Frequency Regulation of Interconnected Power System Using Black Widow Optimization

A frequency regulation of interconnected power system comprising thermal reheat system and photovoltaic panel systems is disclosed in this research article with Proportional Integral Derivative (PID) controller optimized using Black Widow Optimization Algorithm (BWOA) based on distinct feature of cannibalism of black widow spiders. With rising demand for perfectly optimized power systems, a best optimal solution for controller gains besides merit of faster convergence and avoidance of trapping in local minimal are becoming key requirements for system engineers. In tune with these requirements, we have developed an optimized solution based on BWOA in the power system realm to minimize the fitness function which is Integral Time Absolute Error composing of frequency and tie-line power variations. Superiority of BWOA optimized controller in power system realm is established by comparing and analyzing its simulation results with some other known tuned controllers which uses different optimization algorithms namely firefly algorithm, genetic algorithm, whale optimization algorithm and modified whale optimization algorithm. Results in this paper lays out that BWOA optimized PID controller outperforms other reported controllers in terms of fitness function value, settling time, undershoot/overshoot of the incremental variations in frequency and tie-line power of the interconnected power system. Further, the potency and robustness of the proposed tuned controller are also proven by considering large variation in load demand, real-time constraints namely generation rate constraint and governor dead band in the system. Additionally, the sensitivity analysis of the optimized controlled system is performed to conclude that the proposed BWOA optimized PID controller optimized controller is insensitive to changes in system parameters and eliminates the necessity of resetting of controller parameters. The performance of the proposed control technique is also tested on two-area non-reheat thermal power system with non-linear constraints namely time delay, generation rate constraint and governor deadband.


