Design and Comparison of a Multi-Purpose PID Controller using Classical and Zeigler-Nichols Technique

Design and Comparison of a Multi-Purpose PID Controller using Classical and Zeigler-Nichols Technique

Seemab Gul1,

1Deptt. of Electrical Engineering, University of Engineering & Technology Peshawar, Pakistan

Muhammad Naeem Arbab2,

2Deptt. of Electrical Engineering, University of Engineering & Technology Peshawar, Pakistan

Uzma Nawaz3

3Deptt. of Electrical Engineering, University of Engineering & Technology Peshawar, Pakistan

Abstract-PID controller tuning is designed using Matlab (Simulink). The design also gives us optimization of PID controller without too much mathematic calculations. Ziegler-Nichols closed loop method is used for the design of tuning PID controller. Some disadvantages have been found in this technique, it is time consuming method because trial

1. PID CONTROLLER

   The letters P, I and D stands for P Proportional, I Integral and D- Derivative. Transfer function for PID controller is written as

   () = + + (1)

   and error procedure is involved. The traditional PID controller is replaced by Ziegler Nichols tuning PID

   () = 2++

   (2)

   controller so that is applied to wide range of processes and to obtain the minimum steady state error, also to improve the other dynamic behavior. The problem has been solved by using Matlab (Simulink) which has the ability to characterize both compensated and uncompensated relationship and we can learn this relationship from the data being modeled. These results can then be marked authorized by using Matlab (Simulink) and manual calculations. , , and used in

   Ziegler-Nichols formula can be calculated manually.

   Keywords: PID controller, Ziegler-Nichols, Matlab (Simulink), () Proportional gain, () integral time, () derivative time.

   I. INTRODUCTION

   PID controllers are commonly used in the process industries for the reason of simplicity and outstanding performance. More than 95% of closed loop process use PID controllers. Control systems are designed to achieve specific objectives. For control system design some characteristics are required. A good quality control system

   Where = Proportional gain, = Integral gain and =

   Derivative gain. All of these , and are tuning parameters.

   Figure 1: Block diagram of PID controller in cascade with the plant

   We assume that controller in the Figure 1 is a closed-loop unity feedback system. The variable () represents the error which is sent to PID controller. The signal () is equal to the proportional gain times error signal plus the integral gain times integral of the error signal plus the derivative gain times derivative of the error signal [3].

   has a lesser amount of error, excellent response, high

   () = () + () +

   ()

   (3)

   accuracy, damping that has no unnecessary overshoot and fine stability [1]. Several tuning methods have been

   0

   proposed up to now for getting more accurate and stable control response. Based on our requirement we want to characterize process dynamics by few features. Some tuning methods considered only one feature as a condition for their tuning algorithm. Some of these tuning methods considered more than one feature as a condition for their tuning algorithms [2]. In this study we will give an idea about new tuning rules in spirit of Ziegler and Nichols.

2. ZIEGLER-NICHOLS CLOSED LOOP METHOD Thismethod is a trial and error tuning based method on continuous oscillations was first proposed by John G. Ziegler and Nathaniel B. Nichols in 1942. This method is widely used for tuning PID controllers and is also recognized as continuous cycling method or ultimate gain tuning method. Ziegler and Nichols use ¼ decay ratio as a design criterion for this method.

   In the Ziegler-Nichols closed loop method First of all the system is stabilized into steady state now put on the PID controller into P controller by setting = and = 0 as shown in Figure 2. Increase until the system oscillates continuously. Use Table 1 to get the approximate values for the controller gains , and [4].

   Controller
   P	0.5		0
   PI	0.45	1.2	0
   PID	0.6	2	8

   Figure 2: Closed loop system with Proportional gain () Table 1: Controller parameter for closed loop Ziegler-Nichols method

   1. Lag-Lead compensator

      1()

      6162 + 1908 + 184.4

      = 5 + 27.214 + 207.6723 + 432.072 + 764.29 + 7.6

      The gain that gives us these continuous oscillations is ultimate gain , is the period of oscillation at as shown in the Figure 3 [5].

