The objective of the experiment is to tune the control system of an aircraft so that it is dynamically stable.
This experiment focuses on the rolling dynamics of aircraft. First, the controller is designed with an open
system. With the open system, it is shown that the aircraft’s response is completely unexpected. With a
pilot input angle of 1 degree, the aircraft would continue to roll exponentially. In addition, the aircraft was
simulated to collide with an eagle.
A closed loop system was then designed. Using the Ziegler-Nichols method, the proportional controller of
the system was gradually increased until a marginally stable response was reached. With only a
proportional control action and a pilot input angle of 5 degrees, the aircraft stabilized to the desired output
of 5 degrees. In other word, in real-life example of this control system would be the control system of
an aircraft where a closed-loop system is applied to keep the aircraft always stable at any given input
angle or even when a noise is on the system the closed loop system would get the aircraft back to the
Discussion and Conclusion
A closed and open loop system generate different results but are also relatable to one another. An open
loop system focuses on what is designated as the input and the output has no effect on the desired action.
A closed loop system is a control system works with the concept of an open loop system but also focuses
on the output because it will be altered to give the desired results. Using the scenarios of the step response
and disturbance acting against a flying airplane are what demonstrates the different results when applying
an open loop system for the step input collision and the disturbance with a closed loop system. When the
step input scenario is used along with the aircraft it gives a growing error response for the aircraft. The
graph demonstrating this response can be found in Figure 1.
To achieve these results a set of differential equations were obtained and assigned to the block diagram in
accordance to every input and output. The block diagram was used to demonstrate how an aircraft with
rotational motion about the roll can and can not be stabilized when outside interferences.
In an open loop response with a disturbance, the aircraft will settle down over time but have an error. The
created block diagram is set so that if any interference were to affect the aircraft the disturbance will be
continuous and settle down after a certain period but will always have an error in the roll angle. In other
words, the aircraft would not be able to return to its original equilibrium. The results of the open loop
impact response can be viewed in Figure 1. Having the same scenario in play a step response can be
added to the block diagram and the results will differ. Having the added step response will show that the
error in the roll will always be increasing. The open loop with a step function result can be viewed in
Now, for a closed loop system the same aircraft and disturbance are in play but instead have a response
feedback. The feedback assists in the control action for both roll angles. To achieve this result, the
Zeigler-Nicholas Method in relation to the closed loop system is referred to achieve the desired
performance and meet design requirements.
In the current labs experimental situation, the desired response is to decrease the rise time which will
allow the peak response to be reached more quickly. The stabilizing process of the I(Integral) and
D(Derivative) gains are set to zero. Next, increasing the Kp value will aid in the decrease of the rise time
and increasing Kf will decrease rise time as well. The Proportional Controller in a closed loop system has
a large overshoot and settling time, while the Proportional Derivative Controller has a lower overshoot
and settling time. The P vs. PD comparison with an input of 5 degrees can be viewed in Figure 4. Neither
case has the result of a steady state. To establish a steady state, the Integrator Controller is used to
eliminate the steady state error from the P and PD controllers. The purpose of the Proportional Controller
and Proportional Derivative Controller is that they are two different controller options that are used to
tune the stability of the aircraft.
In a closed loop system with a step response in accordance with a Proportional Controller and
Proportional Derivative Controller, the peak of the P controller is reached quicker than the PD controller.
The results can be viewed by referring to Figure 5. Both controllers can achieve the required results and
have a low error between the two of them.
The disturbance in the Proportional Controller has a large peak response and overshoot percentage than
the Proportional Derivative Controller. The comparison in peak value and overshoot percentage can be
found in Table 2. According to Figure 5 the peak reference can be compared for both scenarios. The
reason for the difference in both plots is that the disturbance has a greater impact than the original nonstep function. The Proportional Derivative Controller would be the better choice in assisting the aircrafts
specifications. This is because the error in trouble shoot is lower and stabilizing the aircraft after an
impact has a lower error. The percentage of overshoot (P) in a closed loop system is 68.2% and steady
state error (PD) of 23.44%. The percentage overshoot (P) of a closed loop disturbance is 28.14% and the
steady state error (PD) is 25.15% The comparison in error can be found in the Appendix labeled Table’s 3
and 4. The reason for the step input having a smaller percentage error is because the disturbance was of
a greater value that was being applied to the aircraft.
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