H-infinity Feedback Controller Research Articles

Nonlinear optimal control for robotic exoskeletons with electropneumatic actuators

Nonlinear optimal control for robotic exoskeletons with electropneumatic actuators

Nonlinear Optimal Control for a PMLSG-VSC Wave Energy Conversion Unit

This article aims to treat the nonlinear control problem for the complex dynamics of a wave energy unit (WEC) that consists of a Permanent Magnet Linear Synchronous Generator (PMLSG) and a Voltage Source Converter (VSC). The article has developed a globally stable nonlinear optimal control method for this wave power generation unit. The new method avoids complicated state-space model transformations and minimizes the energy dispersion by the control loop. A novel nonlinear optimal control method is proposed for the dynamic model of a wave energy conversion system, which includes a Permanent Magnet Linear Synchronous Generator (PMLSG) serially connected with an AC/DC three-phase voltage source converter (VSC). The dynamic model of this renewable energy system is formulated and differential flatness properties are proven about it. To apply the proposed nonlinear optimal control, the state-space model of the PMLSG-VSC wave energy conversion unit undergoes an approximate linearization process at each sampling instance. The linearization procedure relies on a first-order Taylor-series expansion and involves the computation of the system’s Jacobian matrices. It takes place at each sampling interval around a temporary operating point, which is defined by the present value of the wave energy conversion unit’s state vector and by the last sampled value of the control inputs vector. An H-infinity feedback controller is designed for the linearized model of the wave energy conversion unit. To compute the feedback gains of this controller, an algebraic Riccati equation is repetitively solved at each time step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis.

Nonlinear optimal control for the multi-variable tumor-growth dynamics

The multivariable tumor-growth dynamic model has been widely used to describe the inhibition of tumor-cells proliferation under the simultaneous infusion of multiple chemotherapeutic drugs. In this article, a nonlinear optimal (H-infinity) control method is developed for the multi-variable tumor-growth model. First, differential flatness properties are proven for the associated state-space description. Next, the state-space description undergoes approximate linearization with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. The linearization process takes place at each sampling instant around a time-varying operating point which is defined by the present value of the system’s state vector and by the last sampled value of the control inputs vector. For the approximately linearized model of the system a stabilizing H-infinity feedback controller is designed. To compute the controller’s gains an algebraic Riccati equation has to be repetitively solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. Finally, the performance of the nonlinear optimal control method is compared against a flatness-based control approach.

Nonlinear optimal control for permanent magnet synchronous spherical motors

Nonlinear optimal control for permanent magnet synchronous spherical motors

A nonlinear optimal control approach for multi-DOF redundant robotic manipulators

A nonlinear optimal (H-infinity) control approach is proposed for the dynamic model of multi-DOF redundant robotic manipulators. Because of the complicated kinematics and dynamics and the high dimensionality of the state-space model of such robots, the related control problem is of elevated difficulty. In the present article, a three-link planar robotic manipulator it considered. The article’s approach relies first on approximate linearization of the state-space model of the redundant robotic manipulator, according to first-order Taylor series expansion and the computation of the related Jacobian matrices. For the approximately linearized model of the manipulator, a stabilizing H-infinity feedback controller is designed. To compute the controller’s gains an algebraic Riccati equation is solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. The proposed control method retains the advantages of typical optimal control, that is fast and accurate tracking of the reference setpoints under moderate variations of the control inputs.

Precision Motion Control of a Piezoelectric Actuator via a Modified Preisach Hysteresis Model and Two-Degree-of-Freedom H-Infinity Robust Control.

The nonlinear hysteresis phenomenon can occur in piezoelectric-driven nanopositioning systems and can lead to reduced positioning accuracy or result in a serious deterioration of motion control. The Preisach method is widely used for hysteresis modeling; however, for the modeling of rate-dependent hysteresis, where the output displacement of the piezoelectric actuator depends on the amplitude and frequency of the input reference signal, the desired accuracy cannot be achieved with the classical Preisach method. In this paper, the Preisach model is improved using least-squares support vector machines (LSSVMs) to deal with the rate-dependent properties. The control part is then designed and consists of an inverse Preisach model to compensate for the hysteresis nonlinearity and a two-degree-of-freedom (2-DOF) H-infinity feedback controller to enhance the overall tracking performance with robustness. The main idea of the proposed 2-DOF H-infinity feedback controller is to find two optimal controllers that properly shape the closed-loop sensitivity functions by imposing some templates in terms of weighting functions in order to achieve the desired tracking performance with robustness. The achieved results with the suggested control strategy show that both hysteresis modeling accuracy and tracking performance are significantly improved with average root-mean-square error (RMSE) values of 0.0107 μm and 0.0212 μm, respectively. In addition, the suggested methodology can achieve better performance than comparative methods in terms of generalization and precision.

