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PID CONTROL OF AIRFLOW HEATING PROCESS

ABSTRACT PID which stands for Proportional-Integral-Derivative control is a three-term control parameter widely used in control systems because of its ability to give designers more possibilities of changing the dynamics of a system. Summarise the aims and objective and the discussion and conclusion. The aim and objective of this experiment is to investigate proportional control (P), integral control (I) and derivative control (D) of the process when heated air flows through a polypropylene tube. Other objectives include deriving an open loop transfer function and implementing a model-based tuning on a PI controller. After analysing the experiment, it is found out that, a proportional controller reduces a steady state error but never eliminates it, an integral controller gives zero steady state error whilst the derivative control term produces faster response and stability. When compared with the theory, the behaviours of the graphs are very similar but not the same due to unideal conditions and reading errors. It was concluded that every PID parameters is unique in its own way and they can all be used based on the requirement at hand.

Contents ABSTRACT..................................................................................................................................0 `1. INTRODUCTION.............................................................................................................3 1.1 Background Information......................................................................................................3 1.2 PID Controller......................................................................................................................4 1.3 History of PID Controllers...................................................................................................4 1.4 Uses and Advantages of PID Controllers.............................................................................4 2. PID THEORY..........................................................................................................................6 2.1 Proportional Control.............................................................................................................6 Effects of change in Kp...........................................................................................................6 2.2 Integral Control....................................................................................................................7 Effects of change in Ki............................................................................................................7 2.3 Derivative Control................................................................................................................8 Effects of change in Kd...........................................................................................................8 2.4 Overshoot, Settling time and Rise time...............................................................................9 2.5 Process reaction curve..........................................................................................................9 3. Aims and Objectives..............................................................................................................10 Objectives.............................................................................................................................10 4. DESCRIPTION OF APPARATUS.......................................................................................11 1|Page

4.0 THE EQUIPMENTS..........................................................................................................11 4.1 Process Trainer 37-100...................................................................................................11 4.2 How the Process Trainer 37-100 works:.........................................................................11 4.3 The Process Trainer Control Computer..........................................................................12 4.2 The Process Trainer Simulation Computer....................................................................13 5. EXPERIMENTAL METHODOLOGY...............................................................................14 6. RESULTS................................................................................................................................15 6.1 Tf of an Open Loop Step Response Plots-Obj. 1................................................................15 Calculated result...................................................................................................................15 6.2 Closed Loop Step Response Plots-Obj. 2..........................................................................16 6.2a Proportional control......................................................................................................16 6.2b Proportional plus Integral control.................................................................................17 6.2c Proportion plus Derivative control...............................................................................18 6.3 Closed Loop Step Response Simulation Plots-Obj. 3........................................................19 6.3a Varying Values for Ki for Optimal Values for Settling Time, Ts and Maximum Overshoot, MP......................................................................................................................20 6.3b Closed Loop Step Response Simulation Plots- optimal values....................................20 Ki =1.173 Ts =3.86 and Mp=20.1........................................................................................20 6.4 The Optimal Value on the Process Controller-Obj.4..........................................................21 The Tuned Value on The Process Controller........................................................................21 7. DISCUSSION.........................................................................................................................22 7.1 Effect and Analysis of Proportion factor, Kp......................................................................22 Steady state and Stability......................................................................................................22 Speed and Stability...............................................................................................................22 7.2 Effect and Analysis of Integral control, Ki........................................................................22 7.3 Effect and Analysis of Derivative control, Kd....................................................................22 7.4 Effect of Tuning the Pid control for optimal Ts and Mp....................................................23 7.5 Effect of transposing simulation results on the trainer control computer..........................23 7.6 Other Error analysis...........................................................................................................23 8. CONCLUSION......................................................................................................................24 9. REFERENCE LIST..............................................................................................................25

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`1. INTRODUCTION 1.1 Background Information The purpose of feedback control is to create a desired output for a system. This can be done with An Open Loop System, where the input signal to a process is determined based on a reference signal only or with A Closed Loop System where the input signal is determined by measuring the output i.e. feedback signal(Parr, 1996). In the case of a closed loop system the feedback is often the difference between the desired output and the actual values of the output.

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Fig1 Block diagram of an open and closed loop system (Herdingcats.typepad.com, 2017)

1.2 PID Controller A Proportional–Integral–Derivative, PID, controller is a closed loop system found in 95% of industrial automations (Electronic Projects for Engineering Students, 2017). In this closed system, the control signal produced depends on present error-Proportional control; the accumulated error in the past-Integral control and the predicted future error -Derivative control (Rome, 2017). A control loop can be tuned to adjust its control parameters to achieve optimum closed loop system response.

