H-infinity Tracking Performance Research Articles

Nonlinear optimal control for robotic exoskeletons with electropneumatic actuators

Nonlinear optimal control for robotic exoskeletons with electropneumatic actuators

Differential flatness properties and multivariable adaptive fuzzy control of hormonal system dynamics

Computer-based control for hormonal (ovarian) system dynamics and for administering in a computationally optimized manner the associated pharmaceutical treatment has been little investigated up to now. Although there has been prior work on the modeling of the ovarian system dynamics and its stability features, there have been hardly any results for applying to the ovarian system exogenous computer-based control. This is due to the complexity, nonlinearity and the high dimensionality of this system. Actually, the ovarian system exhibits nonlinear dynamics which is modeled by a set of thirteen coupled nonlinear differential equations, while receiving only two control inputs. Besides, the fact that the parameters of the model cannot be precisely identified and the fact that any mathematical model for such a biosystem is likely to be subjected to uncertainties and external perturbations, make the application of model-based control schemes for this system be questionable. To overcome this, the paper proposes model-free adaptive fuzzy control based on differential flatness theory for the complex dynamics of the ovarian system. It is proven that the dynamic model of the ovarian system, having as state variables the LH and the FSH hormones and their derivatives, is a differentially flat one. This means that all its state variables and its control inputs can be written as differential functions of the flat output and its derivatives. By exploiting differential flatness properties the system's dynamic model is written in the multivariable linear canonical (Brunovsky) form, for which the design of a state feedback controller becomes possible. After this transformation, the new control inputs of the system contain unknown nonlinear parts, which are identified with the use of neurofuzzy approximators. Lyapunov stability analysis shows that H-infinity tracking performance is achieved for the feedback control loop and this assures improved robustness to the aforementioned model uncertainty as well as to external perturbations.

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

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.

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.

Adaptive H-infinity tracking control for microgyroscope

An adaptive H-infinity tracking control is proposed for a z-axis microgyroscope with system nonlinearities. All the signals can be guaranteed in a bounded range, and tracking error is uniformly ultimately bounded, an H-infinity tracking performance is also achieved to a prescribed level. Adaptive control methodology is integrated with H-infinity control technique to achieve robust adaptive control, and adaptive algorithm is used to estimate the unknown system parameters. Simulation studies for microgyroscope are conducted to prove the validity of the proposed control scheme with good performance and robustness.

Nonlinear optimal control of autonomous submarines’ diving

The article presents a nonlinear H-infinity (optimal) control approach for the problem of the control of the depth and heading angle of an autonomous submarine. This is a multivariable nonlinear control problem and its solution allows for precise underwater navigation of the submarine. The submarine’s dynamic model undergoes approximate linearization around a temporary equilibrium that is recomputed at each iteration of the control algorithm. The linearization procedure is based on Taylor series expansion and on the computation of the submarine’s model Jacobian matrices. For the approximately linearized model, the optimal control problem is solved through the design of an H-infinity feedback controller. The computation of the controller’s gain requires the solution of an algebraic Riccati equation, which is performed at each time-step of the control method. The global stability of the control scheme is proven through Lyapunov analysis. First, it is demonstrated that for the submarine’s control loop, the H-infinity tracking performance criterion holds. Moreover, under moderate conditions, it is shown that the control scheme is globally asymptotically stable.

A Nonlinear H-infinity Control Approach for Autonomous Truck and Trailer Systems

A nonlinear optimal control method is developed for autonomous truck and trailer systems. Actually, two cases are distinguished: (a) a truck and trailer system that is steered by the front wheels of its truck, (b) an autonomous fire-truck robot that is steered by both the front wheels of its truck and by the rear wheels of its trailer. The kinematic model of the autonomous vehicles undergoes linearization through Taylor series expansion. The linearization is computed at a temporary operating point that is defined at each time instant by the present value of the state vector and the last value of the control inputs vector. The linearization is based on the computation of Jacobian matrices. The modeling error due to approximate linearization is considered to be a perturbation that is compensated by the robustness of the control scheme. For the approximately linearized model of the autonomous vehicles an H-infinity feedback controller is designed. This requires the solution of an algebraic Riccati equation at each iteration of the control algorithm. The stability of the control loop is confirmed through Lyapunov analysis. It is shown that the control loop exhibits the H-infinity tracking performance which implies elevated robustness against modeling errors and external disturbances. Moreover, under moderate conditions the global asymptotic stability of the control loop is proven. Finally, to implement state estimation-based control for the autonomous vehicles, through the processing of a small number of sensor measurements, the H-infinity Kalman Filter is proposed.

Nonlinear optimal control for the inertia wheel inverted pendulum

ABSTRACTDue to underactuation and nonlinearities, the control of the inertia wheel inverted pendulum is a non-trivial problem. The article proposes a nonlinear optimal control approach for the inertia wheel inverted pendulum. First, the dynamic model of the pendulum undergoes approximate linearisation around a temporary operating point which is recomputed at each time-step of the control method. The linearisation procedure makes use of first-order Taylor series expansion and requires the computation of the system’s Jacobian matrices. For the approximately linearised model of the pendulum, a stabilising H-infinity feedback controller is designed. 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 scheme are proven through Lyapunov analysis. It is demonstrated that the control method satisfies the H-infinity tracking performance criterion, which signifies robustness against model uncertainty and external perturbations. Next, it is proven that the control loop is globally asymptotically stable. The nonlinear optimal 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 input.

