Lab Rotary Control

7/29/2019 Lab Rotary Control

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Objectives

The objective in this experiment is:

To introduce the fundamentals of control using the PID family of compensators.

To mathematically model the servo plant from first principles.

To understand of the different tuning parameters in the controller.

To design and simulate a PV controller to meet the required specifications.

To implement your controller and evaluate its performance.

Theory

Mathematical Model

We shall begin by examining the electrical component of the motor first. In Figure 1,

you see the electrical schematic of the armature circuit.

Figure 1 - Armature circuit in the time-domain



Using Kirchhoff’s voltage law, we obtain the following equation:

[3.1]

Since Lm << Rm, we can disregard the motor inductance leaving us with:

[3.2]

We know that the back emf created by the motor is proportional to the motor shaft velocity

ωm such that: K m

[3.3]

We now shift over to the mechanical aspect of the motor and begin by applying Newton’s

2nd law of motion to the motor shaft:

[3.4]



Where is the load torque seen thru the gears. And is the

Efficiency of the gearbox. We now apply the 2nd law of motion at the load of the motor:

[3.5]

Where Beq is the viscous damping coefficient as seen at the output.

Substituting [3.4] into [ 3.5], we are left with:

[3.6]

We know that and (where is the motor efficiency),

we can re-write [3.6] as:

[3.7]

Finally, we can combine the electrical and mechanical equations by substituting [3.3] into

[3.7], yielding our desired transfer function:

[3.8]

Where:



Lab Procedure

Wiring and Connections

1. The first task that we need upon entering the lab was to ensure that the completed

system is wired as described in the SRV02 Experiment #0 – Introduction.

2. During wiring, if we were unsure of the wiring, we need to referred to the SRV02

User Manual or ask for assistance from a TA assigned to the lab.

3. After all the signals are connected properly, MATLAB was start-up and Simulink

was started.

Controller Specifications

This lab requires you to design a Proportional + Velocity (PV) controller to control the

position of the load shaft with the following specifications:

1. The Overshoot should be less than 5%. ( ζ > 0.707 )

2. The time to first peak should be 100ms (Tp = 0.150).

Simulation of the Plant

This model includes the modelled plant (SRV-02 Plant Model), as well as the PV controller.

Kp and Kv are both set by slider gains. Before we begin we must run an M-File called

“Setup_SRV02_Exp1.m”. This file initializes all the motor parameters and gear ratios. Click

on Simulation->Start , and bring up the Simulated Position scope. We monitor the response,

and then adjust Kp and Kv using the slider gains. We try using the variety of combinations,

and note the effects of varying each parameter.

We make a table of system characteristics (and) with respect to changes in Kp and

Kv. (Hold one variable constant while adjusting the other).

We try to find out does the system response reacts to how we had theorized in section

3.1.



After we have familiar with the actions of each parameter, we enter in the designed Kp and

Kv that we had calculated to meet the system requirements.

From there, we need to find out either the response look like we had expected or notand what is our per cent overshoot.

We calculate our Tp and see either it match the requirements or not.

*Hint: To get a better resolution when calculating Tp , decrease the time range under the

parameters option of the scope.



Result

From Post Lab Question:-

1) Figure 2 shows the closed loop PV controller implementation, using equation [3.8]:

and substituting the state feedback control signal equation [3.9] into [3.8]:

we are left with the following transfer function:

with the following characteristic equation:

• As K p increase, ω n will also increase.

• As Kv increase, ζ will also increase.• As Kp increase, ζ will decrease (because ω n will increase).



2) For the in-lab portion of this experiment, we are required to design a PV controller that

will yield the following time requirements:

• The Overshoot should be less than 5% (ζ ≥ 0.707).

• The time to first peak should be 100ms (Tp = 0.150).

K p = 14.234 V/rd K v = 0.11157 V/rd/s

3) From Question 3, we have tabulated data for different value of changes in Kp

and Kv

Graph K p K v Percentage overshoot

(PO)%

Tp

1 14.2343 0.11106 8.47 0.1481

2 15.5844 0.17273 5.88 0.1477

3 16.6697 0.21881 4.39 0.1487

4 18.7061 0.29868 2.47 0.1509

5 20.4076 0.36017 1.467 0.1535



Graph 1

Graph 2

Graph 3



Graph 4

Graph 5

4) After we find the calculated Kp and Kv , the desired output of our response come out as

expected. As we increase the value of Kp , the natural frequency also increase. The



condition goes same for the Kv. The damping ratio of the response is increasingly with the

increment value of Kv. The percentage overshot is 4. 39 %, the value of approximately is

about less than 5 %. The time peak of the response is 0.1487.

Discussion

For this experiment, we have to manipulate the value of K p and K v in order to achievethe target values required by this experiment. The target values are the time to first peak, t p =

0.15s and the percent overshoot, PO < 5 %. Theoretical values were calculated in order to

compare with experimental values.

The output response comes out as expected. We have tabulated several data for

getting an accurate response. From the data, we managed to have desired result. As usual, for

any experiment, we may encounter with several error throughout the experiment. The

limitation of resource in the lab may be one of our reasons in completing the experiment.

Furthermore, a further understanding about the MathLab software is vital and we

manage to have adequate knowledge regarding the task given. For future study, we find that

is important to have basic knowledge in the software, the PID controller and theories

regarding this session of experiment.

Apart from that, we have managed to have good response for the system and have

completed the experiment.

Lab Rotary Control

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