Carrying out an open-loop step response on the process trainer pt326

Carrying out an open-loop step response on the process trainer pt326 INTRODUCTION: The control systems are based up on the behaviour of the dynamics systems and it is also a branch of the engineering and mathematical model of the process. The desired output of the system is called as reference. A controller is device which observes and outcome the changes in the output that are affected by the input variables. And it is also used to operate the input variables to a system to achieve the desired result on the output of the system. It is very simple and flexible to solve using the mathematical model. In control system design, we have a concept of feedback control system. The main concept of this feedback loop is to control the system performance and it is a negative feedback because the sensed value is subtracted from the desired value to produce the error signal which is amplified by the controller. To avoid the problem of the open-loop control system, the control system initiated the feedback loop. Where as in closed loop system, the control system uses the feedba ck to control the output of the process. One of the most widely used controllers in the design of continuous data control system is the PID controller, where PID stands for the proportional plus integral and derivative control. The PID controller is mostly used in the feedback control design. The controller is used for the operation of the error signal to produce the control signal. Proportional (P) control: This is the one type of action performed and used in the PID controllers is the proportional control. It is the simplest form of continuous control system that can be used in the closed loop system. Proportional control is used to minimize the fluctuation in the process, but it does not allow to bring back to the required set point. P-only controller provides the faster response than other controllers. The system first allows the P-only controller in order to get the system a few seconds/minutes faster. The main advantage of the P-only controller is the faster response time, it produces the deviation from the set point and this deviation is called offset. Mathematical Equations: P-only controller linearly correlates the controller output (actuating signal) to the error (difference between measured signal and set point). In the mathematical form, the p-controller is given below Y(t) = Kc e(t) + b Where Y(t)= controller output Kc = controller gain e(t)= error b= bias In the above equation the controller gain and bias are constant to each controller. The controller gain is the change in the controller output per change in the controller input. Bias is simply a controller output, when the error is zero. In the PID controller, when the signals are transmitted then the controller gain relates the changes in the output voltage to the changes in the input voltage. Thus, the gain ultimately changes in the input and output properties. If the controller output changes more than the input, Kc is greater than one. If the change in the input is greater the controller output, Kc is less than one. Ideally, Kc is equal to infinity then the error will be reduced to zero. Exact equalities cannot be achieved in the control logic. In this, the error will be allowed up to certain range of the system. Integral (I) Control: This is another type of action performed in the PID controllers is the integral control. Integral control is the second form of feedback control system. It is obtained used to remove the deviations that may exit. Thus the system moves to the steady state and original settings. A positive error will cause the signal to be increase and whereas a negative error will cause the signal to be decrease the system. However, I-only controller is much slower in response time than the P-controller. Thus, the slower response time will be reduced by combining with another form such as P or PD controller. It is often used to measure the required variables to remain within a narrow range and also require a fine tuning control. Mathematical Equations I-controller correlates the controller output to the integral of error. The integral of error is taken with respect to time within a specified interval. In the mathematical form, the I-controller equation can be represented as Where C(t)= controller output Ti = integral time e(t)= error c(t0)= controller output before integration. Derivative (D) Control: This is another type of action performed in the PID controllers is the derivative control. I-control and D-control are a form of a feed forward control. D-control anticipates the process conditions by analyzing the change in error. It main function is to minimize the change in error, thus keeping the system in a consistent setting. The main benefits of the D-controller is to resist change in system, the most important of these being is oscillations. PI-controllers: PI-controller is a combination of both proportional plus integral controller. This is the feedback controller which drives the process/plant to be controlled with sum of error and also the integral of that value. In PID controllers, we have not yet used the D-controller (D=kd=0). The basic block diagram of the PI controller is shown below, The controller output for the above closed loop system is Where ÃŽ is the error of actual measured value from the desired set point. ÃŽ = SP PV. The main advantage of the PI controller; the integral terms in the PI controller causes the steady state error to be zero for a ramp input. The main disadvantes of using with the PI controller is the phase lag. This means that the phase margin decreases. Required Apparatus: The report of this experiment is carried out on the Feedback Process Trainer, PT326. The design of the control system consist of a computer ,A/D and D/A converters, and a printer used to provide the copies of the response system. The networked PCs used to obtain the system design using the nyquist simulation method employing the design and simulation program CODAS. Explanation of PT326: According to the industrial situation, the PT326 process trainer model is commonly used. This situation appears when the temperature control is required in the presence of transport delay and transfer lags. In this PT 326 process trainer, the trainer involves air that is strained from the atmosphere through a centrifugal blower and it is heated and passed over the heater through duct before it is being heated. The objective of the control is to sustain the temperature of the air at the required level. The temperature control can be achieved by varying the electrical power supplied to the heater grid. By using the bead thermistor which is placed in the flow at any three position along the duct, the air temperature may be sensed. The process trainer introduces the transport delay in the system which is located between the thermistor and heat coil. By setting the opening of the throttle, the mass flow of the air can be adjusted through the duct. The temperature sensors can be placed at any three of the position in the