Design and Tuning of PID Controller for Brick Cart with Escalator Engine

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Introduction:
Control system plays important role in the field of engineering covering wide applications
ranging from satellite, missiles, biomedical, electrical, mechanical, and traction. The close
loop control schemes involve, feedback of the system taken from output side and compared
with the desired value of system parameter if any deviation found corrective actions taken
accordingly. Here in this problem brick cart with escalator driven by the engine need to be
controlled with specification of various parameters including velocity, acceleration and the
overshoot. The use of PID controller in close loop environment is suggested to be done.
PID parameter can be set with the use of various conventional and modern techniques.
Here in this particular problem tuning of parameter is done with the use of Zeigler Nichols
method.
Aim:
Here the main aim of the problem is to move the brick cart (as illustrated in figure 1) from a
base point to some destination point to be controlled by the escalator engine. The brick cart
starts at the base of the escalator and must move along the escalator's rails. To control the
process PID controller must be use.
Figure 1 Brick cart controller example
Methodology

Two types of control system are generally use in the field of engineering known as open
loop control and closed loop control. Firstly, the system designed under the open loop
environment than if the performance of the system found not satisfactory closed loop
control is implemented. Figure 2 illustrated the open loop control scheme and figure 3
present closed loop control with feedback.
Figure 2 Open Loop system
Figure 3 Close loop with feedback
. The controller in figure 3 presented can be PID controller. Figure 4 illustrate the PID
controller scheme.
Figure 4 PID Controller
Here in the given problem aim is to design the PID controller for the brick cart which act
for controlling the numerous parameters of the cart to travel for a distance d from point X
to point Y. The cart must stop at point Y with overshoot not exceed of 0.1m otherwise it

may lead to create catastrophe to the structure.
Various forces acting on the brick cart is resulted from the dynamic motion of the cart.
The gravitational force is given by,
The frictional force due to dynamic motion is given by,
So, the force generated by brick cart dependent on the output parameter of PID controller
which is given by,
The net force action on the brick cart is given as,
The main three parameter of the brick cart are displacement, velocity and the acceleration is
given as,
The velocity of the cart is given as,
And the displacement of the cart is given as,
Finally, the error of the system is represented by e(t) given as,
Where d is the desired displacement and x(t) is the actual displacement done by the brick
cart.
Y