Optimal control of ankle joint moment: Toward unsupported standing in paraplegia

This paper considers part of the problem of how to provide unsupported standing for paraplegics by feedback control. In this work our overall objective is to stabilize the subject by stimulation only of his ankle joints while the other joints are braced, Here, we investigate the problem of ankle joint moment control. The ankle plantarflexion muscles are first identified with pseudorandom binary sequence (PRBS) signals, periodic sinusoidal signals, and twitches. The muscle is modeled in Hammerstein form as a static recruitment nonlinearity followed by a linear transfer function. A linear-quadratic-Gaussian (LQG)-optimal controller design procedure for ankle joint moment was proposed based on the polynomial equation formulation, The approach was verified by experiments in the special Wobbler apparatus with a neurologically intact subject, and these experimental results are reported. The controller structure is formulated in such a way that there are only two scalar design parameters, each of which has a clear physical interpretation. This facilitates fast controller synthesis and tuning in the laboratory environment. Experimental results show the effects of the controller tuning parameters: the control weighting and the observer response time, which determine closed-loop properties. Using these two parameters the tradeoff between disturbance rejection and measurement noise sensitivity can be straightforwardly balanced while maintaining a desired speed of tracking. The experimentally measured reference tracking, disturbance rejection, and noise sensitivity are good and agree with theoretical expectations

Integral MRAC with Minimal Controller Synthesis and bounded adaptive gains: The continuous-time case

Model reference adaptive controllers designed via the Minimal Control Synthesis (MCS) approach are a viable solution to control plants affected by parameter uncertainty, unmodelled dynamics, and disturbances. Despite its effectiveness to impose the required reference dynamics, an apparent drift of the adaptive gains, which can eventually lead to closed-loop instability or alter tracking performance, may occasionally be induced by external disturbances. This problem has been recently addressed for this class of adaptive algorithms in the discrete-time case and for square-integrable perturbations by using a parameter projection strategy [1]. In this paper we tackle systematically this issue for MCS continuous-time adaptive systems with integral action by enhancing the adaptive mechanism not only with a parameter projection method, but also embedding a s-modification strategy. The former is used to preserve convergence to zero of the tracking error when the disturbance is bounded and L2, while the latter guarantees global uniform ultimate boundedness under continuous L8 disturbances. In both cases, the proposed control schemes ensure boundedness of all the closed-loop signals. The strategies are numerically validated by considering systems subject to different kinds of disturbances. In addition, an electrical power circuit is used to show the applicability of the algorithms to engineering problems requiring a precise tracking of a reference profile over a long time range despite disturbances, unmodelled dynamics, and parameter uncertainty.Postprint (author's final draft

Feedback control of unsupported standing in paraplegia. Part I: optimal control approach

This is the first of a pair of papers which describe an investigation into the feasibility of providing artificial balance to paraplegics using electrical stimulation of the paralyzed muscles. By bracing the body above the shanks, only stimulation of the plantarflexors is necessary. This arrangement prevents any influence from the intact neuromuscular system above the spinal cord lesion. Here, the authors extend the design of the controllers to a nested-loop LQG (linear quadratic Gaussian) stimulation controller which has ankle moment feedback (inner loops) and inverted pendulum angle feedback (outer loop). Each control loop is tuned by two parameters, the control weighting and an observer rise-time, which together determine the behavior. The nested structure was chosen because it is robust, despite changes in the muscle properties (fatigue) and interference from spasticity

Robust H8 design for resonant control in a CVCF inverter application over load uncertainties

CVCF (constant voltage, constant frequency) inverters are electronic devices used to supply AC loads from DC storage elements such as batteries or photovoltaic cells. These devices are used to feed different kinds of loads; this uncertainty requires that the controller fulfills robust stability conditions while keeping required performance. To address this, a robust H8 design is proposed based on resonant control to track a pure sinusoidal voltage signal and to reject the most common harmonic signals in a wide range of loads. The design is based on the definition of performance bounds in error signal and weighting functions for covering most uncertainty ranges in loads. Experimentally, the H8 controller achieves high-quality output voltage signal with a total harmonic distortion less than 2%Peer ReviewedPostprint (published version

