Experimental Study of Time Domain Response Characteristics in Second-Order Systems

In this experiment, you need to follow these steps to design and study the parameters and response patterns of second-order systems:

1. First, you need to independently select second-order system models and parameters, and design experimental procedures and steps to simulate the effects of the parameters. You will investigate how the natural oscillation frequency and damping coefficient influence the system's time domain response characteristics. Additionally, you will study the impact of adding a single pole and a single zero on the system's time domain response. In code implementation, this typically involves defining transfer functions using control system toolbox functions like tf() in MATLAB, where system parameters can be systematically varied through loops or parameter sweeps.

2. Next, select no fewer than six different values for each parameter and simulate their step or impulse responses. Use plotting to demonstrate how parameters affect time domain responses, with different parameter variations displayed in two separate graphs. For code implementation, you can use functions like step() or impulse() for response simulation and subplot() or multiple figure windows for visualization, with appropriate labeling to distinguish parameter variations.

3. Use graphical methods to obtain various time domain response indicators (such as rise time, settling time, overshoot, and peak time), compare them, and summarize how changes in second-order system parameters affect time domain response characteristics. Algorithmically, this involves extracting response metrics from simulation data using peak detection algorithms and timing calculations based on threshold crossings.

4. Then, select no fewer than six values for additional zeros and poles, and simulate their step or impulse responses. Plot the response curves in two separate graphs and compare them with the response without zeros or poles. In implementation, this requires modifying the original transfer function by adding polynomial terms in the numerator (for zeros) or denominator (for poles) while maintaining system stability.

5. Finally, use graphical methods to obtain time domain indicators for each response and perform comparative analysis to determine how adding zeros and poles affects the time domain response characteristics of second-order systems. Through these experiments and analyses, you will gain deep insights into second-order system response patterns and achieve comprehensive research results. We wish you success in your experiment!