Nonlinear H-infinity control for switched reluctance machines

AbstractThe 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.

Nonlinear optimal control for the synchronization of biological neurons under time-delays.

The article proposes a nonlinear optimal control method for synchronization of neurons that exhibit nonlinear dynamics and are subject to time-delays. The model of the Hindmarsh-Rose (HR) neurons is used as a case study. The dynamic model of the coupled HR neurons undergoes approximate linearization around a temporary operating point which is recomputed at each iteration of the control method. The linearization procedure relies on Taylor series expansion of the model and on computation of the associated Jacobian matrices. For the approximately linearized model of the coupled HR neurons an H-infinity controller is designed. For the selection of the controller's feedback gain an algebraic Riccati equation is repetitively solved at each time-step of the control algorithm. The stability properties of the control loop are proven through Lyapunov analysis. First, it is shown that the H-infinity tracking performance criterion is satisfied. Moreover, it is proven that the control loop is globally asymptotically stable.

Nonlinear H-infinity control for underactuated systems: the Furuta pendulum example

The article applies nonlinear optimal (H-infinity) control to underactuated robotic systems using as a case study Furuta’s pendulum. The pendulum’s dynamic model is first transformed to an equivalent form after applying partial feedback linearization. The later description of the pendulum’s dynamics undergoes approximate linearization which takes place round a temporary operating point (equilibrium) recomputed at each iteration of the control algorithm. The linearization makes use of Taylor series expansion of the state-space model of the system and needs computation of the associated Jacobian matrices. For the approximately linearized model of the pendulum an H-infinity feedback controller is developed. The controller’s gain is computed through the repetitive solution of an algebraic Riccati equation which is also performed at each step of the control method. The stability analysis is based on Lyapunov’s method. First it is shown that the control loop satisfies the H-infinity tracking performance condition. Next, under moderate conditions it is also shown that the global asymptotic stability of the control loop can be assured.

A Nonlinear H-Infinity Control Approach for Three-Phase Voltage Inverters

The article proposes a nonlinear H-infinity (optimal) control approach to the problem of control of three-phase inverters. The dynamic model of the three-phase inverter undergoes approximate linearization, round a local operating point. This local equilibrium is re-calculated at each time instant and consists of the present value of the state vector of the inverter and of the last value of the control input that was exerted on it. The linearization is based on Taylor series expansion and the computation of the associated Jacobian matrices. The modelling error due to truncation of higher order terms from this expansion is compensated by the robustness of the control scheme. Next, an H-infinity feedback controller is designed. The feedback gain is computed after solving an algebraic Riccati equation at each iteration of the control algorithm. Through Lyapunov stability analysis it is proven that the control loop satisfies an H-infinity tracking performance criterion, which signifies elevated robustness to model uncertainty and external perturbations. Moreover, under moderate conditions the global asymptotic stability of the control loop is proven.

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.

A Nonlinear H-Infinity Approach to Optimal Control of PEM Fuel Cells

A new nonlinear H-infinity control approach is applied to PEM fuel cells. First, the dynamic model of the PEM fuel cells undergoes approximate linearisation, through Taylor series expansion, round local operating points which are defined at each time instant by the present value of the system's state vector and the last value of the control input that was exerted on it. The linearisation procedure requires the computation of Jacobian matrices at the aforementioned operating points. The modelling error, which is due to the truncation of higher order terms in the Taylor series expansion is perceived as a perturbation that should be compensated by the robustness of the control loop. Next, for the linearized equivalent model of the PEM fuel cells, an H-infinity feedback control loop is designed. This approach, is based on the concept of a differential game that takes place between the control input (which tries to minimize the deviation of the state vector from the reference setpoints) and the disturbance input (that tries to maximize it). In such a case, the computation of the optimal control input requires the solution of an algebraic Riccati equation at each iteration of the control algorithm. The known robustness properties of H-infinity control enable compensation of model uncertainty and rejection of the perturbation terms that affect the PEM fuel cells system. The stability of the control loop is proven through Lyapunov analysis. Actually, it is shown that H-infinity tracking performance is succeeded, while conditionally the asymptotic stability of the control loop is also demonstrated. The efficiency of the proposed control scheme for the PEM fuel cells model is further confirmed through simulation experiments.

