A control system is basically an interconnection of different components that form a particular system configuration that is capable of providing a desired system response. Linear system theory provides the basis for analyzing a system by assuming a cause-effect relationship for the system components. The cause-effect relationship of the process is represented by the input-output relationship. An open loop control system is one without a feedback while a closed-loop control system utilizes an additional measure of the actual output for comparing the actual output with the desired output response. The measure of the output is the feedback signal. The concept of feedback forms the foundation of analysis and design of a control system. The course on control systems begins with introducing the general approach in designing and building a control system. The next important aspect of control systems is the introduction to mathematical models of different types of systems – electrical, mechanical and fluid. In this section of control systems, students get to learn how to represent any system through linear differential equations and linear approximations. Another important aspect of this section is learning to evaluate the input-output transfer function of a system for which a thorough knowledge of Laplace transform is needed. This section of control systems also includes the formulation of block diagram models, block diagram reduction rules and the construction and evaluation of signal flow graphs. The next section of control systems deals with the study of feedback system characteristics, performance and stability analysis techniques of linear feedback systems. This includes time domain analysis, root locus analysis, frequency domain analysis and state-variable analysis. Time-domain analysis includes studying the time response of continuous data systems to different type of inputs –step, ramp and parabolic and the computation of steady-state error in each case. The time-domain transient and steady-state response of a prototype first-order system is studied and also the time-domain transient response of a prototype second order system is studied thus introducing the concepts of rise time, settling time, maximum overshoot, delay time, undamped natural frequency and damping ratio. Basic control system configurations and the effects of adding poles and zeros to transfer functions are also studied in this section of control systems. Also this section gives an idea about the dominant poles of a transfer function and appropriately neglecting the insignificant poles with consideration for the steady-state response. Root locus analysis is an integral part of control systems design and analysis which deals with the study of construction of a root locus which basically gives the locus of the closed loop poles of a system as the gain varies from zero to infinity. Stability analysis of linear continuous systems also includes the Routh-Hurwitz stability criterion. In the frequency domain analysis section of control systems, students learn the construction of Bode plots and study of the relative stability of systems through the determination of gain and phase margins through the Bode plot. This section also includes the Nyquist criterion analysis and the construction of Nyquist plots. After studying this section, students are expected to be able to comment on the relative stability of a system by the determination of gain and phase margins and also the effects of the addition of poles and zeros on the shape of the Nyquist plot. Next up is the most crucial section in the study of control systems that deals with the design of control systems based on design specifications and controller specifications. This section gives an explicit idea about the different possible controller configurations and the procedures for designing any of these for a system. This section includes the design of proportional type, proportional-integral type, proportional-derivative type and proportional-integral-derivative type controllers through time-domain as well as frequency-domain techniques. Also, in this section, students learn to design phase-lead and phase-lag type controllers and their analogy with PI and PD controllers. Minor loop rate-feedback control and feed-forward control are among the other basic types of control that are studied in this section of control systems. Next up is the section that deals with state-variable analysis. This part of the control systems course deals with the representation of systems in state-variable form and the conversion from transfer function domain to the state-variable domain and vice versa. This section introduces the very basic and important concepts of eigenvalues and eigenvector analysis, canonical forms, controllability and observability. Also this section deals with different types of similarity transformations and decompositions of transfer functions. The state-variable analysis section of control systems also deals with state-feedback control, pole-placement through state-feedback, state-feedback with integral control, full-order observer design, design of reduced-order observers and state-feedback based observer design. The full-fledged course on control systems can be simultaneously backed up by making the students learn and get used to a design and simulation software like MATLAB that can be used for verifying the results.
NARULA INSTITUTE OF TECHNOLOGY
IIT Patna, IIT kharagpur