Soft Computing Based Tuning of PI Controller With Cuckoo Search Optimization For Level Control of Hopper Tank System

: The paper work focuses on soft computing and Conventional tuning approach to design of PI controller, which provides a better sustainable performance for a nonlinear hopper tank system which is used in Wastewater treatment applications. The system processes the combination of a conical and cylindrical tank for providing Multi-region based mathematical modelling to obtain the first order with delay time (FOPDT) process transfer function model. The Ziegler Nichols, Cohen-coon, Tyreus Luben, CHR (Chien, Hrones, and Reswick), IMC (Internal Model Control), Direct Synthesis, FOPI( Fractional Order PI) Conventional tuning formulae and Cuckoo Search Optimization (CSO) algorithm are used to optimize the servo regulatory responses of PI controller. The integral and proportional gain of the PI controller is said to produce the fastest settling time and reduces the error using performance indices and achieves Liquid Level control in hopper tank. Comparison is made for the various conventional controller tuning methods with Cuckoo Search Optimization tuning responses and identified to CSO-PI method offers enhanced Optimized Performance while comparing to Conventional tuning methods for a region based system.


Introduction:
In recent days the industrial process mainly uses Proportional Integral Derivate controllers to control process parameters. The major role of these parameters is to maintain the effectiveness and Environmental disturbance that occurs during the operation. The controller gain of the three main constraints like gain of proportional, gain of Integral & gain of derivative controller is usually a constant value based on the tuning parameters. It may have uncertainty while dealing with the plant operation, but it can reduce by tuning the gain values. The control of water level, pressure, flow and temperature is essential to maintain using these parameters. The error due can be reduced using the performance indicators like Integral of Square Error (ISE), Integral of Absolute Error (IAE), Integral -Time Absolute Error (ITAE). All these practices are being implemented in the Hopper tank system which provides the advantages of easy flow of materials and having large storage capacity.
The research framework carried out by different researchers with nonlinear processes and their controller techniques were discussed. Dhanalakshmi, R et. al [1] worked on real time implementation of various control techniques using matlab toolboxes for analysis of its parameters. Vadivazhagi, S et.al [2] introduced the stable operating region of the first order system using the process reaction method. Kala, H et.al [3] developed the transfer function for region based operating systems to make the comparison between the Direct Synthesis-PI control & Model Predictive-PI control (MPC). Anand, S et.al [4] done their research work in identifying the FOPTD model for a conical tank system and verified their performance of adaptive PI controller by implementing using MATLAB software. Saravanakumar, G et.al [5] proposed an internal model based optimum controller to obtain a good servo regulatory response. Sarif, B. Mabu et.al [6] have done their work on various PID controllers to obtain suitable performances indices and time integral criteria for the superheated steam temperature system. Marshiana, D et.al [7] developed the Fractional Order Proportional Integral Controller using the down order calculus method for a conical tank system. The nonlinear system designed performed by digital algorithm [13] based dead beat controller provides better performance when compared with the analogy type PID algorithm. It is stated that many of the chemical industries [14] uses conical or hopper tank system for easy flow of materials without any loss. Venkatesan, M et.al [8] offered a relative study on the characteristics and performances of Sliding Mode controller using Sliding Mode Luenberger observer.
Ravi, V. R et.al [9] proposed a multivariable process based PID controller design for an interacting two first order conical tank system to determine its effectiveness on its operating ranges. The above model was compared with of Gain Scheduling Adaptive Controller over GA tuned multiregional PI controller was featured [10]. Optimization of the Genetic algorithm [11] based linear model predictive algorithm approach used for a conical interacting system with 2 tank model was validated all the way through simulated result. The decentralized PI-Controller combined with the decouplers used for the stability analysis with TCTILS to minimize the interactivity property of the conical process tank. Anandanatarajan, R et.al [15] analyzed that the variations in the system parameters will affect the controller performance which can be controlled using the tuning parameters and the gain scheduling method is best suited for this technique. Kesavan et.al [16] worked on the real-time execution of a PID controller with conical region of hopper tank and optimized the performance with the error criteria for various tuning methods. Murugananthan, V et.al [17] highlighted the performance of modified IMC with other techniques using error criterion and time domain analysis for a nonlinear hopper tank system. Gireesh, N et.al [18] discussed the tuning parameters of conventional PID controllers using different methods for a conical nonlinear system. The uncertainty of the process can be rectified by using these methods.

