ISSN Vol.04,Issue.02, February-2016, Pages:

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1 ISSN Vol.04,Issue.02, February-2016, Pages: A Comparative Study of Lead, Lag, Lead-Lag and Robust Controllers for A Position Control System VATTI ANJALI 1, N. RAMESH RAJU 2 1 PG Student, Dept of EEE, Siddhartha Institute of Engineering and Technology, Chittoor (Dt), AP, India, vatti.anjali@gmail.com. 2 Professor, Dept of EEE, Siddhartha Institute of Engineering and Technology, Chittoor (Dt), AP, India, Abstract: Controlling the sun based boards to concentrate most extreme sunlight based energy is an essential worry of control designers now days. A rough second request model of a sun seeker control framework is controlled utilizing lead, slack, and lead-slack controller. The reaction of these controllers is contrasted and the proposed strong controller. Along these lines it is watched that the powerful controller beats in giving dependability and solidness if there should arise an occurrence of parameter varieties under down to earth circumstances. The results are reproduced in MATLAB. Keywords: PI, PD, PID, Seeker Control Framework. I. INTRODUCTION In this modem universe of dying assets, it has ended up important to spare the non-renewable assets and make ideal utilization of renewable assets. Sun based vitality stands third among the top renewable assets being internationally introduced, the main two being the hydro and wind vitality. Sun based vitality is straightforwardly changed over into electrical vitality utilizing sun oriented cells. The measure of power being delivered is specifically relative to the measure of surface range presented to the sun. In all reasonable applications it is fundamental to control the sun based board so that their greatest surface is presented to the sun. A sun seeker control framework controls the elevation of a space vehicle so that it can proficiently track the sun. Like whatever other control framework, its target is to keep up the mistake signal as near zero as conceivable. The target can be met by utilizing different controllers for example, lead, slack, lead-slack and so forth. In the wake of waning situation of customary vitality sources, the researcher world over are attempting to utilize renewable vitality sources all over the place conceivable. Examinations of the essentialness of renewable vitality sources with the goal of preservation of nature and environment have been done in. A few books help comprehend the issue of oil reliance over the globe and likewise propose approaches to conquer this fixation. Sun oriented vitality is a standout amongst the most key wellsprings of renewable vitality that has seen honorable headways lately. Substantial scale sun oriented force framework outline has been taken into thought. Has assessed relationship in the middle of time and recurrence area portrayals of straight, time-invariant frameworks furthermore considered the impacts of input on such frameworks it talks about the impact of state variable input on controllability, perceptibility, and shaft zero designs. Brings into light the restrictions forced by right half plane posts and zeroes of the open-circle framework specifically as far as affect ability and complimentary affectability elements of the shut circle framework. In a down to earth outline prospect on multi variable feedback control in this variable criticism control issues has been exhibited. It sums up the known SISO proclamations and limitations of the outline issue to the MIMO cases. A few books, give an extraordinary establishment in comprehension the control framework nuts and bolts. It additionally gives knowledge into the vigor issue. In a similar investigation of different controllers, for example, PI, PD, PID what's more, lead-slack for force framework stabilizer. Power framework steadiness is of critical worry in electric framework operation. The project does a near study for velocity deviations, load point deviations and terminal voltage deviations. In this paper a near study has been made between the exhibitions of the sun seeker framework by utilizing a lead, slack and lead-slack controllers. The outcomes have been reproduced in MATLAB. At that point finally vigor issue is looked into. A vigorous controller is at long last utilized which guarantees soundness and consistency in execution regardless of parameter variety in the plant. Such parametric varieties can occur in any framework because of defects in plant with time or ecological variables. II. MODELING OF SUN SEEKER SYSTEM The square chart of the sun-seeker control framework is as appeared in fig l. This framework may be mounted on a space vehicle so it can track the sun with incredible exactness. The variable speaks to the reference point of the sun powered beam, and signifies the vehicle hub. The target 2016 IJIT. All rights reserved.

2 of this sun seeker framework, similar to whatever other control framework is to keep up the blunder signal a between, and near zero. The framework parameters are given as takes after: VATTI ANJALI, N. RAMESH RAJU (5) A wonderful change in the framework execution is watched. As far as time-area particulars, a portion of the changes are: Expanding the damping of the framework. Enhancing the ascent time and settling time. Does not influence the relentless state mistake. The same has been appeared by MATLAB reproductions. B. Phase lag controller As the name proposes, a phase lag controller presents a negative stage to the framework over some recurrence range. It is a low-pass channel. The way transfer function of a basic slack controller is given as: Fig.1. Block diagram o f a sun seeker system. The forward way transfer function, of the uncompensated framework is given as, Where and and A(s) are the Laplace transforms of respectively. Substituting the numerical estimations of the different parameters in the framework way transfer function we get, (2) Before applying any control plot, the stride reaction of the uncompensated framework is reproduced utilizing MATLAB. III. CONTROL SCHEMES A. Phase lead controller As the name proposes, a phase lead controller presents a positive stage to the framework over some recurrence range. It is a high-pass channel. The way transfer function of a basic lead controller is given as: (3) In the above portrayed sun seeker framework (k=l), a phase lead controller with the accompanying way transfer function is consolidated, (4) The general shut circle way transfer function of the framework can be composed as, (1) (6) In the above depicted sun seeker framework (k=l), now a phase lag controller with the accompanying transfer function, (7) The general shut circle way transfer function of the framework will be presently given as, (8) The effect of a lag controller on the framework can be compressed as: Enhances relative security of the framework. Data transmission of the framework is diminished. 3. Rise time and settling time of the framework increments. Framework is more delicate to parameter varieties for frequencies more prominent than the data transmission of the framework. The aforementioned effects have been delineated utilizing MATLAB. C. Phase lead-lag controller As examined over a phase lead controller enhances rise time furthermore, settling however in the meantime expands the regular recurrence of the framework. Likewise a stage slack controller in spite of the fact that, moves forward damping and upgrades the relative security of the framework, however it results in longer ascent time and settling time. Along these lines we can say that every plan has its own particular benefits and negative marks. Regularly in pragmatic genuine frameworks it is key to meet some stringent determinations which are unrealistic utilizing both of the plans alone. In every single such circumstance it is required to utilize a mix of lead and lag controllers, with the goal that one can appreciate decency of both. The way transfer function of a straightforward lead-slack controller is given as,

