A Comprehensive Step-by-Step Approach for Introducing Design of Control System

Control Systems classes cover many new topics and concepts. By the time instructors begin to teach design of controllers, students have already learned some analysis and synthesis tools such as Root Locus, Routh-Hurwitz criteria for stability, Bode plot and its relation to stability, and Nyquist plot and its stability criterion. The problem is that at this point in time, these topics can still be fragmented and partially disconnected in students’ minds. Oftentimes, the relations between the topics are not fully clear. When it comes to design of feedback control systems, we have repeatedly found out that, despite continuous attempts to improve our teaching, there were still some problems in students’ understanding. These include: •Connecting the concept of a controller to real-life, and to sensing-based daily examples •Understanding the true meaning of controller design and its implementation •“Translating” the plant model and the design specifications to different control tools, and inter-relating them In this paper, we report on work in progress of an intuitive and visual approach to teaching design of controllers in a closed loop control system using a specific comprehensive third order system. For example, all explanations use different colors consistently to show stability (green), instability (red), and marginally stable (orange) systems on related plots. This paper presents several topics, such as clarifying the meaning and importance of controllers, through daily, story-telling-based examples. It uses a comprehensive approach for analyzing and understanding a plant (to be controlled) in open loop, the controller, and the final design. For example, multiple synthesis tools are used to analyze the plant’s open loop gain and show its effect on closed loop marginal stability; this shows the effect of the open loop gain on the Bode Plot (shift in gain expressed in dB), the Nyquist Plot (shrinking and expanding effect of the plot), the Root Locus plot (new locations of closed loop poles), and the first column of Routh Table. In addition, this paper shows the effects of different controllers (P, I, D, PD, PI, and PID) and their relations to the desired performance. We intentionally show unsuccessful designs: this helps in explaining some pros and cons of different controllers. This is followed by a successful design of a controller. Lastly, we present multiple ways to observe and analyze the effect of the final controller design using multiple design tools, as well as MATLAB simulations. This also includes discussing design “rules of thumb” and how they are manifested in each tool. It should be noted that the material presented in this paper is not meant to replace existing textbooks chapters. It is merely an add-on to better explain, learn, and comprehend the topic of design, and see the bigger picture. This is work in progress. However, we have tested the approach a few times and received a very positive feedback from students. A more comprehensive assessment approach is planned for the near future.