      Figure 3: Sustained oscillation with period ()

3. GENERALIZED MODEL FOR PID CONTROLLER Observe that PID controller tuned by Ziegler-

   Nichols closed loop method gives:

   Figure 5: Simulink model of Lag- lead compensator

   Figure 6: Lag- lead compensator response

   1. Ziegler-Nichols closed loop method

      By setting = and = 0 we obtain the closed loop transfer function as follows:

      Now from Eq. (1)

      () =

      () = +

      + (4)

      () ( + 10)(2 + 2 + 5) +

      Where

      =

      and

      =

      Characteristic equation for the closed loop system is;

      () = (1 + 1

      + ) (5)

      3 + 122 + 25 + (50 + ) = 0

      Where is proportional gain, is integral time and is referred as derivative time [6].

      Using Rouths stability criterion we find that continuous

      For PID-controller

      () = ..2+.+

      (6)

      oscillation will occur at the ultimate gain .

4. SIMULATIONS AND RESULTS

   = 250

   Consider the control system as shown in Figure 4 in which PID controller is used to control the system the PID controller has the transfer function.

   () = 1

   ( + 10)(2 + 2 + 5)

   = 2 = 2= 1.25

   5

   Figure 4: PID controlled system

   Figure 7: Simulink diagram for Sustained Oscillations

   Figure 8: Sustained oscillation for = 250

   From Table 1 we determine , and as follows:

   = 0.6= 0.6* 250 = 150

   = 0.5= 0.5*1.25= 0.625

   = 0.125 = 0.125*1.25= 0.15625

   Using eq. (5) we get

   = 150

   = 240

   = 23.43

   Figure 9: Simulink model of Ziegler-Nichols closed loop method

   Figure 10: Ziegler-Nichols closed loop method response

   1. Lag lead compensator and Ziegler Nichols closed loop method

   Figure 11: Simulink model of Lag-lead compensator and Ziegler-Nichols closed loop method

   Figure 12: Lag-lead compensator and Ziegler-Nichols closed loop method responses

5. CONCLUSIONS

In this research, comparison between classical lag- lead compensator and Ziegler-Nichols technique is applied to an under damped system. The analysis is done based on mathematical calculations and then system response is obtained from the SIMULINK. The result of simulation shows that both methods improve system performance to a desired value. System response is mainly depends on both transient response an steady state response. In classical lag-lead compensator, both transients and error is improved to a significant value. While in Ziegler-Nichols technique, steady state error is effectively improved while there is no change in transient response. Ziegler-Nichols tuning is applicable to specific applications while it is not considered as optimal. This tuning gives maximum reduction in disturbance parameter in PID loop. But the gain and overshoot is high in this technique which is acceptable in some applications. So it is concluded that both methods are applicable to tune system response as per desired values.

REFERENCES

1. U.A. Bakhi, V.U. Bakshi, Compensation of control systems, Control system Engineering, 1st ed. Mumbai, India: Technical publication Pune, 2010, ch. 14, pp.14-1 to 14-2.

2. M. Shahrokhi and A. Zomorrodi, "Comparison of PID controller tuning methods," Department of chemical & Petroleum Engineering sharif University of Technology, pp. 1-12, Apr 2013.

3. H. Ahmad and A. Rajoriya, Performance Assessment of Tuning Methods for PID Controller Parameter used for Position Control of DC Motor, International Journal of u- and e-Service, Science and Technology, pp. 139-150, 2014.

4. C.A. Smith, Feedback controllers, Automated contineous process control, New York, Wiley publishers, 2002, ch. 3, pp. 38-54.

5. http://www.cpdee.ufmg.br/~palhares/PID_Ogata.pdf

6. R. Bansal, A. Patra, and V. Bhuria, "Design of PID Controller for Plant Control and Comparison with ZN PID Controller." International Journal of Emerging Technology and Advanced Engineering, pp. 312-314, 2012.