A Nonlinear Optimal Control Approach of Insulin Infusion for Blood Glucose Levels Regulation

The article proposes a nonlinear optimal control method for the administered infusion of insulin, aiming at regulation of patients’ blood glucose levels. The dynamic model of blood glucose concentration which receives as control input the insulin’s infusion rate, undergoes approximate linearization through Taylor series expansion and through the computation of the associated Jacobian matrices. The linearization takes place round a temporary equilibrium which is updated at each iteration of the control method and which is defined by the last value of the system’s state vector and the last value of the control inputs vector exerted on it. For the linearized model, a robust H-infinity feedback controller is designed. To find the feedback control gain of the controller, an algebraic Riccati equation is solved at each iteration of the control algorithm. Through Lyapunov stability analysis it is first proven that the control loop satisfies the H-infinity tracking performance criterion, which signifies elevated robustness to model uncertainty and external perturbations. Moreover, the global asymptotic stability of the control loop is proven. The proposed control method can contribute to the treatment of diabetes patients and to blood glucose levels regulation in patients of intensive care units.

Nonlinear Optimal Control of Oxygen and Carbon Dioxide Levels in Blood

Nonlinear H-infinity control is proposed for the regulation of the levels of oxygen and carbon dioxide in the blood of patients undergoing heart surgery and extracorporeal blood circulation. The levels of blood gases are administered through a membrane oxygenator and the control inputs are the externally supplied oxygen and the aggregate gas supply (oxygen plus nitrogen). The proposed control method is based on linearization of the oxygenator’s dynamical model through Taylor series expansion and the computation of Jacobian matrices. The local linearization points are defined by the present value of the oxygenator’s state vector and the last value of the control input that was exerted on this system. The modelling errors due to linearization are considered as disturbances which are compensated by the robustness of the control loop. Next, for the linearized model of the oxygenator an H-infinity control input is computed at each iteration of the control algorithm through the solution of an algebraic Riccati equation. With the use of Lyapunov stability analysis it is demonstrated that the control scheme satisfies the H-infinity tracking performance criterion, which signifies improved robustness against modelling uncertainty and external disturbances. Moreover, under moderate conditions the asymptotic stability of the control loop is also proven. To estimate non-measurable state vector elements of the oxygenator the H-infinity Kalman Filter is proposed and thus state estimation-based control is also applied. The efficient performance of the control scheme is confirmed through simulation experiments.

Nonlinear H-infinity control of multi-phase electric machines

Abstract: The use of multi-phase electric machines exhibits specific advantages such as increased power comparing to the three-phase machines and robustness to failures. In this paper, the dynamic model of the 6-phase synchronous electric machine undergoes first an approximate linearisation, through Taylor series expansion. The linearization is performed round local operating points which are defined at each time instant by the present value of the system’s state vector and the last value of the control input that was exerted on it. The linearisation procedure requires the computation of Jacobian matrices at the aforementioned operating points. The modelling error, which is due to the truncation of higher order terms in the Taylor series expansion is perceived as a perturbation that should be compensated by the robustness of the control loop. Next, for the linearized equivalent model of the 6-phase synchronous electric machine, an H-infinity feedback control loop is designed. This approach, is based on the concept of a differential game that takes place between the control input (which tries to minimize the deviation of the state vector from the reference setpoints) and the disturbance input (that tries to maximize it). In such a case, the computation of the optimal control input requires the solution of an algebraic Riccati equation at each iteration of the control algorithm. The known robustness properties of H-infinity control enable compensation of model uncertainty and rejection of the perturbation terms that affect the 6-phase synchronous machine. The stability of the control loop is proven through Lyapunov analysis. Actually, it is shown that H-infinity tracking performance is succeeded, while conditionally the asymptotic stability of the control loop is also assured. The efficiency of the proposed control scheme for the 6-phase synchronous machine is further confirmed through simulation experiments.

Adaptive Neural LMI-Based H-Infinity Control for MEMS Gyroscope

A novel adaptive radial basis function neural network H-infinity control strategy with robust feedback compensator using linear matrix inequality (LMI) approach is proposed for micro electro mechanical systems vibratory gyroscopes involving parametric uncertainties and external disturbances. The proposed system is comprised of a neural network controller, which is designed to mimic an equivalent control law aimed at relaxing the requirement of exact mathematical model and a robust feedback controller, which is derived to eliminate the effect of modeling error and external disturbances. Based on the Lyapunov stability theorem, it is shown that H-infinity tracking performance of the gyroscope system can be achieved, all variables of the closed-loop system are bounded, and the effect due to external disturbances on the tracking error can be attenuated effectively. Numerical simulations are investigated to demonstrate that the satisfactory tracking performance and strong robustness against external disturbances can be obtained using the proposed adaptive neural H-infinity control strategy with robust feedback compensator by LMI technique.

An H-infinity approach to optimal control of doubly-fed reluctance machines

Abstract: An H-infinity approach is developed for the problem of nonlinear optimal control of doubly-fed reluctance machines. The dynamic model of the machines is subjected to linearization round local operating points, through Taylor series expansion and the computation of Jacobian matrices. For the linearized model an H-infinity feedback controller is designed, capable of compensating for the modelling error of the approximate linearization as well as for external perturbations affecting the machine. The computation of the feedback control gain is based on the solution of an algebraic Riccati equation that is performed at each iteration of the control algorithm. Lyapunov stability analysis for the control loop of the reluctance machine arrives at an H-infinity tracking performance criterion, and finally the asymptotic stability of the control loop is demonstrated. The excellent tracking performance of the H-infinity control method is confirmed through simulation experiments.