Feedback-feedforward Structure Research Articles

Nonlinear suboptimal tracking control of spacecraft approaching a tumbling target**Project supported by the Major Program of the National Natural Science Foundation of China (Grant Nos. 61690210 and 61690213).

We investigate the close-range relative motion and control of a spacecraft approaching a tumbling target. Unlike the traditional rigid-body dynamics with translation and rotation about the center of mass (CM), the kinematic coupling between translation and rotation is taken into consideration to directly describe the motion of the spacecraft’s sensors or devices which are not coincident with the CM. Thus, a kinematically coupled 6 degrees-of-freedom (DOF) relative motion model for the instrument (feature point) is set up. To make the chaser spacecraft’s feature point track the target’s, an optimal tracking problem is defined and a control law with a feedback-feedforward structure is designed. With quasi-linearization of the nonlinear dynamical system, the feedforward term is computed from a specified constraint about the dynamical system and the reference model, and the feedback action is derived starting from the state-dependent Ricca equation (SDRE). The proposed controller is compared with an existing suboptimal tracking controller, and numerical simulations are presented to illustrate the effectiveness and superiority of the proposed method.

Nonlinear Suboptimal Tracking Controller Design Using State-Dependent Riccati Equation Technique

In this brief, a new technique for solving a suboptimal tracking problem for a class of nonlinear dynamical systems is presented. Toward this end, an optimal tracking problem using a discounted cost function is defined and a control law with a feedback-feedforward structure is designed. A state-dependent Riccati equation (SDRE) framework is used in order to find the gains of both the feedback and the feedforward parts, simultaneously. Due to the significant properties of the SDRE technique, the proposed method can handle the presence of input saturation and state constraint. It is also shown that the tracking error converges asymptotically to zero under mild conditions on the discount factor of the corresponding cost function and the desired trajectory. Two simulation and experimental case studies are also provided to illustrate and demonstrate the effectiveness of our proposed design methodology.

Control of a non-isothermal continuous stirred tank reactor by a feedback–feedforward structure using type-2 fuzzy logic controllers

A control system that uses type-2 fuzzy logic controllers (FLC) is proposed for the control of a non-isothermal continuous stirred tank reactor (CSTR), where a first order irreversible reaction occurs and that is characterized by the presence of bifurcations. Bifurcations due to parameter variations can bring the reactor to instability or create new working conditions which although stable are unacceptable. An extensive analysis of the uncontrolled CSTR dynamics was carried out and used for the choice of the control configuration and the development of controllers. In addition to a feedback controller, the introduction of a feedforward control loop was required to maintain effective control in the presence of disturbances. Simulation results confirmed the effectiveness and the robustness of the type-2 FLC which outperforms its type-1 counterpart particularly when system uncertainties are present.

PID Control of Unstable Time-Delay Systems: Tuning and Robustness

The paper is aimed to the design of a general class of PID like linear controllers for first order systems with time delays. Several approximations for time delay were used. All of them can be covered by a second order transfer function. Then explicit PID formulas were derived for SISO systems with a feedback as well as with a feedback-feedforward structure of the controlled system. The approach is especially suitable for integrator and unstable first order time-delay systems. The proposed control synthesis is based on general solutions of diophantine equations in the ring of proper and Hurwitz stable rational functions RPH and the Youla-Kučera parametrization of controllers is utilized. The conditions for asymptotic tracking are obtained through the divisibility conditions in the ring RPH. The proposed methodology covers stable and unstable plants with time delays. Moreover, a scalar tuning parameter which influences properties of the closed-loop system has been introduced. Robustness of proposed algorithms can be studied through the infinity (H∞) norms and through the sensitivity functions of controlled systems. A Matlab + Simulink program system for automatic design and simulation has been developed. The program system is suitable for a wide engineering utilization without a deep insight into the control theory. Some simulations and Nyquist plots of unstable time-delay systems are included.