3 A Comparative Study of Lead, Lag, Lead-Lag and Robust Controllers for A Position Control System Where. Consider a lead-lag controller with the accompanying way transfer function, (10) This controller when joined in the sun-seeker framework (k=l), would bring about the accompanying shut circle way transfer function, (9) (15) To check the power of the framework, step reaction of the framework is analyzed by shifting the estimation of K. The stride reaction of the framework has been reproduced by taking K=O.5, 1, 2 utilizing MATLAB. Not at all like the past results appears an amazing change concerning strength of the framework under parametric varieties. These things have been outlined in table I. TABLE I: (11) The phase lead a portion of the controller is in charge of enhancing the ascent time, settling time and the transmission capacity. The phase lag bit goes into enhancing the relative strength of the framework. Both of these focal points can be extremely well seen in the MATLAB. D. Robust Control Scheme In every single viable application it is fundamental not just to meet the required details regarding time-space and recurrence area, yet to yield execution that is harsh to outer aggravations and parameter varieties. This is very fundamental since for all intents and purposes it is difficult to dispose of outer unsettling influences and parameter varieties. Under such circumstances the controllers portrayed above neglect to give productive results. The framework utilizing phase lead controller demonstrates a striking change in its stride reaction under parametric varieties. The varieties in the Stride reaction of the framework utilizing phase lag and phase lead-lag controllers individually under parametric uncertainty. There are a few techniques for outlining a powerful controller. The outline philosophy utilized here is that the zeroes of the controller are set close to the fancied shut circle posts of the repaid framework. Here the stage slack repaid sun seeker framework is being adjusted to illuminate the issue of power. The forward way transfer function, of the phase lag remunerated framework is given, IV. SIMULATION RESULTS Simulation results of this paper is as shown in bellow Figs.2 to 15. (12) The craved shut circle shafts are f. Presently to plan the strong controller, its zeroes must be found near the coveted shut circle shafts. Let the controller's zeroes be - 13±10i. At that point the controller way transfer function is given as, (13) The transfer function of the forward controller is given as, (14) The Closed circle transfer function of the framework with k=1 then gets to be, Fig.2. Step response of phase lead controller under parametric variations (K=O.5, 1, 2).

4 VATTI ANJALI, N. RAMESH RAJU Fig.3. Step response with phase lag controller under parameter variations (K=O.5, 1, 2). Fig.6. Step response with robust controller under parameter variation (K=O.5, 1, 2). Fig.4. Step response of the system using phase lead. Fig.7. Step response of the system using phase lag. Fig.5. Step response of the system using phase lead. Fig.8. Step response with phase lead-lag controller under parametric variations (k=o.5, 1, 2).

5 A Comparative Study of Lead, Lag, Lead-Lag and Robust Controllers for A Position Control System Fig.9. Step response of the system using phase lag. Fig.12. Step response of phase lead controller under parametric variations (K=O.5, 1, 2). Fig.10. Step response of the system using phase lag. Fig.13. Step response of the system using phase lead, phase lag, phase lead-lag controller. Fig.11. Step response of the system using phase lead, phase lag, phase lead-lag controllers. Fig.14. Step response with phase lag controller under parameter variations (K=O.5, 1, 2).

6 VATTI ANJALI, N. RAMESH RAJU Fig.15. Step response of the system using phase lead. IV. CONCLUSION The framework has been tried for its stride reaction utilizing diverse controllers. Utilizing MATLAB the outcomes have been plotted for examinations. Firstly the uncompensated framework was reproduced, then diverse controllers, for example, phase lead, lag and lead-lag controllers have been utilized to repay the framework. Thusly to guarantee framework adjustment under parametric varieties because of different blemishes, a food forward hearty controller has been composed and the framework execution has been reproduced utilizing MATLAB. At last correlation between vigorous and different controllers is made under parameter varieties. It is watched that the vigorous controller displays considerably less varieties in the stride reaction when the estimation of K is differed as contrasted with alternate controllers. In this way a hearty controller is exceptionally unfeeling to parametric varieties and different unsettling influences when contrasted with different controllers. V. REFERENCES [1] J.Abdul Jaleel, Thanvy N, "A comparative study between PI, PD, PID and lead-lag controller for power system stabilizer, International conference on Circuits, Power and Computing Technologies [ICCPCT-20 13], [2] R. W. Brockett, "Poles, Zeros, and Feedback: State Space Interpretation," IEEE Transaction on Automatic Control, AC-I 0 (2), pp , [3] J C. Doyle, and G. Stein, "Multi variable Feedback Design: Concepts for a Classical/Modem Synthesis," IEEE Transaction on Automatic Control, AC- 26 (1), pp. 4-16, [4] JS. Freudenberg and D. P. Looze, "Right Half Plane Poles andzeros and Design Tradeoffs in Feedback Systems," IEEE Transactions on automatic Control, AC-30(6), pp