A nonlinear optimal control approach for voltage source inverter-fed three-phase PMSMs

A nonlinear optimal control approach for voltage source inverter-fed three-phase PMSMs

Anti-disturbance control of a piezo-driven micromanipulator with a non-minimum phase

In precision micromanipulation tasks, operation accuracy and anti-disturbance performance of micromanipulators are critical. This paper presents anti-disturbance control for a piezo-driven micromanipulator with a non-minimum phase. The micromanipulator is constructed by mounting a flexible manipulator on a parallel positioning stage. The micromotion and dynamic behavior of the micromanipulator are analyzed. Then, an anti-disturbance control strategy combining H-infinity feedback control and disturbance observer-based control for a non-minimum phase is designed to reduce disturbances and ensure control accuracy. Finally, the experimental measurement and control system is built. The observed phenomena show that sinusoidal disturbances are almost eliminated and the overshoot of step disturbances is significantly reduced. In addition, the time for suppressing the step disturbance is shortened from 0.9 to 0.3 s. Experiments verify the viability of the anti-disturbance control strategy.

Nonlinear Optimal Control for the Nine-Phase Permanent Magnet Synchronous Motor

Abstract Multi-phase electric motors and in particular nine-phase permanent magnet synchronous motors (9-phase PMSMs) find use in electric actuation, traction and propulsion systems. They exhibit advantages comparing to three-phase motors because of achieving high power and torque rates under moderate variations of voltage and currents in their phases, while also exhibiting fault tolerance. In this article a novel nonlinear optimal control method is developed for the dynamic model of nine-phase PMSMs. First it is proven that the dynamic model of these motors is differentially flat. Next, to apply the proposed nonlinear optimal control, the state-space model of the nine-phase PMSM undergoes an approximate linearization process at each sampling instance. The linearisation procedure is based on first-order Taylor-series expansion and on the computation of the system’s Jacobian matrices. It takes place at each sampling interval around a temporary operating point which is defined by the present value of the system’s state vector and by the last sampled value of the control inputs vector. For the linearized model of the system an H-infinity feedback controller is designed. To compute the feedback gains of this controller an algebraic Riccati equation is repetitively solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. First it is demonstrated that the H-infinity tracking performance criterion is satisfied, which signifies robustness of the control scheme against model uncertainty and perturbations. Moreover, under mild assumptions it is also proven that the control loop is globally asymptotically stable. Additionally it is experimentally confirmed through simulation tests, that the nonlinear optimal control method achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs. Finally, to apply state estimation-based control without the need to measure the entire state vector of the nine-phase PMSM, the H-infinity Kalman Filter is used as a robust state estimator.

A nonlinear optimal control approach for underactuated offshore cranes

ABSTRACT The article proposes a nonlinear optimal control approach for the model of boom cranes being mounted on vessels. The dynamic model of the boom cranes undergoes approximate linearisation with the use of Taylor series expansion around a temporary operating point which is recomputed at each iteration of the control method. For the approximately linearised model, an H-infinity feedback controller is designed. The linearisation procedure relies on the computation of the Jacobian matrices of the state-space model of the system. For the computation of the controller's feedback gains, an algebraic Riccati equation is solved at each time step of the control method. The new nonlinear optimal control approach achieves fast and accurate tracking for all state variables of the boom cranes, under moderate variations of the control inputs. The stability properties of the control scheme are proven through Lyapunov analysis.

A Nonlinear Optimal Control Method for Attitude Stabilization of Micro-Satellites

Attitude control and stabilization of micro-satellites is a nontrivial problem due to the highly nonlinear and multivariable structure of the satellites’ state-space model. In this paper, a novel nonlinear optimal (H-infinity) control approach is developed for this control problem. The dynamic model of the satellite’s attitude dynamics undergoes first approximate linearization around a temporary operating point which is updated at each iteration of the control algorithm. The linearization process relies on first-order Taylor series expansion and on the computation of the Jacobian matrices of the state-space model of the satellite’s attitude dynamics. For the approximately linearized description of the satellite’s attitude a stabilizing H-infinity feedback controller is designed. To compute the controller’s feedback gains, an algebraic Riccati equation is solved at each time-step of the control method. The stability properties of the control scheme are proven through Lyapunov analysis. It is also demonstrated that the control method retains the advantages of linear optimal control that is fast and accurate tracking of the reference setpoints under moderate variations of the control inputs.