I. INTRODUCTION
Load frequency control (LFC) is well known in the art to ensure that electric power is delivered at a consistent frequency and keeps tie-line power within defined limits and is one of the most important auxiliary services in electrical power system operations [1]. Because of growing environmental concerns about conventional power sources, the integration of renewable energy sources (RESs) into the electric power grid has become increasingly crucial in recent years. The solar and wind energy are the two main renewable energy sources that are being integrated for electric power generation to mitigate the concerns with conventional energy sources [2]. In view of the advantages such as low maintenance cost and suitability for distributed power generation and off-grid system, solar photovoltaic (PV) system is one of the propitious renewable energy sources for electric power generation. However, a major concern posed by the solar PV system is the intermittency of input solar power and requirement of large battery energy storage system, due to which stand-alone systems composing of only PV grid are not reliable for providing continuous and reliable delivery of power. A hybrid system is one of the solutions for providing reliable power supply including renewable energy sources. It is to apprise that the hybrid system may also suffer from frequency regulation problem due to intermittent nature of solar power in view of partial shadow areas and sudden variation in load demand which essentially in turn transpires to the need of incorporation of controllers to keep frequency and tie-line power variations within defined limits.
It is critical to design a load frequency control system correctly to reduce frequency and tie-line power oscillations [3]. A detailed literature survey of various control strategies implemented by power system engineers for managing frequency regulation in traditional and deregulated power system with or without inclusion of renewable energy sources is presented in [4]- [7]. The authors in [1], [4], [5] compare different control strategies for LFC of systems integrated with wind turbines, PV systems, battery energy storage (BES) etc. and discussed in details the merits and demerits of controllers based on classical, optimal, soft computing, centralized and decentralized control. The findings of using single reheat turbine instead of two reheat turbines and appropriate values of non-linearities of hydrothermal system are presented in [6]. In addition to review of controllers, the future scope of LFC presented in [7] unveils to explore the integration of RESs and their impact on frequency regulation problem. These studies reveal the importance and scope of advance control techniques for regulating load frequency in a power system with increasing integration of RESs. In this regard, many researchers over the recent past have worked on various types of controllers such as proportional, integral, derivative, proportional integral, proportional integral derivative [8], fuzzy logic, artificial neural network [9], optimal, sub-optimal [10] etc. for regulating frequency in power systems. Bhatt et al. in [11], [12] presented the integral controller based LFC of RES integrated power system. The performance of integral (I), proportional integral (PI) and proportional integral derivative (PID) controller is analyzed in [13] for LFC of three-area thermal system integrated with solar thermal power plant (STPP). Davtalab et al. in [14] illustrated the performance of modern control i.e. fuzzy control technique for solar PV integrated thermal power system. The modern control techniques are well suited for non-linear, integrated and complex power system problems. However, these techniques pose the limitations of increased complexity of controller logic and large processing time for large size power systems [15]. On the contrary, the classical control techniques are easy to implement and have simple control logic for large dimension power systems. The concern with the classical control techniques is the requirement of considerable efforts in tuning the controller gain parameters. To overcome this limitation of classical controllers, many researchers have used physicsbased algorithms such as simulated annealing (SA) [16], big bang big crunch (BBBC) [17], Gravitational Search Algorithm (GSA) [18] etc.; swarm based algorithms such as artificial bee colony (ABC) algorithm [19], ant colony optimization (ACO), cuckoo search (CS) [20], craziness based particle swarm optimization (CRPSO) [10], [12] etc. and evolutionary algorithms such as genetic algorithm (GA) [21], evolutionary strategies (ES), differential evolution (DE) [22], firefly algorithm (FA) [14], [23], flower pollination algorithm (FPA) [24], whale optimization algorithm (WOA) [27], water cycle algorithm (WCA) [33], grasshopper optimization algorithm (GOA) [36] etc. to solve the frequency regulation problem. The critical review of different controllers and optimization techniques presented in [37] clearly shows that there is abundant scope to solve frequency regulation using more nature inspired and hybridized algorithms. The meta-heuristic algorithms reported in literature suffer from some limitations such as susceptibility to trap in local minima, slow convergence and large processing time for large dimensional problem [13] besides the advantages of giving better optimal solution and possessing attributes of good exploration and exploitation as these algorithms are based on the distinct characteristics of a living being [25]. With the noticeable points of the meta-heuristic techniques, the importance of design of advanced evolutionary algorithm based optimized controller design is evident to handle the imbalance amid generation and load demand to overcome the limitations of being trapped in local optima, sluggish convergence rate and more memory usage. To overcome the limitations of reported algorithms and design optimally tuned controllers, researchers are working continuously to propose new algorithms and obtain the best optimal solutions. In line with this, Hayyolalam et al. has recently introduced Black Widow Optimization Algorithm (BWOA) in [25] based on distinctive mating behavior of black widow spiders. The BWOA branches out from the unique mating behavior of the black widow spiders which hold an exclusive stage of cannibalism. The exclusive stage of cannibalism aids in regulating the individual population size and renders the cannibalistic Black Widow Spider (BWS) in achieving the most optimal conditions for their survival. The advantages and competence of the algorithm in terms of not being trapped in local minima, faster convergence and more optimal results for standard functions and real-world engineering problems motivate the authors of the present work to utilize this optimization technique for addressing the LFC problem.
The following are the important contributions of this research article, which are highlighted in light of the importance of proposed evolutionary based method for optimally fine-tuning the controller gain values to minimize the frequency and tie-line power deviations of two-area power systems: • Key goal of this research is to present a simple, and superior load frequency regulation controller in comparison to existing controllers.
• A BWOA optimized controller is proposed to regulate incremental variation in frequency and tie-line power of interconnected system composing of thermal reheat turbine and PV panel system.
• The controller's robustness is demonstrated by analyzing the performance of the optimized controller as load demand varies and in the presence of non-linearities namely time delay, generation rate constraint (GRC) and governor deadband in the system.
• Sensitivity analysis demonstrates that the suggested controller is unaffected by variations in system parameters.
• A comparison of the proposed BWOA tuned PI and PID controllers with GA tuned PI, FA tuned PI, WOA tuned PI, and MWOA tuned PID controller described in the current literature establishes the superiority of the suggested BWOA tuned PID controller in LFC.
• Performance analysis of proposed BWOA tuned PID controller on two area thermal non-reheat system with non-linear constraints and comparison with FA tuned PID and hybrid firefly algorithm and Pattern Search (hFA-PS) tuned PID controller reported in literature The structure of the article is organized as: The mathematical model of the two-region power system is described in Section 2. The implemented fitness function for improving the controller gains is shown in Section 3. Section 4 describes the BWOA suggested algorithm for developing LFC controllers. Section 5 contains the simulations findings, observations and analysis. Section 6 summed up the conclusions of the work.