Durga
Vivek et.al [19] states that the optimum PID process variable is achieved by cuckoo search algorithm for the second order with delay time process. Saeed Balochian et.al [20] states that the best suitable optimization technique is the cuckoo search method for identifying the optimal value in control of a water tank system. The merits of Sugeno type FLC with respect to the CSO method can obtain a rapid convergence were implemented. Meenakshi Kishnani et.al [21] implement the cuckoo algorithm for optimize the PID control parameter through levy flights and to reduce error the through its fitness function for a linear plant. Petchinathan Govidan [22] states that the performance identification for an automatic voltage regulatory system is done by optimization of PID parameters using PSO and CSO algorithms. Abdelaziz et al [23] found that the cuckoo search algorithm offers better performances related to the performance indices and settling times. The PI value obtained from CSO for Load frequency control provides better results when compared with the Conventional control method and Genetic algorithm. Marshiana et.al [24] develops PI parameters for a nonlinear system using the cuckoo search evolutionary algorithm. The advantage of this technique is because of its simplicity and cable to provide best results.

Experimental Schematic Setup and Modelling of Hopper Process Tank:
A Mathematical model was developed for a hopper tank system which is said to be Non-Linear. The construction of hopper process is the arrangement of both the bottom conical-section & top cylindrical-section. The top cylindrical region is being used for storage purpose by varying its height and bottom conical region is being used for discarding or removal of materials like liquids, solids and slurries. The mathematical illustration of the hopper process tank was done by means of the subsequent assumptions.
 Controlling variable is the liquid level of hopper tank  Inlet flow to hopper tank is considered as manipulate variable The transfer function model for the hopper tank is converted into a first categorize with dead time system by considering conditions of gain of process Kg, time constant τ and delay time of the process is td. Figure 1 demonstrates the plan view of the production of Hopper tank setup.  Based on the single system identification, various regions are identified and its corresponding transfer function was developed and shown in Table 2.

PI Controller Design with Conventional Tuning Techniques:
The proportional Integral controller plays a major task in the control of the level process. Different types of tuning techniques are available for the level process hopper tank system. The P and I controller depends on the variation in gain of proportional (Kp) and the gain of integral (Ki) parameters. The mathematical expression of PI controller is specified as follows. (6) The Ziegler Nichols, Cohen-coon, Tyreus Luben, CHR (Chien, Hrones, and Reswick), IMC (Internal Model Control), Direct Synthesis, and FOPI( Fractional Order PI) are the tuning methods implemented for the hopper tank system. In General the proportional controller produces offset error and it can be reduced by integral controller. The overshoot produced will be an acceptable range. The tuning methods are comparing among the simulation responses attained from the Matlab Simulink. The formulae used for calculating the gain parameters are exposed in Table 3.

PI Controller Tuning with Cuckoo Search Optimization Technique:
A cuckoo Search based Optimization finding is a new metaheuristic technique and has been presented by Yang and Deb in 2009 [19]. CSO algorithm is executed dependent on powerful offspring freeloading activities of cuckoo variety in blend through Levy Flight performance of certain cuckoo birds [22]. These sorts of cuckoos used to lay their own eggs in other host bird nests via raising the shot at hatching through picking recently brought forth settles and disposing of setting up eggs. The host birds will deal among those eggs by means of accepting those eggs are their own. In some cases, few of the host birds may notice that the eggs are not their own & afterward either it can through those eggs out or build the new nest in new place [19]. In view of this cuckoo hatching address, an Optimized solution is gained for the issue. The underlying populace taken is the number of cuckoos and their eggs. Cuckoo method of optimization will be carried out with following 3 supreme rules [22].
Rule 1: The cuckoo will lay its egg in a nest randomly and it will lay just each egg in turn. Rule 2: The egg with superior grade in the best nests will be taken to subsequent generations.

