IntroductionIn the gains P, I, and D

IntroductionIn this project, we will be using Matlab and Simulink. Matlab is a software used for the implementation of algorithms and creations of user interfaces.  Simulink is a data flow graphical programming language tool for modeling and simulating dynamic systems. Both software is designed by MathWorks. Since the depth of the methematical modeling and control theory is not covered, we are to explore and learn how to use the tools in the design process. For the simulation process, Simulink will be used to understand how the PID controller affects the pitch of the aircraft.A proportional–integral–derivative controller (PID controller) is a closed-loop system with a feedback mechanism which is widely used in industrial control systems and a variety of other applications requiring continuously modulated control. A PID controller calculates the differences between the setpoint and the error measured and applies a correction based on proportional, integral, and derivative terms (denoted P, I, and D respectively) which gives the controller its name.The overall control function can be expressed mathematically as:Block diagram of a PID controller:Section APID Controller:The transfer function of Aircraft dynamic (the plant) is 12s+20s3+5s2+13sThe transfer function of the servo actuator is 0.5As+8 where A is different for different studentPlease use the serial no in your attendance list as the variable that is in your servo actuator block, in this case is 8Types of Controller:Open-Loop ControllerP controlPD controlPID controlCL RESPONSERISE TIMEOVERSHOOTSETTLING TIMES-S ERRORKpDecreaseIncreaseSmall ChangeDecreaseKiDecreaseIncreaseIncreaseDecreaseKdSmall ChangeDecreaseDecreaseNo ChangeGeneral Tips for Designing a PID ControllerWhen you are designing a PID controller for a given system, follow the steps below to obtain a desired response.Obtain an open-loop response and determine what needs to be improvedAdd a proportional control to improve the rise timeAdd a derivative control to reduce the overshootAdd an integral control to reduce the steady-state errorAdjust each of the gains P, I, and D until you obtain a desired overall response. For P controller:The Proportional gain(P gain) affects the control signal and causes more overshoot which also reduces the steady-state error when increased. Here are 2 responses, the left graph is where the P gain is 1 and the right graph is where the P gain is 2.5. As we can see, with a higher gain the rise time is faster, it is important to have a faster rise time as it reduces the delay for the pitch control. However we can also see that the response is not very stable due to an overshoot and also a long settling time. If we were to continue to increase the gain of the P controller, the overshoot will be larger.PD Controller:For PD Controller, by adding the derivative gain, it adds the ability to “expect” an error. With a fixed P gain, the only way to increase the control is when the error increases. D gain does not affect the steady state error. Here we can see that the controller is now more stable because it no longer has an overshoot, however there is still a longer settling time. By increasing the D gain, the overshoot and rise time will decrease.PID Controller:Since there is no steady-state error, the integral term is set to 0. However I still have to consider how to decrease the settling time, hence P gain is increased to 10 and D Gain to 2.5 . The response comparison can be seen below. With a higher Kp and Kd, it enables the PID controller to be faster, through the testings that has been made, we can see from the final response(right graph) that although the rise time is short and steady-state error is near zero, there are still some errors in the signal during the time it settles. Simulink has enabled us to understand how the different components in the PID controller work to achieve the desired output of a control surface. It is important to understand the requirements of the control system so that we can understand and expect a certain type of response, in this case for the pitch control. For the pitch controller, we have to make sure that the rise time is fast, thus reducing the settling time. This allows the pilot to control the control surfaces of the aircraft to control the pitch without much delay.Section BTwo-Axis Auto Pilot SystemAuto piloting is to allow the aircraft to fly on its own without much human supervision. A two-axis autopilot manages elevators and ailerons which controls the pitch and roll respectively. Pitch control allows the pilot to operate the planes easily with the help of servomechanisms in which a small force is needed to move the bigger load (the control surfaces of the plane).  Pitch control is also used as a stabilizer which allows the plane to be stabilized automatically, reducing the need for supervision. This are all done through a system call the closed-loop system.The autopilot or Automatic Flight Control System (AFCS) is used mainly to stabilize the dynamic response of the airplane automatically and ensure the safety of the flight. It controls the attitude of the aircraft with control surface movements. The mode of operations controls the functions in the pitch, roll and yaw axes which are achieved from the set of servos operating the control surfaces.Autopilot is done by the computer in the aircraft by communicating with the primary flight control surfaces, as well as gathering data from the plane systems and equipment such as the accelerator, gyroscope, altimeter, airspeed indicator and compass. A servomechanism is used in the aircraft which receives orders from the aircraft computer and carries it out. It provides automatic corrections of deviations to the input set by the operator. Usually a small power of input is used to control the much larger output.Not all the passenger planes flying today carry an autopilot system. Older and smaller aircrafts are still flying mechanically, as well as smaller airliners with no more than twenty seats are also without an autopilot as they are usually used for short-duration flights with two pilots. There are three levels of control in autopilots for smaller aircraft. A single-axis autopilot controls an aircraft in the roll axis, causing limitations. A two-axis autopilot controls an aircraft in the pitch and roll axis, and may lack pitch control ability or it may receive inputs from on-board radio navigation systems to provide true automatic flight guidance once the aircraft has taken off until shortly before landing. A three-axis autopilot adds control in the yaw axis and is not common in many smaller aircrafts.   