Apply Second Order System Identifications

This paper presents a 2 order system identification of a linear time invariant system in an undergraduate junior level control systems laboratory. In this laboratory students identify a system transfer function from the parameters of cascade Resistor-Inductor-Capacitor (RLC) circuit by computer programming and analyze the output response. Electrical Engineering students use MATLAB software to determine the relationship between the standard 2 order system transfer function with the simple RLC circuit parameters. This laboratory reinforces students’ learning about the effect of tuning the system parameters and demonstrates a wide range of system performance in time and frequency domains. Students learn about the relationship between the locations of poles and the system output responses. They learn about the relationship between the damping ratio and natural frequency response with the RLC circuit parameters in time domain and frequency responses. In the second part of this laboratory students estimate the system parameters from a given time domain step response of a vessel output response. A continuous time transfer function of the vessel is identified from the measurement data. The vessel roll dynamics has been defined as a transfer function of roll-angle and the disturbance torque input. In this lab students apply the principle of standard 2 order system identification to the vessel motion about its roll axis. Students in this lab demonstrate achievement of numerous a-k ABET criteria. Introduction The United States Coast Guard Academy (USCGA) like many institutions around the world enhances an active teaching procedure in the Autonomic Control Systems course. One of the challenges in engineering education today is to motivate students to learn about the fundamental control systems concepts in an undergraduate control course. This paper present a process of teaching the concept of integration from the 2 order transfer function of a simple cascade Resistor-Inductor-Capacitor (RLC) circuit to the standard 2 order system transfer function in control course. This laboratory also teaches students about an application of standard 2 order transfer function that they would see in their career. Students determine the 2 order modeling for a linear time invariant system. They exercise how the location of poles can be changed based on the variation of damping ratio and natural frequency parameters. These responses illustrate as over damped, under damped, undamped, and critically damped. They learn about the impact of damping ratio and natural frequency responses on the step and the frequency response performances. In the second part of this laboratory students estimate the system parameters from a given time domain response of a vessel at sea. This laboratory allows students an active learning about some of the main concepts in the text books in a 160 minutes laboratory based on computer programming. Many institutions around the world established control system laboratory . O’Brien and Watkins developed new methods in teaching controller design for undergraduate students. They defined a unified approach for teaching root locus, Bode design, and then applied it to a physical system for the control system laboratory. Joel Lenoir created a combined course for mechanical vibrations and controls course. In this course students applied the mathematical modeling and simulation skills to a system in lab to support the theoretical concepts that they learned in class. Jack supported the laboratory and project for the control course by using microcontrollers in junior level for mechanical and manufacturing students. Emami developed a laboratory for teaching the process of 1 order system modeling for a DC motor system. Emami and Benin developed how the computer helped to teach the concept of Routh Hurwitz criterion in undergraduate control systems and software engineering courses. The current paper presents the processes of the 2 order system identification in one control systems laboratory. In the first part of laboratory students learn about finding the transfer function in terms of RLC circuit and the standard 2 order system transfer function parameters. The relationship between RLC circuit with damping ratio, natural frequency, and the pole locations are studied in both time and frequency responses. In the second parts of laboratory students estimate the damping ratio and the natural frequency response from the step response data of a vessel at sea. They apply the principle of standard 2 order system identification to the vessel motion about its roll axis. The vessel roll dynamics is defined as a transfer function of roll-angle and the disturbance torque input. Part 1: Relationship between RLC Circuit and Standard 2 Order System Consider a second order low pass filter shown in Figure 1; the continuous time transfer function of this cascade RLC circuit can be defined as the ratio of Laplace transform of output voltage, ( ), out V s across the capacitor and the input source voltage ( ), in V s such as: ( ) ( ) ( ) out