II. SYSTEM UNDER STUDY
The suggested control technique is tested on a two-region power system that includes a thermal reheat system in one area and a PV plant with maximum power point tracking (MPPT) [23], [26], [32] in the other. Previous research [23], [27] used a two-area power scheme similar to the used in the present article. The values and parameter abbreviations used in this paper are listed in Appendix [23], [27]. Fig. 1 depicts the simulation model of system under investigation. The detailed modeling and transfer functions of PV plant with MPPT and reheat thermal turbine are given in [23], [26].  MPPT. T g is time constant of governor in area-2; K r is gain of turbine and T t & T r are reheat turbine time constants; R is regulation droop, B is frequency bias constant, T ptie is tieline power coefficient, K ps & T ps are power system gain and time constant respectively. The load demand in n th area of the system is denoted by P Ln .
Under normal operating conditions, the demand is satisfied by the generated power within the respective control areas. However, if the system has additional load demand, this leads in a mismatch between real and projected power exchange, resulting in frequency and tie-line power fluctuations. To mitigate these perturbations, secondary control action is initiated by the controllers. The u 1 and u 2 represents the controller outputs of area 1 and area-2 respectively in the transfer function block diagram. The transfer function, G cn , of PID control [32] of n th area is given as equation (1) and expressed as: where K pn , K in and K dn is proportional (P), integral (I), derivative (D) controller gain values of n th area. The oscillations in frequency and tie-line power due to incremental load requirement in the system must be minimized by suitable controller action which in turn depends on the controller gain values. The optimization technique to optimally tune the controller parameters is explained in the subsequent section.

III. PROBLEM FORMULATION
This study focuses on identification of the optimum PID controller gains for frequency regulation using recently introduced black widow optimization algorithm for diminishing the perturbations in frequency and tie-line power of the interconnected system including RESs. The same objective function (OF) i.e. integral time absolute error considered in [23], [27], [33] is taken as the fitness function for BWOA algorithm and given as: where T is the total simulation time, e(t) is the error signal obtained from summation of deviation in frequency, f n , at time instant t, of n th areas and tie-line power ( P tie ) of interconnected areas. The fitness function in the RES integrated power system is designed to reduce frequency and tie-line power fluctuations that exists after a long time after the occurrence of disturbance in the system. Using this fitness function, oscillations in system settles faster in comparison to any other fitness function [28]. The system constraints are the minimum and maximum limits of controller gains. Hence, the optimization problem for the present work is defined as: where K pnmin , K inmin and K dnmin are minimum value and K pnmax , K inmax and K dnmax are maximum values of P, I and D controllers respectively. These controller gains in equation (3) are optimized using recently introduced black widow optimization algorithm explained in the next section.

IV. BLACK WIDOW OPTIMIZATION ALGORITHM (BWOA) FOR LFC
The authors developed a bio-inspired Black Widow Optimization Algorithm (BWOA) in [25], [29], which is based on an incomparable property of black widow spider mating. The Black widow is primarily nocturnal, with the female FIGURE 2. Flowchart of BWOA [25], [29].
remaining hidden during the day and spinning her web at night. The female widow spends the majority of her adult life in the same location. When a female black widow wants to mate, she sprays pheromone on selected parts of her net to attract the male. The first male to enter the web reduces the attractiveness of females to rivals by reducing their web size. During or after mating, the female swallows the male, then transfers the eggs to her egg sock. The offspring engages in sibling cannibalism after hatching the egg [38]. They do, however, remain on their moms' web for a short while, and they may even swallow the mother. The fit and powerful individuals survive as a result of this cycle and thus, the global optimum of the goal function is the best. In terms of faster convergence, not being trapped in local optima, and decent balance between exploration and exploitation of the search space, the proposed algorithm outperforms other evolutionary algorithms. BWOA is used in this paper to overcome the frequency regulation problem by optimizing the PI and PID controller gain parameters. The flowchart of BWOA is depicted in Fig. 2. The step-by-step mapping of the algorithm used to solve LFC's engineering optimization problem [25], [29] is given below: BWOA initializes the population Np 1 of widow spiders randomly having dimension Np 1 × N c which contains the values of controller parameters within defined limits. N p1 is population size and N c denote number of controller gains. For each array of widow, objective function/function given by equation (2) is evaluated.