Fig2 Block diagram of a PID controller (Rome, 2017)]

1.3 History of PID Controllers In 1911, Elmer Sperry an American inventor was the first to develop a PID type controller. He was driven by his quest to create an automated steering system for the US navy. Others like Nicolas Minorsky (in 1922) - who was the first to published a theoretical analysiswent ahead to develop PID controller even further. The PID began to make its mark in the automatic control field in the beginning of the last century (Bennett, 2000). It has since become the industrial preference mainly because of its simplicity and intuitiveness, in addition to satisfactory performance which it is able to provide with a wide range of processes. 4|Page

1.4 Uses and Advantages of PID Controllers The use of PID controllers in control process industries has become very wide as the years go by. They are mostly used for automatic processes and help to control pressure, temperature, flow level and a lot of other industrial process variables. As stated by W Bolton (Bolton, 1998), some of the advantages that makes it widely used are listed below; • • • •

In most instances, only minimal knowledge of the controlled process is required It produces good performance and stability for a lot of real processes It uses a reduced amount of control parameters PID controllers are versatile and robust

As with everything in engineering and life, PID controllers also have their disadvantages. Some of them are; • PID controller isn’t able to give predictive control action in compensation for the effects of measured disturbances. •

Tuning the PID control based on trial and error means that they is room for human error.

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2. PID THEORY Proportional–Integral–Derivative controller, as the name implies, requires to combination of one or more of its three terms to produce a response. These three terms and their effects are discussed below.

2.1 Proportional Control The proportional control action is dependent on the difference between the set point v and the output y (t). This difference is known as the control error or error term, e. The control action is proportional to the control term, as expressed in the equation; u(t) = Kpe(t) = Kp(v(t) − y(t)) …where Kp is the proportional gain The transfer function can be derived trivially as below; C(s) = Kp.

Effects of change in Kp A change in proportional gain is bound to have an effect on the response of the system. As seen in the diagram below, this is what happens when Kp is increased;    

Stability is reduced Changes occur in steady state responses Steady –state error is reduced as well Changes also occur in transient response (Bamidele, 2017)

Fig 3 A graph showing the effect of change in Kp (Rome, 2017)

It is worthy of mention that commercial product often have their proportional gain replaced by the proportional band PB. This is the range of error that causes a full range change of the control variable, 6|Page

i.e., PB = 100 /Kp (Kiong et al., 1999)

2.2 Integral Control In this case, the integral controller is proportional to the integral of the control error. This means that even a small error term will cause the integral factor to increase slowly. u(t) = Ki t ∫�� �(�) dt,…. …where Ki is the integral gain

The corresponding transfer function is; C(s) = Ki /s The integral action appears to be related to the past values of control error and in most cases Ki is used with Kp.

Effects of change in Ki The addition of integral gain to proportional gain as a major effect of ensuring there is no change in steady state error. This is why it is also called automatic reset. Other effect includes;    

Reduction in stability; that is increased oscillations and maximum overshoot A minimal increase in settling time As mention, no change in steady state error. The combination of Ki and Kp produce a transfer function of C(s) = Kp (1 + 1 /Tis ) (Ogata, 2010)

Fig 4 A graph showing the effect of change in Ki (Bamidele, 2017) 7|Page

2.3 Derivative Control It has been established that the proportional action is based on the current values of the control error and the integral action is based on the past value of the control error. However, the derivative value is based on the predicted future values of the control error. It is proportional to the first derivative (the slope) of the error with respect to time (Bamidele, 2017). u(t) = Kd

��

(�)

where Kd is the derivative gain

��

The corresponding transfer function is; C(s) = Kd s

Effects of change in Kd The derivative control is never used on its on, therefore its effects with a constant proportional factor are as follows;  Reduction in rise and settling time  Increased stability thus reduced oscillations and maximum overshoot  No change in steady-state error

Fig 5 A graph showing the effect of change in Kd (Bamidele, 2017)

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2.4 Overshoot, Settling time and Rise time. Overshoot

Settling time

Rise time

Fig 6 A graph showing overshoot, rise and settling time(Wei,2017) • • •

Overshoot- the percentage of the final values exceeded at first oscillation. Rise time- the time span from 10-90% of the final value. Settling time- the time to reach within 2% of the final value

2.5 Process reaction curve The diagram below shows an open loop response of a process;

Fig 7 An open loop step response (Bamidele, 2017)

where K is steady state gain 9|Page

Tps is the system time constant Td is the system time delay ��−���

And the Transfer function is,

g(s) = � + ���

The figure below shows an analysis of the process reaction curve.

