Question

Question 2: Using >> controlSystemDesigner in MATLAB, design an analog PID controller (find Kp, K, Ka values) for the given plant that satisfies the specifications listed below, Plant transfer function: Y(s)4 GS s-25+5 Design specifications for step response Overshoot : %20 Rise time: 0.5 s Settling time : 1 s Settling : %3 Use default values for others . The control architecture ym Remember that the transfer function for a PID controller is, Thus, you need to add one pole at origin and two more zeros. The gain and position of zeros will yield the Kp, Ki, and Ka values

Could you write down the answer legible please i cannot read most of the answer sheets. Thank you in advance, professor.

Answer 1

I have usedMATLAB to design the PIC controller meeting the specifications.

MATLAB code for generating the required GUI to edit anf tune the compensator is given below in bold letters.

s = tf('s');
G = 4/(s^2-2*s+5);
sisotool(G);

This code will invoke the following GUI window where you can start the design process.

Control and Estimation Tools Manager File Edit Help 笛 っ Architecture Compensator Editor Graphical Tuning Analysis Plots Automated Tuning SISO Design Task 困咆Design History Current Architecture: Control Architecture... Modify architecture, labels and feedback signs. Loop Configuration.. Configure additional loop openings for multi-loop design. System Data Import data for compensators and fixed systems. Sample Time Conversion.Change the sample time of the design Multimodel ConfigurationChange the nominal plant and multimodel options. Undo

Now in the above window, go to analysis plots tab and select step in the plot type of plot1.And select the closed loop r yo y as shown in the following figure.

Control and Estimation Tools Manager File Edit Help Workspace Architecture Compensator Editor Graphical Tuning Analysis Plots Automated Tuning 白.k] SISO Design Task Design History Analysis Plots Plot 1 Plot 6 Plot 2 Plot 3 Plot 4 Plot 5 Type StepNoneNone None None None Contents of Plots Plots Responses 1 2 3 4 5 6 All Closed Loop r to u Input Sensitivi Output Sensiti Noise Sensiti Open Loop L □ Compensator c Prefilter F Add Responses .. Show Analysis Plot Help Show Architecture Store Design Redo

This will plot the unit step response of the system as shown in the below figure.

LTT Viewer for SISO Design Task File Edit Window Help Step Response x 10 -2 .4 20 30 50 60 40 Time (seconds) LTI Viewer Real-Time Update

since the system has poles on the right side of jw axis, it is unstable. therefore the system unit step response is unstable. Now we need to design a PID controller to stabilize the plant and meet the design specifcations. For that, right click on the plot and edit the design requirements as given below.

Edit Design Requirements Design requirement: ...p response bound from 0 to 1.5 seconds Design requirement parameters Initial value: 0 Final value: Step time: Rise time: 0.5000 | % Rise: 90 Settling time: % Settling: 1 2.0000 96 Overshoot 20.0000 96 Undershoot 10 Close Help

Now go to edit comppensator and add two zeros at -1,-1 and integrator (pole at orogin) and set the gain to 20 as shown below.

Control and Estimation Tools Manager File Edit Help Workspace Architecture Compensator Editor Graphical Tuning Analysis Plots Automated Tuning 白れ SISO Design Task Compensator Design History (1 s) (1s) Pole/Zero Parameter Dynamics Edit Selected Dynamics Type Locati... Damp... Frequ... Real Ze... -1 Real Ze...-1 Integra... 0 Select a single row to edit values Right-click to add or delete poles/zeros Help Show Architecture Store Design Redo

The response to unit step is plotted below.3

LTI Viewer for SISO Design Task File Edit Window Help Step Response 1.2 R 0.8 0.6 0.4 0.2 0.2 0.5 1.5 Time (seconds) LTI Viewer Real-Time Update

It is observed that the system response has met the design requirements.

The PID  controller is given by C(s) = 20*(s+1)*(s+1)/s