B. PROCREATION
The survival of the fittest individuals and the creation of better offspring are the basis of evolutionary algorithms. In BWOA, the off springs (OFS) are produced by mating of two widow parents, p 1 and p 2 , with consideration of procreation constant α. The off springs produced [25], [29] are given as equation (4) and (5) and expressed as:

C. CANNIBALISM
Cannibalism is the process of eating up and destroying father spider by the mother spider and weaker spider off springs by the stronger spider off springs. Based upon the cannibalism rate, the population having better objective function value is stored into new population, N P2 and rest of the population is destroyed.

D. MUTATION
The chromosome of some randomly chosen widow spiders from initial population are mutated to generate new population, N P3 .

E. UPDATING AND MUTATION
The population generated at step (c) and (d) are merged to form new population and the fitness function value is assessed for each of the solution in the new population and best optimal solution is returned after sorting the population based upon their fitness function value.
In the present study, the abovementioned BWOA algorithm is implemented to fine tune the PI and PID controller gains. The detailed discussion of results obtained is presented in the next section.

V. SIMULATION RESULTS
Optimized controllers are used to control the load frequency of a two-area interconnected power system made up of a thermal reheat turbine and a PV grid system. The values of the controllers are optimally tuned in the present work using recently introduced BWOA. The simulation of the system is performed on MATLAB R2019a on Dell Laptop with 64bit Operating System, processor Intel R Core TM i5-8265U and 8 Giga Byte RAM. The parameters of the algorithms namely rate of procreation, rate of cannibalism and rate of mutation are set to be 0.6, 0.44 and 0.4 respectively [25] and population size is considered to be 30. These values are chosen because the best optimal solution is obtained for problems solved in [25] using these values when the algorithm is run multiple times for different values of algorithm parameters. The algorithm returns the optimal solution in a very few iterations. However, to demonstrate the not being trapped in local optima, the present paper uses the 500 iterations as stopping criterion for BWOA. Further, for the comparative analysis of the proposed optimized controller with reported tuned controllers, the same saturation limits of the controller gains considered in [23] i.e. between −2 to 2 is considered in the current work. The system parameters of [23], [27] are factored in for the present work and shown in the Appendix. The convergence of the proposed algorithm to solve LFC problem is shown in Fig. 3. It is clear that the fitness function value saturates to 1.4098 which is less than the value obtained using GA [23], FA [23], WOA [27] and MWOA [27] reported in Table 1 and also, it is achieved only in 3 iterations which proves its faster convergence. The proposed controller superiority and competency is exhibited by considering the following scenarios: (a) Performance comparison of proposed BWOA optimized controller with other optimization algorithms (b) Impact of high load demand on system performance (c) Sensitivity analysis of optimized controlled interconnected power system (d) Effect of non-linearities on system performance

A. PERFORMANCE COMPARISON OF PROPOSED BWOA OPTIMIZED CONTROLLER WITH OTHER OPTIMIZATION ALGORITHMS
This section presents the simulated response of a RES integrated power system with PV panels. In both regions of the system, a demand of 0.1 p.u. load is imposed. The same system is controlled using GA optimized PI [23], FA optimized PI [23], WOA optimized PI [27], MWOA optimized PID [27], BWOA optimized PI and BWOA optimized PID controller. The simulation results of variation in frequency of both regions and tie-line power of an optimally controlled power system using optimized PI controller are shown in Fig. 4 to Fig. 6 and using PID controllers in Fig. 7 to Fig. 9. When both areas in the system are subject to sudden demand of 0.1 p.u. load, it is evident from the dynamic responses and results reported in Table 1 that the system with BWOA tuned PID controller mitigates the perturbations in system frequency and tie-line    power more effectively in comparison to GA, FA, WOA, MWOA and BWOA tuned PI/PID controllers reported in literature [23], [27] in light of undershoot, overshoot and settling time. The variations in frequency and tie-line power responses depicted in Fig. 4 to Fig. 9 and Table 1 revealed that the overshoot, undershoot and settling time of the oscillations in the system reduces considerably with BWOA optimized PID controller in comparison to other responses obtained from the reported algorithms.
It is observable from the results reported in Table 1, that the system with BWOA tuned controller shows significant improvement in comparison to performance using GA, FA, WOA and MWOA optimized controllers. It is clear that although the overshoot in frequency of both areas is more than the system response with MWOA optimized controller, but the proposed controller has considerable improvement in reducing the undershoot and settling time of the responses. Hence, it is deduced that the BWOA optimized PID controller outperforms the other reported controllers. Table 2 shows the controller gains and fitness function value obtained using the BWOA technique. It is clear that the fitness function value obtained using BWOA algorithm is less than the other VOLUME 10, 2022   reported values of fitness function with GA [23], FA [23], WOA [27], MWOA [27] and BWOA tuned PI controller. The fitness function obtained with BWOA is improved by 88.37%, 81.02%, 65.79% and 9.64% with respect to the values obtained using GA [23], FA [23], WOA [27] and MWOA [27] respectively.

