Implementing a Full-state Feedback Laboratory Exercise in an Introductory Undergraduate Control Systems Engineering Course

Abstract

Many mechanical engineering undergraduate students find the study of control systems engineering to be one of the more challenging subjects that they encounter. These challenges include working in the Laplace and frequency domains, learning new analysis techniques, as well as the breadth of topics that are typically covered in an introductory control systems undergraduate class. The challenges faced by instructors consist of deciding which material to include, balancing the depth and breadth of understanding various topics, selecting the best learning activities for each technique, and providing meaningful hands on experimentation in a predominately theoretical course. Fortunately, control systems engineering is amenable to instruction through laboratory exercises, where students can try different control techniques and observe their effectiveness nearly in real-time. Some effort is required to adequately link theory to experimentation in a theoretical introductory course. In this paper, we describe the implementation of a new full-state feedback laboratory exercise which was designed to illustrate the efficacy of full state control of a fourth order system. The general process of modeling, simulating the system, controller development, then deployment and evaluation in the lab is a common pedagogical process in control systems engineering education. The importance of visualization, in the context of using information technology, is discussed in Bencomo (2003). The laboratory exercise in view utilizes the same aforementioned process with an emphasis on visualizing system performance in state feedback control. The students first complete a pre-lab exercise which covers the modeling, control design, and simulation. Then they utilize commercially available software-hardware package that allows them to deploy their design and observe its real world performance. Specifically, the prelab begins by requiring them through modeling the dynamics of the electro-mechanical system. Furthermore the students then design the controller gains in a full state feedback in order to achieve a desired transient response. They then model the system in SIMULINK prior to coming to the lab, and analyze the effectiveness of their control design. The pre-lab assignments are submitted by the students, graded by the instructor, and then returned in the laboratory. In the laboratory, the students walk through a series of exercises beginning with the open loop response and ending with full state feedback in a closed loop sense. The intermediate steps allow the students to observe the improvements in the response of the system. The students are also introduced to signal processing requirements, for example the need to filter a differentiated signal. The novelty in this exercise lies in the procedural implementation of state feedback (no feedback, partial state feedback(s), and full state feedback with estimation) and evaluation of performance. Specifically, through visual observation of system performance and quantification of system performance through data acquisition and analysis. The full paper will provide the details of the laboratory including implementation instructions and lessons learned through conducting this laboratory exercise with students.