
2.2 s 3.1
2) The relative order of computing system(计算系统相对阶)
After the two column is 0,
The first two lines of all 0,
And:
• On the output for
, Non singular, The system in the neighborhood of a in x, ，The relative order of the
system is 2.
3) Coordinate transformation
4) System is converted into standard type: The output
5) State feedback matrix,
,The system
become a completely controllable linear system
To the automatic control system accurately, it is necessary to get the accurate values of all status system. However, with the increase of system complexity, rely on the state of sensors to measure information will increase the complexity of hardware, may even lead to system instability. And some state information be restricted conditions, through physical measurement. At this point, the state observer provides a new train of thought: if the analytical model of controlled object is known, can through the design of state observer, then based on the system of external variables (input and output variables) of the actual measured values, the estimate of state variables.
2 2s 3
k k 1 7.6, 2 9.55
k 7.6 9.55
3.Design a observer (full‐orde
r or reduced‐order)
The flexible mechanical arm vibration force analysis
The observer design and analysis
(7)
The form of state transformation matrix: ]^T
Hypothesis and the assumption that the variables:
4) Mechanical arm model equation of state:
State equation:
The output of the system equations:
2.The mechanical arm odel linearization
1) The value of the parameter
• Assignment for(4) (5) (6):
a1=3.77 a2= 2.12 a3= 0.70 a4=80.32 a5=24.07
Group 4: single‐link flexible robot arm
1.The dynamics equation of mechanical arm:
（m2 l2）
（m1 l1）
1) Position equation of manipulator operation end：
State transformation:
:
The gravity vector
:
Inertia matrix
The mathematical expression: Simultaneous : (1) (2) (3)
The mathematical expression and The quantitative value:
3) Defined state variables:
2.State feedback control
The constitution of the state feedback
state feedback u=- Kx+ v
..
xx Ax BU y Cx
State description of close‐loopsystem
.
x =(A-BK)x+Bv
single‐link flexible robot arm
wangyuan
Arrangement：
M1: Build this system in Simulinkwith D/A and A/D converte rs M2: Design a state‐feedback controller (any form are OK) M3: Design a observer (full‐order or reduced‐order) M4: Design output‐feedback controller directly (e.g. PID)
s k k k 2 s( 5.6) 5.55 3.1 2.2
1
1
2
Because the system can be control completely, so all its poles can be arbitrary configuration.
s s
(1
2i)
*
s
(1
2i)