A SemiAnalytical Approach to Design a Fractional Order ProportionalIntegralDerivative (FOPID) Controller for a TITO Coupled Tank System In this paper, a new approach to design a fractional order proportionalintegralderivative (FOPID) controller for a TwoInput TwoOutput (TITO) coupled tank system is proposed. In the proposed approach, integral order (xcexbb) and derivative order (xc2xb5) are determined analytically in their suitable stable ranges. The remaining parameters of the controller are obtained by solving the frequency domain specifications. To approximate the fractional integral terms of the controller, Oustaloupu0027s Recursive Approximation (ORA) method is used in the stable frequency bands. To validate the proposed approach, the performances of the controller are compared with some existing controllers designed based on the same specifications. From the simulation and experimental studies, it is shown that proposed approach for designing FOPID gives better performance than the existing results.

PD based Robust Quadratic Programs for Robotic Systems In this paper, inspired by ProportionalDerivative (PD) control laws, we present a class of Control Lyapunov Function (CLF) based Quadratic Programs (QPs) for robotic systems. ProportionalDerivative (PD) control laws are independent of the robot model, however, they fail to incorporate physical constraints, such as torque saturation. On the other hand, most optimization based control design approaches ensure satisfaction of the physical constraints, but they are sensitive to errors in the robot model. The PD based Quadratic Programs (PDQPs), presented in this paper, are a first step towards bridging this gap between the PD and the optimization based controllers to bring the best of both together. We derive two versions of PDQPs: modelbased and modelfree. Furthermore, for tracking timevarying trajectories, we establish asymptotic stability for the modelbased PDQP, and ultimate boundedness for the modelfree PDQP. The performance of the PDQPs is evaluated on two robot models: a fully actuated cartpole and an underactuated 5DOF biped.