Multivariable PID Synthesis Via a Static Output Feedback LMI

This paper proposes a new methodology to design PID controllers for multiple input multiple output (MIMO) linear time-invariant systems. First the PID control design is written as a static output feedback problem. Then, building on recent advances in static output feedback, the PID gains are obtained through a two-step procedure: solution of an algebraic Riccati equation followed by the solution of a semidefinite program, i.e, an optimization program with a linear objective function and Linear Matrix Inequality (LMI) constraints. Several examples show that the method works well in practice.