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ENGR 315Mathematical Models of SystemsTo learn about PID controls.Introduction:The PID controller is the most widely used control strategy in industry. It is used in many control problems such as automated systems or plants. A PID-Controller consists of three different elements, which is why it is sometimes called a three term controller. PID stands for:Proportional control is a pure gain adjustment acting on the error signal to provide the action input to the process.ReportTuning methodsZiegler Nichols Tuning Method1. Select proportional control alone2. Increase the value of the proportional gain until the point of instability is reached (sustained oscillations), the critical value of gain, Kc, is reached.3. Measure the period of oscillation to obtain the critical time constant, Tc.ENGR 315MATLAB / SIMULINK - Laboratory # 7Mathematical Models of SystemsObjectives:To learn about PID controls. Equipment:Computer Lab PCResources:1 - Modern Control Systems, Dorf and Bishop2 - Modern Control Systems - Analysis and Design, Bishop3 – MATLAB, Simulink, Control System Toolbox, Class NotesIntroduction:The PID controller is the most widely used control strategy in industry. It is used in many control problems such as automated systems or plants. A PID-Controller consists of three different elements, which is why it is sometimes called a three term controller. PID stands for: P Proportional control I Integral control D Derivative control.PID control can be implemented to meet various design specifications for the system. These can include the rise and settling time as well as the overshoot and accuracy of the system step response. To understand the operation of a PID feedback controller, the three terms should be considered separately. Proportional control is a pure gain adjustment acting on the error signal to provide the action input to the process. Integral control is implemented through the introduction of an integrator. Integral control is used to provide the required accuracy for the control system.Derivative action is normally introduced to increase the damping in the system. The derivative term also amplifies the existing noise which can cause problems including instability.Experiments:Consider the following PID controller arranged for convenience:Where: Kp is the proportional gain Ti is the integral time constant Td is the derivative time constantSuch a controller has three different adjustments (Kp, Ti, Td) which interact with each other. For this reason, it can be very difficult and time consuming to tune these three values in order to get the best performance according to the design specifications of the system. Consider the following configuration: The design a system for the following specifications: - Zero steady state error - Settling time within 5 seconds - Rise time within 2 seconds - Only some overshoot permitted The process transfer functions is as follows: Test the system (using Simulink) with the different values for Kp, Ti and Td (try first Table 1 and than Table 2). Compare the responses for the three cases. What do you observe?Table 1PID PI P – ControlKp=5 Kp=5 Kp=5Ti=1.5 Ti=2Td=0.8Table 2PID PI P – ControlKp=2 Kp=2.7 Kp=3Ti=0.9 Ti=1.5Td=0.6ReportSummarize your observations and attach relevant MATLAB scripts, Simulink diagrams and plots.Report due next laboratory period.Tuning methodsThe set up procedure or tuning of a controller can be tedious. One approach is to use a technique which was developed in the 1950's but which has stood the test of time and is still used today. This is known asthe Ziegler Nichols tuning method. Ziegler Nichols Tuning MethodThe procedure is as follows: 1. Select proportional control alone 2. Increase the value of the proportional gain until the point of instability is reached (sustained oscillations), the critical value of gain, Kc, is reached. 3. Measure the period of oscillation to obtain the critical time constant, Tc. Once the values for Kc and Tc are obtained, the PID parameters can be calculated, according to the design specifications, from the following table. Control KpTiTdP only 0.5 KcPI 0.45 Kc0.833 TcPID tight control 0.6 Kc0.5 Tc0.125 TcPID some overshoot 0.33 Kc0.5 Tc0.33 TcPID no overshoot 0.2 Kc0.3 Tc0.5 TcTable 1These values are not the optimal values and additional fine tuning may be required to obtain the best performance from the system. The selection of the type of PID-control to be applied depends on the application of the system. i.e. a control system for a pressure vessel strongly requires PID-control with no


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