B. IMPACT OF HIGH LOAD DEMAND ON SYSTEM PERFORMANCE
Large load disturbances that are sudden in occurrence ranging from 0.1 p.u. to 0.4 p.u. are used to demonstrate the sturdiness of the BWOA optimized PID controlled twoarea system with PV grid panels. The simulation results in Fig. 10 to Fig. 12 demonstrate that the propounded controller successfully mitigates the influence of sudden load disturbances and quickly settles incremental variation in frequency and tie-line power.

C. SENSITIVITY ANALYSIS OF OPTIMIZED CONTROLLED INTERCONNECTED POWER SYSTEM
The sensitivity analysis in electrical power system is very important to predict the response of the system in case if any      installed power system component. Keeping this in view, the sensitivity analysis of BWOA tuned PID controlled PV grid integrated system is performed by considering variation in the system parameters. A substantial range of variation i.e. from −50% to 50% in load demand, governor time constant, time constant of turbine, power coefficient of tieline, PV panel time constants C T and D T is considered for analyzing the performance of controller. It is explicable from the simulation results that there is no need to reset the controller gains even if there is change in the system parameters. The responses are only displayed for frequency variation of region-1 in Figs. 13 to 18, and the specification of responses for incremental frequency variation of region-2 and tie-line power is reported in Table 3. The suggested controller operates satisfactorily and is able to stabilize the system oscillations, as shown by the simulation results in Fig. 13 to Fig. 18 and the values presented in Table 3.

D. SYSTEM PERFORMANCE WITH NON-LINEARITIES
In real-time power systems, nonlinearities such as governor dead band and generation rate constraint (GRC) exist, thus it's critical to assess the optimized controller performance while taking these limitations into account [30], [31]. In the present work, governor deadband of 0.036Hz, GRC of   3% p.u. MW/min and time delay of 50ms is considered for simulation [30], [31], [35]. Fig. 19 to Fig. 21 show the simulation results of the system when non-linearities are taken in to account with load disturbance of 0.1 p.u. in both areas. It is evident from the results that the BWOA optimized PID controller successfully handles the non-linearities in the system.

E. CASE STUDY: NON AVAILABLITY OF PV GENERATION
The source of photovoltaic system in area-1 of the power system under consideration is intermittent, non-dispatchable and hence, it becomes necessary to evaluate the performance of the BWOA optimized PID controller to regulate the frequency in case of load sharing of PV system in area-1 and thermal turbine in area-2. The following cases are considered in the present work to support the superiority of the proposed control scheme: (a) 10% participation of PV system and 90% load sharing by thermal system (b) 40% participation of PV system and 60% load sharing by thermal system The sharing factor of PV system and thermal are set to 0.1 and 0.9 respectively in Case study-1. In case study-2, the sharing factor of PV system and thermal are set to 0.4 and 0.6 respectively. The dynamic responses of deviations      in frequency and tie-line power for both case studies are presented in Fig. 22 to Fig. 24. It is clearly evident that BWOA tuned controller effectively regulate the frequency even if there is variation in load sharing of area-1 due to intermittent nature of PV system. The performance of the proposed BWOA optimized PID controlled is analyzed for two-area power system comprising of thermal non-reheat turbine with GRC in each area. The transfer function model of system and parameters are taken and referred from reference [34]. BWOA optimized controller is used to regulate the frequency regulation of thermal area system having rated power of 2000MW and nominal load of 1000MW [34]. The controller gains lie within the range of −1 to 1 [34]. The performance of the proposed BWOA tuned PID controller is compared with firefly algorithm (FA) and hybrid Firefly Algorithm and Pattern Search (hFA-PS) tuned PID controller [34].   The specifications of dynamic responses using optimized controllers with step increase of 5% in load demand of area-1 and GRC of ±0.05 is presented in Table 4 and dynamic responses of variations in frequency and tieline power are shown in Fig. 25 to Fig. 27. The tuned controller parameters and fitness function values are reported in Table 4.
The simulation responses shown in Fig. 25 to Fig. 27 and results reported in Table 4 and Table 5 depict that although there is no much significant improvement in overshoot and undershoot of the responses, BWOA optimized PID controller outperforms the FA optimized PID and hFA-PS tuned PID controller in terms of settling time and fitness function value of deviations in frequency and tie-line power. The settling time of deviations in frequency of area-1, area-2 and tie-line power has been improved by −9.03%, 25.10% and 21.40% respectively and fitness function improved by 29.88% using BWOA tuned PID controller as compared to FA tuned PID controller [34]. The improvement of -20.71%, 18.44%, 15.50% and 18.33% is observed using BWOA    optimized controller in comparison to hFA-PS optimized PID controller in the dynamic responses of frequency deviation of area-1, area-2, tie-line power deviation and fitness function respectively. VOLUME 10, 2022  Further, the analysis has been extended with inclusion of non-linear constraints namely governor deadband of 0.036Hz, GRC of ±0.05 and time delay of 100ms present in the real-time system [34], [35]. The dynamic responses of the two-area thermal interconnected system with no change in controller gains as reported in Table 4 are shown in Fig. 28 to Fig. 30. It is evident that the BWOA optimized controller effectively handles the non-linear constraints establishing the superiority of proposed optimization technique for fine tuning the controller gains.

