UWE Bristol Engineering showcase 2015

Xubin Han
Equivalent system and
dynamics equation of system
By using equivalent unit method to each component
of the multi-body system, the equivalent mass
matrix M can be derived from element mass matrix
m. The equivalent mass matrix M was determined
by the element mass matrix and relation
matrix Q n, m , which shows the relationship between
system possible displacements and unit nodal
coordinates. From
T T F P − F g = T T F − F = 0
can derive the dynamics equation of system as:
T T M R = T T F
Since R was the possible displacement vector of
system and each component was not entirely
independent
R = T q
R = T q + T q
The reason for building R = T q was for solving
the equation easily.
Therefore, the generalized coordinate’s style of
dynamics equation was:
T T M T q + T q = T T F
With tensor, the dynamics differential equation of
system can be shown as:
i
k
T ik M ij
T jk q k + T jkq k
BEng Mechanical Engineering
Engineering Mechanical Arm: analysis
= T ik F i
i
The dynamic performance of engineering mechanical
arm and intelligent control
the comparison of step response while no controller and after adding PID controller. It
could be found that, after adding PID control, the peak y p =1 and it meant no overshot;
the peak time t p =4.8s; the regulation time t s =3.8s and the steady-state
error e ss =0.0036. Compared with the original system, the response time and settling
time are greatly reduced.
the comparison of moving arm's open-loop Bode plot. From the plot, it can be found
that the magnitude margin G m =71.8dB, the crossover frequency of
magnitude ω g =86.4rad/sec, the phase margin P m =87.2deg and the shear
frequency ω c =0.29rad/sec. Compared with the original system, the cutoff frequency
becomes larger and with wider bandwidth. It means the highest frequency range
becomes larger while the boom subsystem operating and it gets faster response and
better dynamic performance.
the sine tracking curve of moving arm's PID control system. After adding PID control
system, for one thing, the sinusoidal tracking signal is substantially no attenuation and
phase delay, for another, the set value can be achieved in a short period of time.
Therefore, it can satisfy the requirements of control in real operations.
Project Supervisor:
Professor Quanmin Zhu
Project summary:
My research including the modelling method of
multi-body dynamics equations of the engineering
mechanical arm and especially I mainly discussed
the equivalent finite element method and the
relevant theory.
According to the trajectory tracking control
expression of the manipulator bucket and the control
theory, set up the PID control model to run the
mechanical arm. Using MATLAB to simulate and
do the calculation for the controlling model and
analysing the steady state error and dynamic
response error of system
Project object:
My report use theory related to mechanical arms as
the main basis, which mainly related to the multibody
dynamics, flexible multibody dynamics, PID
control, I use the theory to study the modelling and
simulation of mechanical arms motion intelligent
control.
Project conclusions:
(1) the motion law of engineering mechanical arm,
the engineering mechanical arm multibody
system dynamics equation base on equivalent
finite element method has been derived.
(2) Specifically, after discoursing the equivalent
force system and the actual force system, the
equivalent system dynamics equation has been
derived in detail.
(3) the PID control model of hydraulic excavator’s
mechanical arm has been built with modelling
and simulation of MATLAB
(4) after the control system adding PID controller,
the response speed of system became faster
obviously, also the system had stronger ability of
tracking the change of input parameters base on
keeping the stability of system. All in all, the
PID control system can achieve the requirements
of control faster than the original system.