A Learning Method for Multivariable PID Control Synthesis Based on Estimated Plant Jacobian

Despite decades of research involving optimal control of multivariable systems, such controllers require accurate linear models of the plant dynamics. Real systems contain nonlinearities and high-order dynamics that may be difficult to model using conventional techniques. This paper presents a novel learning control (LC) method for PID controllers that doesn't require explicit modeling of the plant dynamics. This method utilizes gradient descent techniques to iteratively reduce an error-related objective function. Simulations involving a hydrofoil catamaran show that the proposed PID-LC algorithm improves controller performance compared to LQR controllers derived from multivariable models.