VI. CONCLUSION
The objective of the present study to regulate frequency of photovoltaic integrated power system is achieved through tuned proportional integral and proportional integral derivative controller optimized using the distinct feature of cannibalism of the black widow optimization algorithm. BWOA optimized PID controller is also used to regulate frequency of two-area thermal power system. A comparative analysis of the proposed controlled technique with some known algorithms, namely GA, FA, hFA-PS, WOA and MWOA algorithm optimized controllers, establishes the superiority of the proposed black widow optimization algorithm optimized controller in terms of objective function value, faster convergence, undershoot, overshoot and settling time of responses. The integral time absolute error fitness function shows improvement by 88.37%, 81.02%, 65.79% and 9.64% with respect to the values obtained using GA, FA, WOA and MWO algorithm respectively for photovoltaicthermal interconnected power system. The proposed BWOA tuned PID improves settling time of dynamic responses of frequency in area 1, frequency in area 2 and tie-line power by 54.09%, 54.90% and 71.51% respectively as compared to MWOA tuned PID controller. Moreover, changes in load demand and system characteristics over a range from +50% to -50% proves the proposed bio-inspired optimized controller's robustness and sensitivity. The variation of sharing factor of photovoltaic system from 0.1 to 0.4 in order to study the impact of variable solar radiance and temperature evidently shows that the oscillations in the dynamic responses gets settles down by the proposed BWOA tuned PID controller. Further, the efficacy of the proposed control scheme has also been proven by implementing the technique on widely used two-area interconnected power system comprising of non-reheat thermal power system with non-linear constraints namely time delay, generation rate constraint and governor deadband.
In the future, the work will be extended to multi-area interconnected power system comprising of multiple sources of generation including renewable energy sources such as solar, wind etc. in each area. The work will focus on design of hybridized meta-heuristic algorithm based PID controller to diminish the transient oscillations in power system arising as a result of perturbation or intermittent nature of renewable energy source in the system. Further, the system stability will be analyzed incorporating battery energy storage systems or generators with fast ramp up time which will provide electrical power in case of non-availability of renewable energy sources. APPENDIX PREETI DAHIYA received the Ph.D. degree in electrical engineering from the National Institute of Technology Hamirpur, Himachal Pradesh, India, in 2017. She has been a Postdoctoral Fellow of Electrical, Electronic and Computer Engineering with the University of KwaZulu-Natal, South Africa, and a Skill Assistant Professor at Shri Vishwakarma Skill University, Haryana, India, since 2019. She had also worked at the National Institute of Technology Delhi and the ABES Engineering College. Her research interests include power system integrated renewable energy systems, automatic generation control, deregulated power systems, power system optimization, heuristic techniques, artificial neural networks, and fuzzy control.