Current Literature PID Controller Philosophy Not Sufficient for Helicopter Dynamics and Control: Our Proposed Convex Stability Controller is Necessary

In this paper, we apply the recently introduced Convex Stability concept (as opposed to Hurwitz stability and Schur Stability) of Linear Systems to the Helicopter Dynamics and Control problem, which is of high interest to India’s National Aeronautical Laboratory (NAL) and Hindustan Aeronautics Ltd (HAL) type organizations. In this new, highly innovative approach, the current literature linear algebra dictated eigenvalue based, Transformation Compliant (TC) approaches such as the Routh-Hurwitz criterion and Lyapunov function criterion are discarded and a new Convex Stability concept, inspired by the Phase Variable Allergic (PVA) and Transformation Allergic (TA) Philosophies, is used without needing eigenvalues at all for the controller design. This new TA Convex Stability concept thus results in not only significant cost savings but proves that the current literature Proportional plus Integral and Derivative (PID) control design approach is not even sufficient for the All Real State Variable Convergence (i.e.Convex Stability) of any linear system. Application of our Convex Stability concept to helicopter dynamics and control clearly demonstrates the superiority of controllers designed for convex stability versus those designed based on PID philosophy.