An approach to exact nonlinear feedback control design employing recursive approximations and the null space

A strategy to design exact nonlinear feedback controllers based on a recursive application of approximate linearization methods is examined. The computations are algebraic and computationally simpler than solving the set of coupled nonlinear partial differential equations thereby facilitating practical symbolic computer computations enabling discernment of evolving patterns in the approximate solutions as the order of approximation increases. Utilizing the null space that appears at each step in the computations as part of the computations, a family of analytic solutions can be generated asymptotically. There are possibilities for optimizing the performance by judiciously choice of analytic solution that emerge from the selective use of the null space.

Swing Analysis and Control Research of the Space Tethered Combination in the Maneuver Process

Swing usually occurs in the maneuver process of a tethered combination, which is constituted of a platform, a tether and a target (i.e., space debris) for capture. Therefore, a dynamical model of the space tethered combination was established, based on the maneuver of the mission platform in a short time. The conditions for the three swing formations of the tethered combination were obtained according to the analysis of the dynamical model. In order to solve the swing problem, anti-swing control strategies, based on linear feedback control, approximate linearization control and variable structure control, were proposed, respectively. Furthermore, simulation results verified the correctness and effectiveness of the above strategies. To test the validity of the control strategies, a ground experiment setup was built according to the similarity of dynamics. The experimental results show that linear feedback control and approximate linearization control can suppress the in-plane and out-of-plane swing of the combination rapidly.

Nonlinear optimal control for ship propulsion systems comprising an induction motor and a drivetrain

The article proposes a nonlinear optimal [Formula: see text] control method for electric ships’ propulsion systems comprising an induction motor, a drivetrain and a propeller. The control method relies on approximate linearization of the propulsion system’s dynamic model using Taylor series expansion and on the computation of the state-space description’s Jacobian matrices. The linearization takes place around a temporary operating point which is recomputed at each time-step of the control method. For the approximately linearized model of the ship’s propulsion system, an H-infinity (optimal) feedback controller is developed. For the computation of the controller’s gains, an algebraic Riccati equation is solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis.

Nonlinear H-infinity control for switched reluctance machines

The article proposes a nonlinear H-infinity control method for switched reluctance machines. The dynamic model of the switched reluctance machine undergoes approximate linearization round local operating points which are redefined at each iteration of the control algorithm. These temporary equilibria consist of the last value of the reluctance machine’s state vector and of the last value of the control signal that was exerted on it. For the approximate linearization of the reluctance machine’s dynamics, Taylor series expansion is performed through the computation of the associated Jacobian matrices. The modelling errors are compensated by the robustness of the control algorithm. Next, for the linearized equivalent model of the reluctance machine an H-infinity feedback controller is designed. This requires the solution of an algebraic Riccati equation at each time-step of the control method. It is shown that the control scheme achieves H-infinity tracking performance, which implies maximum robustness to modelling errors and external perturbations. The stability of the control loop is proven through Lyapunov analysis.

Transfer Robustness Optimization for Urban Rail Transit Timetables

A good timetable is required to not only be efficient, but also yield effectiveness in preventing and counteracting delays. When travelling via urban rail transit networks, transferring passengers may miss their scheduled connecting train because of a feeder train delay that results in them experiencing increased travel costs. Considering that running time supplements and transfer buffer times yield different effects on the travel plans of transferring and nontransferring passengers, we formulate an expected extra travel cost (EETC) function to appropriately balance efficiency and robustness, which is then implemented in the construction of a robust transfer optimization model with the objective of minimizing the total EETC. Next, to improve the computational efficiency, we propose an approximate linearization approach for the EETC function and introduce two types of binary variables and auxiliary substitution variables to convert the nonlinear model to a mixed-integer linear model. Experimental results show that our proposed method can yield practically applicable solutions with significant reductions in both EETC and probability of missing a transfer.

Nonlinear optimal control for ship propulsion with the use of an induction motor and a drivetrain

A nonlinear optimal (H-infinity) control method is proposed for an electric ship's propulsion system that consists of an induction motor, a drivetrain and a propeller. The control method relies on approximate linearization of the propulsion system's dynamic model using Taylor-series expansion and on the computation of the state-space description's Jacobian matrices. The linearization takes place around a temporary equilibrium which is recomputed at each time-step of the control method. For the approximately linearized model of the ship's propulsion system, an H-infinity (optimal) feedback controller is developed. For the computation of the controller's gains an algebraic Riccati equation is solved at each iteration of the control algorithm.The stability properties of the control method are proven through Lyapunov analysis,

Nonlinear H-infinity control for 4-DOF underactuated overhead cranes

The article proposes a nonlinear H-infinity control method for four degrees of freedom underactuated overhead cranes. The crane’s system is underactuated because it receives only two external inputs, namely a force that allows the motion of the bridge along the x-axis and a force that allows the motion of the trolley along the y-axis. A solution to the control problem of this underactuated system is obtained by applying nonlinear H-infinity control. The dynamic model of the overhead crane undergoes approximate linearization round local operating points which are redefined at each iteration of the control algorithm. These temporary equilibria consist of the last value of the crane’s state vector and of the last value of the control signal that was exerted on it. For the approximate linearization of the system’s dynamics, a Taylor series expansion is performed through the computation of the associated Jacobian matrices. The modelling errors are compensated by the robustness of the control algorithm. Next, for the linearized equivalent model of the crane an H-infinity feedback controller is designed. This requires the solution of an algebraic Riccati equation at each iteration of the computer control program. It is shown that the control scheme achieves H-infinity tracking performance, which implies maximum robustness to modelling errors and external perturbations. The stability of the control loop is proven through Lyapunov analysis.