A survey on fractional order control techniques for unmanned aerial and ground vehicles

In recent years, numerous applications of science and engineering for modeling and control of unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) systems based on fractional calculus have been realized. The extra fractional order derivative terms allow to optimizing the performance of the systems. The review presented in this paper focuses on the control problems of the UAVs and UGVs that have been addressed by the fractional order techniques over the last decade

Vibration suppression in multi-body systems by means of disturbance filter design methods

This paper addresses the problem of interaction in mechanical multi-body systems and shows that subsystem interaction can be considerably minimized while increasing performance if an efficient disturbance model is used. In order to illustrate the advantage of the proposed intelligent disturbance filter, two linear model based techniques are considered: IMC and the model based predictive (MPC) approach. As an illustrative example, multivariable mass-spring-damper and quarter car systems are presented. An adaptation mechanism is introduced to account for linear parameter varying LPV conditions. In this paper we show that, even if the IMC control strategy was not designed for MIMO systems, if a proper filter is used, IMC can successfully deal with disturbance rejection in a multivariable system, and the results obtained are comparable with those obtained by a MIMO predictive control approach. The results suggest that both methods perform equally well, with similar numerical complexity and implementation effort

Optimal Universal Controllers for Roll Stabilization

Roll stabilization is an important problem of ship motion control. This problem becomes especially difficult if the same set of actuators (e.g. a single rudder) has to be used for roll stabilization and heading control of the vessel, so that the roll stabilizing system interferes with the ship autopilot. Finding the "trade-off" between the concurrent goals of accurate vessel steering and roll stabilization usually reduces to an optimization problem, which has to be solved in presence of an unknown wave disturbance. Standard approaches to this problem (loop-shaping, LQG, $H_{\infty}$-control etc.) require to know the spectral density of the disturbance, considered to be a \colored noise". In this paper, we propose a novel approach to optimal roll stabilization, approximating the disturbance by a polyharmonic signal with known frequencies yet uncertain amplitudes and phase shifts. Linear quadratic optimization problems in presence of polyharmonic disturbances can be solved by means of the theory of universal controllers developed by V.A. Yakubovich. An optimal universal controller delivers the optimal solution for any uncertain amplitudes and phases. Using Marine Systems Simulator (MSS) Toolbox that provides a realistic vessel's model, we compare our design method with classical approaches to optimal roll stabilization. Among three controllers providing the same quality of yaw steering, OUC stabilizes the roll motion most efficiently

Advances In Internal Model Principle Control Theory

In this thesis, two advanced implementations of the internal model principle (IMP) are presented. The first is the identification of exponentially damped sinusoidal (EDS) signals with unknown parameters which are widely used to model audio signals. This application is developed in discrete time as a signal processing problem. An IMP based adaptive algorithm is developed for estimating two EDS parameters, the damping factor and frequency. The stability and convergence of this adaptive algorithm is analyzed based on a discrete time two time scale averaging theory. Simulation results demonstrate the identification performance of the proposed algorithm and verify its stability. The second advanced implementation of the IMP control theory is the rejection of disturbances consisting of both predictable and unpredictable components. An IMP controller is used for rejecting predictable disturbances. But the phase lag introduced by the IMP controller limits the rejection capability of the wideband disturbance controller, which is used for attenuating unpredictable disturbance, such as white noise. A combination of open and closed-loop control strategy is presented. In the closed-loop mode, both controllers are active. Once the tracking error is insignificant, the input to the IMP controller is disconnected while its output control action is maintained. In the open loop mode, the wideband disturbance controller is made more aggressive for attenuating white noise. Depending on the level of the tracking error, the input to the IMP controller is connected intermittently. Thus the system switches between open and closed-loop modes. A state feedback controller is designed as the wideband disturbance controller in this application. Two types of predictable disturbances are considered, constant and periodic. For a constant disturbance, an integral controller, the simplest IMP controller, is used. For a periodic disturbance with unknown frequencies, adaptive IMP controllers are used to estimate the frequencies before cancelling the disturbances. An extended multiple Lyapunov functions (MLF) theorem is developed for the stability analysis of this intermittent control strategy. Simulation results justify the optimal rejection performance of this switched control by comparing with two other traditional controllers