Sliding Mode Variable Structure Control for Linear Double Inverted Pendulum

Sliding mode variable structure control (SMC) is a nonlinear control methodology particularly effective for systems with uncertainties and disturbances. The linear double inverted pendulum represents a classic control benchmark that effectively validates the robustness and fast-response characteristics of sliding mode control.

During simulation and debugging in MATLAB environment, the first step involves establishing the dynamic model of the linear double inverted pendulum, typically using Lagrangian equations or Newtonian mechanics analysis. The core of sliding mode control lies in designing a sliding surface that ensures system states converge to this surface within finite time and subsequently slide along it toward the equilibrium point. In code implementation, this requires defining state variables (pendulum angles and cart position) and deriving the system's mathematical model through symbolic computation tools.

The critical aspect of sliding mode variable structure control is the design of switching functions, commonly implemented using sign functions or saturation functions to suppress high-frequency chattering. Through adjusting control gains and boundary layer thickness, system dynamic response and steady-state performance can be optimized. Algorithm implementation typically involves calculating the sliding surface function s=ce+x', where c represents sliding surface coefficients, and designing control law u=-k*sat(s/Φ) to handle system uncertainties.

This simulation experiment not only verifies the effectiveness of sliding mode control in complex nonlinear systems but also provides theoretical support for practical applications such as robot balance control and aerospace stabilization systems. The MATLAB code structure typically includes modules for system modeling, controller design, stability analysis, and performance visualization through plotting functions.