Complete MATLAB Simulation of Multiple Input Multiple Output Systems

Multiple Input Multiple Output (MIMO) systems have extensive applications in control engineering, communication signal processing, and related fields. MATLAB provides powerful tools for modeling, analyzing, and simulating these complex systems.

MIMO System Modeling MIMO systems typically utilize state-space representation, comprising state equations and output equations. In MATLAB, engineers can directly define state-space models using the `ss` function, which creates a state-space model object by specifying the A, B, C, and D matrices. This approach efficiently handles systems with multiple inputs and outputs simultaneously.

Simulation Implementation System Definition: First, determine the system's state matrix (A), input matrix (B), output matrix (C), and direct transmission matrix (D). These matrices form the mathematical foundation for the MIMO system representation. Input Signal Design: Common input signals include step responses, impulse signals, or custom random signals designed to test the system's dynamic characteristics. MATLAB's Signal Processing Toolbox offers functions like `stepfun` and `impulse` for standardized input generation. Simulation Execution: Use the `lsim` function to perform time-domain simulations of MIMO systems, analyzing output responses under different input conditions. The function syntax `lsim(sys,U,T)` simulates the system response to input U over time vector T, providing comprehensive response data for analysis.

Extended Analysis Beyond basic simulation, MATLAB supports frequency-domain analysis (such as Bode plots and Nyquist diagrams) using functions like `bode` and `nyquist`. Stability criteria analysis includes pole placement techniques and Lyapunov equation solutions via functions like `place` and `lyap`. For high-order MIMO systems, engineers can combine model reduction methods (`balred`, `modred`) or robust control approaches (`hinf`, `mu-synthesis`) to further optimize simulation results and system performance.