Rule 3:
The host bird will found the cuckoo's egg by the way of Probability Pa ∈ [0, 1] & Number of accessible nests for host is fixed.
Flow chart representation of CSO algorithm steps are explained in figure 2 with the help of these 3 idealized rules. While producing a new position xi(t+1), Levy flight random walk stochastic condition [24] is performed by xi(t+1)=xi(t)+S*Et. Here Step size S > 0 and generally S = 1. Much of the time, a random walk is being a Markov chain whose new position just relies upon the current position xi(t) and Et is normal standard levy distribution. CSO algorithm is the population -based algorithm and it is like PSO and the number of tuned parameters is not accurately like PSO and it is most probably more normal to adapt to a more extensive type of optimization issues [22].  [23] In this research work, the cuckoo search Optimization has been carried out for improving the performance of the PI controller [22]. The PI data sets considered for CS optimization are as per the following: Number of nests (Population) np = 10, Alien eggs Detection rate (pa) = 0.25, Total number of Iterations = 200, No of parameters to be enhanced n=2 (kp, ki). In this work, an ISE objective function is considered for the ideal tuning of the PI controller. In CSO-based PI controller tuning, the controller constants (kp,ki) are acclimated to limit the worth of ISE target function and to further develop the time response investigation by lessening peak overshoot and settling time [22,19].

Result and Performance Evaluation:
The Sustainable Level control Responses of hopper tank were obtained by simulating the closed loop control system using MATLAB Simulink software. The time Integral performances are to optimize the demonstration of hopper tank framework by decreasing the error & acquiring the finest value. Various error performances are given beneath.
 Integration on squared error ISE = ∫ E 2 (t)dt  Integration on absolute error IAE = ∫ |E(t)|dt  Integration on time & absolute error ITAE = ∫ t|E(t)|dt The system performance is obtained for different regions. Region 1 is said to be the lower region of the conical tank where the area of cross section varies as the height increases. The nominal height is said to be 15cm & Conventional tuning and Cuckoo search Optimization (CSO-PI) based tuning gain values are exposed in Table 4. The resulting output of Region 1 (Individual region based Level control with Conventional tuning) is exposed in figure 3. The servo level change of 2cm and the load changes are applied to the controller output for various controller techniques. For Region1 the performance indices taken by considering Time Domain analysis and time integral criteria were calculated as exposed in table 5, to determine the best suited controller for region based hopper tank design. It states that the CHR method provides the fastest settling time.  figure 4. The servo level change of 5cm and the load changes are applied to the controller output for various controller techniques. For Region 2 the performance indices taken by considering Time domain investigation & time integral error criteria were calculated as exposed in table 7, to determine the best-suited controller for region based hopper tank design. It states that the Cuckoo method provides the fastest settling time and reduced error values. Region 3 is said to be the middle region of the conical portion where the area of cross section varies as the height increases. The nominal height is said to be 45cm and gain values are exposed with Table 8.  figure 5. The servo level change of 5cm and the load changes are applied to the controller output for various controller techniques. For Region3 the estimation indices taken by in view of time domain study & time integral criteria were calculated as exposed in table 9, to determine the best suited controller for region based hopper tank design. It states that the CSO-PI method provides the fastest settling time.  figure 6. The servo level change of 10cm and the load changes are applied to the controller output for various controller techniques. Figure 6. Controlled Process output with servo regulatory responses for Setpoint=60cm For Region4 the performance indices taken by considering Time Domain analysis and time integral criteria were calculated as exposed in table 11, to determine the best suited controller for region based hopper tank design. It states that the CSO-PI method provides the fastest settling time. 33.4 Region 5 is said to be the upper region of the hopper tank were the area of cross section remains as the height increases. The nominal height is said to be 100cm &gain values (Conventional and Soft computing based) are exposed in Table:12 Table:12 Tuning controller values of Region 5 REGION 5-(60 to 100 cm); ( ) = .
( . + ) − .  figure 7. The servo level change of 20 cm and the load changes are applied to the controller output for various controller techniques. For Region 5 the performance indices taken by considering Time Domain analysis and time integral criteria were calculated as exposed in table 13, to determine the best suited controller for region based hopper tank design. It states that the CSO-PI method provides the fastest settling time with minimum error when comparing with conventional tuning methods respectively, while selecting the Setpoint as 100cm. These overshoots produce an overflow of liquid when the maximum height of the tank is 120cm. These overshoots would be reduced from 28.8 to 13.38 and 35.6 to 14.08 with the help of Combined Region-based level control which combines the model from region 1 to region 5 to control level in the region5. Combined Regionbased Level Control with servo and regulatory responses for Operating Region 5(Setpoint=100cm) is represented in figure 8.  The Different Individual region-based level control responses using Cuckoo Search Optimization (CSO) tuning techniques was publicized in Figure 9. The fastest settling time after applying servo changes & regulator changes could be evaluated using CSO technique.