duct, so that these sensors can acts as a detector. The variation in the resistance of the temperature sensor is converted to the voltage variation through the bridge circui t and is available at terminal Y. The output of the temperature sensor can be used as feedback for connecting the terminal X and Y. The required temperature can be indicated by adjusting the knob label set value. In additionally, the set value can change the step by using the command throwing the switch as internal. An external referrence input can also be provided using the label as external. The difference between referrence input set value and feedback signal is availabel at terminal B and can be supplied to the heater power supply so that the gain can be adjusted by using the prportional band. To select a continuous control, the signal at A can be send directly to the heater power supply by using the switch s. The switch s can be alternatively used as on-off controller as well as it is used to select the two step control. This on-off control command reponds to the maximum heater power when on and for the zero heater power it is off. The hysterisis is an on-off controller which can be adjusted by the knob label as overlap. The maximum heater supply can be adjusted using the knob label as max heater power. The process may be seen to comprise a simple blower in which air is drawn from the atmosphere, blown past a heater grid and along a tube having a provision for several temperature to pick up. The purpose of the control system is to maintain the temperature of the air flowing in the tubeat some required set point. The output of the process is a temperature which is measured by the use f the thermistor bead transducer and bridge circuit. Procedure: In the set of experiments of the PT326 process trainer, a personal computer acts as a contoller. Three controller are going to be investigated, a) Proportional control b) Integral control c) Proportional plus integral control. The final experiment make use of the analytical control system to show how the control theory can be used to calculate the behaviour of the control system. a) Proportional control: Using the computer program go into the controller setting menu. Set the controller to be a proportional only type i.e set the kp= 0.1, ki= 0, kd= 0. On the process trainer, adjust the throttle to 25o and place the sensor in the position away from the heater. Vary the proportional gain and plot the graph of the steady state error against the proportional gain. Choose the value of gain we think for the best response and obtain the screen dump to get a copy from the printer. Finally, indicate on graph the onset of instability. b) Integral control: Using the computer program go into the controller setting menu. Set the controller to be a integral only i.e set the kp= 0, ki=0.1, kd=0. On the process trainer leave the throttle at 25o and kep the sensor in the position away from the heater. Vary the integral gain and plot a graph of steady state error against the integral gain. Choose a value of gain that gives the best response of the system and obtain the screen dump. Finally, indicate on the graph the onset of instability. c) Proportional-plus-Integral control: Using the computer program go into the controller setting menu. Set the controller to be proportional-plus-integral type i.e set the kp=0.1, ki=0.1, kd=0. On the process trainer leave the throttle at 25o, and keep the sensor in the position away from the heater. Vary the proportional and integral gains until we get the best response from the system and obtain the screen dump. d) Open-loop step response: Using the computer program PRESS o this will put the system under the open loop control. The programme will then automatically carry out an open loop step response. Obtain a screen dump for the open loop step response. From the loop step response it is possible to calculate the transfer function of the process trainer. The tranfer function has the form: Where K is the open loop D.C gain of the system and Td is the pure time delay present in the system and Tp is the time constsnt for the system. It is possible to measure these values directly from the open loop step response. The steady state error for the control system can be derived as : Steady state error = V/(1+kp k) e) After obtaining the open loop step response values like K, Tp, Td, e and R from the graph. Place the values of K,Tp and Td in MATLAB simulink. To simulate the plant only in open loop in CODAS. Compare the time response with the actual plant open-loop response. f) Introduce the controller into the simulation and in frequency domain, adjust proportional gain to give the gain margin of 2 i.e., Nyquist plot (controller plus plant, open-loop) cuts the real axis at -0.5. observe the corresponding time response(controller plus plant, closed loop in time domain). g) Following the Nyquist method (f), introduce an integral control term and observe the time response. h) Keeping the proportional plus integral control established in (g), adjust the overall gain(k) to give gain margin of 4,2,1.333,1 and 0.8 (corrresponding to the Nyquist plot cutting the real axis at -0.25, -0.5, -0.75, -1.0 and -1.25 respectively). Comparing the corresponding time responses on the same graph. i) Now,changing the overall gain back to 1 and substituting the proportional and integral gains as calculated using the (i) ziegler-Nichols and (ii) cohen and coon formulas. And comparing the time responses for the three methods (Nyquist,Ziegler-Nicholos and cohen and coon) on the same graph. j) Moving back to the industrial trainer, and substituting the PI gains that where obtained using the Nyquist method and observe the closed loop response. And finding to get fine tune PI gain to improve the performance of the system. MATLAB CODE (CODAS Program): The diagram represents the open loop step response of the system is The code for the plotting of the open loop step response of the sytem is hold on xlabel(Time) ylabel(Input (red), Output (green)) title(System response to a step input) plot(t,x,r) plot(t,y,g) grid on The code for the plotting of the closed loop step response of the system is hold on axis([0.0 10.0 -10.0 2900.0]) xlabel(Time) ylabel(Desired Output (blue), Actual Outputs) title(System responses to a step input) plot(t,x,k) plot(t,y,b) grid on The code for the nyquist process trainer in the nyquist plot for the closed loop response of the system is % Plant : Gp(s)=K*exp(-Td*s)/(1+Tp*s) % K=1.266; % DC Gain Td=0.35; % Time Delay Tp=0.729; % Time Constant % num_p=K; den_p=[Tp 1]; disp(Plant Transfer Function : ) plant_tf=tf(num_p, den_p,InputDelay,Td) % % Compensator: Gc(s)=Km*(Kp+(Ki/s)+Kd*s) = Km*(Kd*s^2+Kp*s+Ki)/s % disp(Km :) %Km=1.0 Km=2.0/(2) %Km=1.0 % Multiplier Kp=2.1397; % Proportional Gain Ki=0.857; % Integral Gain Kd=0.0; % Derivative Gain % num_c=Km*[Kd Kp Ki]; den_c=[1 0]; disp(Compensator Transfer Function : ) comp_tf=tf(num_c,den_c) % OL_tf=comp_tf*plant_tf % %Gain and Phase Margins % [Gm,Pm,Wcg,Wcp]=margin(OL_tf); disp(Gain Margin: ); Gm disp(Phase Margin: ); Pm % % Nyquist plot of OL TF for 0.2