A nonlinear optimal control method against the spreading of epidemics

To define a vaccination policy and antiviral treatment against the spreading of viral infections a nonlinear optimal (H-infinity) control approach is proposed. Actually, because of the scarcity of the resources for treating infectious diseases in terms of vaccines, antiviral drugs and other medical facilities, there is need to implement optimal control against the epidemics deployment. In this approach, the state-space model of the epidemics dynamics undergoes first approximate linearization around a temporary operating point which is recomputed at each time-step of the control method. The linearization is based on Taylor series expansion and on the computation of the associated Jacobian matrices. Next, an optimal (H-infinity) feedback controller is developed for the approximately linearized model of the epidemics. To compute the controller’s feedback gains an algebraic Riccati equation is solved at each iteration of the control algorithm. Furthermore, the global asymptotic stability properties of the control scheme are proven through Lyapunov stability analysis. This paper’s results confirm that optimal control of the infectious disease dynamics allows for eliminating its spreading while also keeping moderate the consumption of the related medication, that is vaccines and antiviral drugs.

A Nonlinear Optimal Control Approach for Multi-DOF Brachiation Robots

This paper proposes a nonlinear optimal control approach for mulitple degrees of freedom (DOF) brachiation robots, which are often used in inspection and maintenance tasks of the electric power grid. Because of the nonlinear and multivariable structure of the related state-space model, as well as because of underactuation, the control problem of these robots is nontrivial. The dynamic model of the brachiation robots undergoes first approximate linearization with the use of Taylor series expansion around a temporary operating point which is recomputed at each iteration of the control method. For the approximately linearized model, an H-infinity feedback controller is designed. The linearization procedure relies on the Jacobian matrices of the brachiation robots’ state-space model. The proposed control method stands for the solution of the optimal control problem for the nonlinear and multivariable dynamics of the brachiation robots, under model uncertainties and external perturbations. For the computation of the controller’s feedback gains an algebraic Riccati equation is solved at each time-step of the control method. The global stability properties of the control scheme are proven through Lyapunov analysis. The new nonlinear optimal control approach achieves fast and accurate tracking for all state variables of the brachiation robots, under moderate variations of the control inputs.

Nonlinear Optimal Control for the Translational Oscillator with Rotational Actuator

In this article, the problem of nonlinear optimal (H-infinity) control for a translational oscillator with rotating actuator (TORA) system is treated. The dynamic model of a translational oscillator with rotational actuator is generated through Euler-Lagrange analysis. This model undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the computation of the associated Jacobian matrices. For the linearized state-space model of the system, a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution to the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller’s feedback gains, an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. Finally, to implement state estimation-based control without the need to measure the entire state vector of the TORA the H-infinity Kalman Filter is used as a robust state estimator.

A Nonlinear Optimal Control Approach for the Vertical Take-off and Landing Aircraft

The paper proposes a nonlinear optimal control approach for the model of the vertical take-off and landing (VTOL) aircraft. This aerial drone receives as control input a directed thrust, as well as forces acting on its wing tips. The latter forces are not perpendicular to the body axis of the drone but are tilted by a small angle. The dynamic model of the VTOL undergoes approximate linearization with the use of Taylor series expansion around a temporary operating point which is recomputed at each iteration of the control method. For the approximately linearized model, an H-infinity feedback controller is designed. The linearization procedure relies on the computation of the Jacobian matrices of the state-space model of the VTOL aircraft. The proposed control method stands for the solution of the optimal control problem for the nonlinear and multivariable dynamics of the aerial drone, under model uncertainties and external perturbations. For the computation of the controller’s feedback gains, an algebraic Riccati equation is solved at each time-step of the control method. The new nonlinear optimal control approach achieves fast and accurate tracking for all state variables of the VTOL aircraft, under moderate variations of the control inputs. The stability properties of the control scheme are proven through Lyapunov analysis.

Nonlinear Optimal Control for the Synchronization of Distributed Marine-turbine Power Generation Units