Autopilot system found in smaller aircrafts.For two-axis autopilot aircrafts generally divide a flight into takeoff, climb, cruise (level flight), approach, and landing phases. An autopilot-controlled landing on a runway and controlling the aircraft on rollout (i.e. keeping it on the centre of the runway) is known as a CAT IIIb landing or Autoland, available on many major airports’ runways today, especially at airports subject to adverse weather phenomena such as fog. Landing, rollout, and taxi control to the aircraft parking position is known as CAT IIIc. This is not used to date, but may be used in the future. An autopilot is often an integral component of a Flight Management System.Modern autopilots use computer software to control the aircraft. The software reads the aircraft’s current position, and then controls a flight control system to guide the aircraft. In such a system, other than classic flight controls, many autopilots incorporate thrust control capabilities that can control throttles to optimize the airspeed.The autopilot in a modern large aircraft typically reads its position and the aircraft’s attitude from an inertial guidance system. Inertial guidance systems calculate errors over time. They will incorporate error reduction systems such as the carousel system that rotates once a minute so that any errors are dissipated in different directions and have an overall nulling effect. Error in gyroscopes is known as drift. This is due to physical properties within the system, be it mechanical or laser guided, that corrupt positional data. The disagreements between the two are resolved with digital signal processing, most often a six-dimensional Kalman filter. The six dimensions are usually roll, pitch, yaw, altitude, latitude, and longitude. Aircraft may fly routes that have a required performance factor, therefore the amount of error or actual performance factor must be monitored to fly those routes. The longer the flight, the more error accumulates within the system. Radio aids such as DME, DME updates, and GPS may be used to correct the aircraft position.Autopilot is an example of a closed-loop control system. A closed-loop control system is dependent on the initial input set and on the actual output of the load. This type of system requires a measurement(feedback) to be connected between the load and the control device. This system must be able to carry out continuous operation and be able to have error detection, amplify error signals and control the servomechanism by providing a feedback.There are two types of servo mechanism:Position Control ServomechanismRate Control ServomechanismPosition Control ServomechanismIt consists of five parts, control shaft, amplifier, servo motor, load and output shaft. The movements are measured by potentiometers at the control shaft and the output shaft.Position Control ServomechanismRate Control ServomechanismA rate control servomechanism produces error signals, because of voltage differences corresponding to input and output speeds, to control the speed rate of the motor and load. Rate control ServomechanismThe error signal is amplified and fed to the motor which accelerates the load towards the required speed. The motor also drives the tachometer generator. The tachometer generator provides an output voltage proportional to the speed of the load. This voltage is fed back to the amplifier to reduce the output to the motorAutopiloting is the core of every automatic flight system. This provides stability in maintaning the aircraft’s flight as it controls the three axes of the aircraft, roll, pitch and yaw. For two-axis autopilot system, only pitch and roll is considered.The AFCS has an inner loop and an outer loop. The inner loop consist of accelerators, sensors, servo motors and control surfaces. The elements help to sense attitude changes of the aircraft about its axis and changes in terms of error signals, process error signals and convert them into servomechanism operations and convert processed signals into the flight control surface. The outer loop consisit of external sources such as the central air data computer, magnetic heading reference system, altimeter and airspeed indicator, to control the aircraft laterally to maintain the seelected heading or course, as well as longitudinal control to maintain the preset altitude or vertical speed. Above are the typical Autopilot ModesAutopilot operations of the aircraft flying control is usually done by hydraulic power-operated actuators as they are mostly used in large aircrafts. The machines used are electrically driven mechanics, hydraulic or pneumatic machines that move the control surfaces. This allows the pilot to use less afford to move the big control surfaces of larger aircrafts.The flight director is also another autopiloting system. Different from the AFCS, the FDS requires manual supervision to control the aircraft’s flight path and they do not have servos to operate the aircraft control surfaces. This system provides flight commands by integrating the display of the aircraft attitude in terms of roll and pitch, also with radio navigational data to provide directional commands. The flight director provides a command bar for the pilot to fly according to the preset heading or course, as well as the altitude and speed.Autopilot for ILS landingsFor an AFCS to be able to perform automatic landing, it must contain a minimum of two independent autopilot systems and also meet the safety requirements. Depending upon the degree of redundacy, the auto landing system can be classified as, fail passive system or fail operational system. Fail passive system consist of 2 indeppendent autopilots. If one fails, the other will stop working as 2 autopilots are needed for landing automatically. It also requires a self-monitoring system to ensure that both autopilots are working together at all times. If a failure occurs on either autopilot or monitoring system during approach, the approach continues on one auto pilot however automatic landing is no longer available. Thus flight operators has to take over for manual control.Fail operation system consist of 3 independent autopilots and 2 independent monitoring systems. A single failure in either systems will operate the system fail passive, but it still has sufficient redundancy to meet the criteria for automatic landing. In fail operational system, all the autopilots and self-monitoring systems must be engaged for approach and landing.