APPROACHES FOR PID CONTROLLER DESIGN WITH APPLICATIONS AND EXPERIMENTAL VALIDATION

Abstract

Control systems are ubiquitous in everyday life. A control system is a mathematical law that enables the achievement of desired characteristics. Among many such laws, one of the most popular ones is a PID controller. It is a fundamental control algorithm that that is widely used for the control in industry due to its simplicity and flexibility. There exist innumerable techniques in the control literature for tuning a PID controller, however no such technique has been developed that can suffice for all types of situations. This calls for further research and challenges in tuning of PID controllers. Most of the conventional techniques of tuning a PID controller like Ziegler Nichols, Chiens- Hrones-Reswick (C-H-R), Cohen-Coon are simple but are applicable to only a certain class of systems. Hence, there is a need to develop techniques that are not only applicable to a more general class of systems but simultaneously avoid the computational complexity which is exhibited in many soft computing techniques. Further, the techniques must be easily implementable on a hardware system as well. It is observed that the major drawback of the optimal control techniques is that they cannot be implemented on a hardware. Hence, a new approach known as the QRAWCP is developed which transforms an optimal LQR controller into a classical PID controller. This technique is also accompanied by the augmentation of an additional pole to the closed loop system consisting of a LQR controller. In this thesis, a well-structured manner of selecting the additional pole is proposed. Further, it is entirely possible, that all the states of the system are not measurable. To ameliorate this limitation, a LQG based PID controller is designed that comprises of a Kalman filter which acts as an observer and the LQR controller that can be utilized for optimal tuning of the resulting system. Further, both the schemes elucidated above are validated via hardware simulations. The hardware setups used in this thesis for validation of the proposed techniques are QUBE DC servo system, Cart inverted pendulum system and the rotary inverted pendulum (RIPS) system. There are numerous techniques of tuning a PID controller, and each one has its own advantages and limitations. The adaptive control scheme, first proposed in this thesis, uses multiple candidate controllers, each of which is tuned via different control approaches and the resultant output of the iii system follows the best of these multiple approaches via the assignment of appropriate weights for each control scheme. It is observed that the proposed adaptive strategy outperforms the individual control techniques. The proposed scheme, in its current form is then modified via the addition of a median filter and an epsilon term to get rid of the problem in which the derivative term becomes zero. To validate the effectiveness and strength of the modified scheme, it is then tested on a hardware setup of a Cart Inverted pendulum system. Next, all the approaches developed above are tested primarily on two setup, i.e., DC servo system and Cart Inverted Pendulum system (CIPS). Various illustrative examples are provided to compare the proposed technique with the existing techniques in the literature. To investigate the robustness of the proposed technique, the effect of input disturbances, measurement noise, addition of input gains, are also taken into consideration. The simulation examples are compared via time response plots and performance indices. An interactive and animated graphical user interface is also developed for analysis, design and validation of controllers for cart inverted pendulum system (CIPS). Finally, the problem of load frequency control of a power system is presented. Both the QRAWCP and the adaptive scheme developed above are applied to different models of the power system. The effect of non-linearities such as governor dead-band and generation rate constraint is also explored for different studies. To investigate the strength of the proposed technique for a more realistic power system model in the presence of non-linearities, a 10 machine New England system, having a topology similar to IEEE 39 bus system is also considered. The effect of parametric uncertainty is ascertained by the perturbation of parameters by 50%. To analyze the effectiveness of the proposed controller design techniques, a comprehensive comparative study with respect to the performance indices and time response is also undertaken. The simulation studies are a testimony to the effectiveness and efficiency of the proposed technique. Overall, in this thesis, an attempt has been made by the author to develop simple and reliable control schemes to design a controller to obtain an improved time response and better disturbance rejection behaviour. Through illustrated examples and hardware validation, it is evident that the schemes are practically useful in the analysis and design of the control system.