Power generation from marine-turbines offers a vast potential for raising the contribution of renewable energy sources to the electricity grid. Typically, marine-turbine power units comprise marine-turbines that receive mechanical excitation from sea currents or tidal streams and synchronous or asynchronous generators that are finally connected to the electricity grid. Due to connection to the same transmission lines, interactions between the excitations of the individual generators appear. To achieve stabilization of the generators’ functioning, as well as synchronization to the grid’s frequency the generators’ control has to compensate for such interactions. The article proposes a nonlinear optimal control approach for distributed marine-turbine power units that use synchronous generators. First, the dynamic model of the distributed power system undergoes approximate linearization around a temporary operating point which is re-computed at each time-step of the control algorithm. The linearization relies on first-order Taylor series expansion and on the computation of the associated Jacobian matrices. For the approximately linearized model of the distributed power system a stabilizing H-infinity (optimal) feedback controller is designed. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each time-step of the control method. The global stability properties of the control scheme are proven through Lyapunov analysis. The proposed control method retains the advantages of optimal control, that is fast and accurate tracking of the reference setpoints, under moderate variations of the control inputs. Among the advantages of the proposed control method one can note: (i) the presented nonlinear optimal control method has improved performance when compared against other nonlinear control schemes that one can consider for the dynamic model of the distributed marine power system (actually other control methods are neither of proven optimality, nor of proven global stability), (ii) avoids complicated state-space transformations and the related appearance of singularities in the computation of the control inputs which are applied to the nonlinear model (iii) minimizes the consumption of energy by the control system of the distributed marine-turbine generators, thus also reducing the functioning cost of such power units.

Nonlinear optimal control for the dynamics of the underactuated slosh-container system

ABSTRACT Using Euler-Lagrange analysis the state-space model of the slosh-container system is obtained. This state-space description undergoes approximate linearization with the use of Taylor series expansion and the computation of Jacobian matrices around a temporary operating point which is recomputed at each iteration of the control method. For the approximately linearized model, an H-infinity feedback controller is designed. The proposed control method stands for the solution of the nonlinear optimal control problem for the slosh-container system, under model uncertainties and external perturbations. To find the controller's feedback gains an algebraic Riccati equation is solved at each time-step of the control method. The new nonlinear optimal control approach achieves fast and accurate tracking of setpoints for all state variables of the slosh-container system, under moderate variations of the control inputs. The stability properties of the control scheme are proven through Lyapunov analysis.

A nonlinear optimal control approach for the UAV and suspended payload system

The article proposes a nonlinear optimal control approach for the UAV and suspended load system. The dynamic model of the UAV and payload system undergoes approximate linearization with the use of Taylor series expansion around a temporary operating point which recomputed at each iteration of the control method. For the approximately linearized model an H-infinity feedback controller is designed. The linearization procedure relies on the computation of the Jacobian matrices of the state-space model of the system. The proposed control method stands for the solution of the optimal control problem for the nonlinear and multivariable dynamics of the UAV and payload system, under model uncertainties and external perturbations. For the computation of the controller’s feedback gains an algebraic Riccati equation is solved at each time-step of the control method. The new nonlinear optimal control approach achieves fast and accurate tracking for all state variables of the UAV and payload system, under moderate variations of the control inputs. The stability properties of the control scheme are proven through Lyapunov analysis.

Nonlinear optimal control and synchronization for chaotic electronic circuits

To achieve control and synchronization of chaotic electronic circuits, a nonlinear optimal (H-infinity) control method is developed and is tested on Chua’s circuit. Although this electronic circuit is deterministic, for specific values of its parameters its phase diagrams may change in a random-like manner, thus exhibiting a chaotic behavior. In the article’s control approach, an approximate linearization procedure is applied first to the dynamic model of the circuit. The linearization takes place around a temporary operating point which is recomputed at each iteration of the control method. It actually uses Taylor series expansion and the computation of the system’s Jacobian matrices. At a next stage, an H-infinity feedback controller is developed for the approximately linearized model of the circuit. This controller is obtained after solving an algebraic Riccati equation at each time step of the control method. To prove the stability properties of the control scheme and the elimination of the synchronization error, Lyapunov analysis is used. The proposed control scheme is demonstrated to satisfy the H-infinity tracking performance condition, and this indicates elevated robustness against model uncertainty and external perturbations. Moreover, the global asymptotic properties of the control method are proven. Finally, under the proposed nonlinear optimal control approach, it is shown that different Chua’s circuits can get synchronized and that chaotic behavior can be replicated by them.

A Nonlinear Optimal Control Approach for Tracked Mobile Robots

The article proposes a nonlinear optimal (H-infinity) control approach for the model of a tracked robotic vehicle. The kinematic model of such a tracked vehicle takes into account slippage effects due to the contact of the tracks with the ground. To solve the related control problem, the dynamic model of the vehicle undergoes first approximate linearization around a temporary operating point which is updated at each iteration of the control algorithm. The linearization process relies on first-order Taylor series expansion and on the computation of the Jacobian matrices of the state-space model of the vehicle. For the approximately linearized description of the tracked vehicle a stabilizing H-infinity feedback controller is designed. To compute the controller’s feedback gains an algebraic Riccati equation is solved at each time-step of the control method. The stability properties of the control scheme are proven through Lyapunov analysis. It is also demonstrated that the control method retains the advantages of linear optimal control, that is fast and accurate tracking of reference setpoints under moderate variations of the control inputs.