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# Dynamic Systems & Controls (saylor.org)

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The study of dynamic systems focuses on the behavior of physical systems as well as the physics of individual components and the interactions between them. Control systems are designed to enable dynamic systems to respond in a specific manner. In this course, we will learn about the mathematical modeling, analysis, and control of physical systems that are in rest, in motion, or acted upon by a force.

Dynamic systems can be mechanical, electrical, thermal, hydraulic, pneumatic, or any combination thereof. An electrical motor is a good example of a dynamic system in which electricity is used to drive the motor’s mechanical movement. The operation of the motor is controlled by altering the electric current or voltage. Another good example is a car’s suspension system, which is designed to curb abnormal vibrations while riding on a bumpy road. In order to design a suspension system, you must analyze the mathematical equations of the physics of the suspension and its response (i.e. how effectively the system absorbs the vibrations). The springs between the tires and the chassis balance the weight and maintain the height of the car. The suspension system is controlled by actuators (serving as shock absorbers) that curb the vibrations and therefore make for a more comfortable driving experience.

This course explores the dynamics of mechanical, thermal, fluid, electrical, and hybrid systems and sub-systems. We will learn the mathematical models (i.e. differential equations) that govern these systems and work to understand how these systems respond to various inputs both in time-domain and frequency-domain. The course will also focus on stability analysis of these systems with regards to controller designs. (We will take a look at a range of designs, from simple feedback controls to advanced lead-lag compensators). Controller design involves complex mathematical calculations which should be handled by mathematical computation tools like SCILAB, MATLAB, MathCAD, Maple, and so forth. As SCILAB is a freely available tool used for designing, analyzing, and optimizing systems and controls, we will use SCILAB, which will save us time and provide us with more accurate results. You have already used SCILAB in Introduction to Mechanical Engineering . MATLAB users who are not familiar with SCILAB can used a tool in SCILAB (please see UNIT 4) that converts MATLAB codes to SCILAB codes.

We will begin by learning about the different types of dynamic systems through various examples and reviewing relevant mathematical material (much of which you may already know), which will enable you to better understand the material covered in this course. We will then learn how to represent these systems using different mathematical forms before analyzing them in terms of frequency, time domain, and stability with respect to controller design. You will also take a close look at various controller designs and learn how to apply SCILAB. Finally, we will conclude the course by visiting advanced topics and case studies in the field.