Fig 8 An open loop step response analysis (Bamidele, 2017)

The measurements shown above where used to work out DC gain K, Time constant �� and Time delay � with the aid of a ruler.

3. Aims and Objectives The aim of this experiment is to assess the performance and response of the PID control of an airflow heating process. After this aim was met, various task had to be done and there are enumerated below.

Objectives The objectives of this experiment are listed as follows; 1. Estimate the open process transfer function, Tf (from the process trainer). 2. Investigate the effects of proportional control (P), integral control (I) and derivative control (D) actions on closed loop step response. 3. Carry out model-based tuning of a PI controller in MATLAB. 4. Implement the tuned PI controller for the closed loop process (On the process trainer)

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4. DESCRIPTION OF APPARATUS 4.0 THE EQUIPMENTS 4.1 Process Trainer 37-100 This is a self-sufficient process and control equipment that is capable of performing the basic functions of an industrial process and control trainer. A basic process and control trainer, like the 37-100, is able to demonstrate the distance/velocity lag, transfer lag, proportional control, closed and open-loop continuous control as well as two-step control (Feedback-instruments.com, 2017).

4.2 How the Process Trainer 37-100 works: The process trainer consist of the following to execute it functions; • • • •

•

A thyristor controls a heating element that feeds heat into an airstream circulated by an axial fan along a polypropylene tube. The air tube, with an effective length of 298mm, as a thermistor placed at one of three point along its length. The thermistor measures the temperature at its position and thus determines a value for transportation lag. A potentiometer is used to change the speed of the axial fan which in turn determines the volume of air flow in the pipe. Adjusting the setting causes a supply side disturbance which is demonstrated easily. For the purpose of comparison with a separate control signal, the detector output is amplified. This provides both an indication of the measured temperature and a feedback signal. The comparison of these signals generates a deviation signal which is applied to the heater control circuit to maintain the desired value.

Fig 9 University of Safford Control lab- Process Trainer 37-100

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For this experiment the process trainer is used with two processing computers. The first one is the process trainer control computer while the other is the process trainer stimulation computer.

4.3 The Process Trainer Control Computer The process trainer control computer has a digital PID controller used to control the process. It consists of a white system unit and a white operator interface; monitor and keyboard. On the operator keyboard; • • •

Keys ‘O’ and ‘C’ are used to change to open-loop or closed loop operation of the process trainer. Key ‘K’ is used to change the PID control gains. Key ‘P’ is used to print the process time responses displayed on the monitor.

Fig 9.1 University of Safford Control lab- The process trainer control computer

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4.2 The Process Trainer Simulation Computer The process trainer simulation computer carries out the task of simulating the process of control system using MALAB. It is made up of a black system unit, a monitor and keyboard.

Fig 9.2 University of Safford Control lab- The process trainer simulation computer

5. EXPERIMENTAL METHODOLOGY The experimental methodology is based off the objectives enumerates in section 3. The individual steps taken to complete this experiment are listed below; 1. MATLAB was opened on the process trainer simulation computer. In other to use the required code format, the steps below were followed; 13 | P a g e

the browse folder button was clicked to create a current folder library; documents; my documents; Matlab were navigated sequentially • learning materials for Control Engineering was opened from blackboard • from the folder named control lab, an attachment named L5_PT_Matlab_Sim.m was open from a Matlab file. • the above attachment was saved into the folder Various data for the closed-loop responses were taken from the process trainer by varying the values of the proportional, integral and differential control as shown below; • Proportional control(Ki=Kd=0) with Kp=0.5, 1, 2 • Proportional plus integral control (Kp= 1.0, Kd = 0) with Ki =0.25, 0.5, 1.0 • Proportional plus derivative control (Kp= 0.5, Ki= 0) With Kd= 0.1,0.2,0.5 Afterwards the open loop step response of the process was obtained. The values for K, Tp and Td are obtained from this plot using specific measurements and equations as describe in Fig 8 in the theory. The simulation programme L5_PT_Matlab_Sim.m was opened and lines 14-16 were edited to assign the values of the process parameters obtained in open loop response. By editing lines 22-24 a step response simulation programme was carried out by assigning the values for the controller gains Kp, Ki and Kd. The PI controller was tuned using the following steps; • Ki and Kd were set to zero • the value for Kp was increased until the output was at a sustained oscillation (Kp= Kp, cr) • the value of Kp was then reduced to 0.5 Kp for a ‘quarter amplitude decay’ type response • the values for Mp, tss and yss (maximum overshoot, settling time and final output, respectively) were annotated on the closed loop response plot produced. • finally, the above plot was copied and pasted in MS word. In order to obtain a satisfactory maximum o...