H∞ robust control design for unsupported paraplegic standing: experimental evaluation

This paper is concerned with the design of robust feedback H~-control systems for the control of the upright posture of paraplegic persons standing. While the subject stands in a special apparatus, stabilising torque at the ankle joint is generated by electrical stimulation of the paralyzed calf muscles. Since the muscles acting as actuators in this setup show a significant degree of nonlinearity, a robust H~-control design is used. The design approach is implemented in experiments with a paraplegic subject. The results demonstrate good performance and closed loop stability over the whole range of operation.

Performance analysis of the unconstrained FxLMS algorithm for active noise control

The paper analyzes the performance of the unconstrained filtered-x LMS (FxLMS) algorithm for active noise control (ANC), where we remove the constraints on the controller that it must be causal and has finite impulse response. It is shown that the unconstrained FxLMS algorithm always converges to, if stable, the true optimum filter, even if the estimation of the secondary path is not perfect, and its final mean square error is independent of the secondary path. Moreover, we show that the sufficient and necessary stability condition for the feedforward unconstrained FxLMS is that the maximum phase error of the secondary path estimation must be within 90°, which is the only necessary condition for the feedback unconstrained FxLMS. The significance of the analysis on a practical system is also discussed. Finally we show how the obtained results can guide us to design a robust feedback ANC headset.

Novel developments in process optimisation using predictive control

In industrial practice, constrained steady state optimisation and predictive control are separate, albeit closely related functions within the control hierarchy. This paper presents a method which integrates predictive control with on-line optimisation with economic objectives. A receding horizon optimal control problem is formulated using linear state space models. This optimal control problem is very similar to the one presented in many predictive control formulations, but the main difference is that it includes in its formulation a general steady state objective depending on the magnitudes of manipulated and measured output variables. This steady state objective may include the standard quadratic regulatory objective, together with economic objectives which are often linear. Assuming that the system settles to a steady state operating point under receding horizon control, conditions are given for the satisfaction of the necessary optimality conditions of the steady-state optimisation problem. The method is based on adaptive linear state space models, which are obtained by using on-line identification techniques. The use of model adaptation is justified from a theoretical standpoint and its beneficial effects are shown in simulations. The method is tested with simulations of an industrial distillation column and a system of chemical reactors.

Model predictive control using dynamic integrated system optimisation and parameter estimation (DISOPE)

DISOPE is a technique for solving optimal control problems where there are differences in structure and parameter values between reality and the model employed in the computations. The model reality differences can also allow for deliberate simplification of model characteristics and performance indices in order to facilitate the solution of the optimal control problem. The technique was developed originally in continuous time and later extended to discrete time. The main property of the procedure is that by iterating on appropriately modified model based problems the correct optimal solution is achieved in spite of the model-reality differences. Algorithms have been developed in both continuous and discrete time for a general nonlinear optimal control problem with terminal weighting, bounded controls and terminal constraints. The aim of this paper is to show how the DISOPE technique can aid receding horizon optimal control computation in nonlinear model predictive control.

A new approach for the solution of the optimal set-point tracking problem for nonlinear systems

In this paper, a discrete time dynamic integrated system optimisation and parameter estimation algorithm is applied to the solution of the nonlinear tracking optimal control problem. A version of the algorithm with a linear-quadratic model-based problem is developed and implemented in software. The algorithm implemented is tested with simulation examples.

Development and application of a novel algorithm for steady-state optimising control using dynamic information

A novel optimising controller is designed that leads a slow process from a sub-optimal operational condition to the steady-state optimum in a continuous way based on dynamic information. Using standard results from optimisation theory and discrete optimal control, the solution of a steady-state optimisation problem is achieved by solving a receding-horizon optimal control problem which uses derivative and state information from the plant via a shadow model and a state-space identifier. The paper analyzes the steady-state optimality of the procedure, develops algorithms with and without control rate constraints and applies the procedure to a high fidelity simulation study of a distillation column optimisation.

Implementation of robust hybrid feedback FxLMS active noise cancellation headset

Instability is a serious problem for acoustic Active Noise Cancellation (ANC) headsets as a result of large errors in estimating the transfer function of the plant. Typically this occurs when, for example, a wearer adjusts the headset. In this paper, the instability problem of adaptive ANC headset is addressed. To ensure stability of the whole system, we propose a hybrid solution consisting of an analog feedback loop parallel to the digital loop, and the role of the analog loop in stabilizing the headset is analyzed theoretically. Finally the methodology of implementing such a hybrid ANC headset is described in detail. The experiments carried out on the headset prototype show that the headset is robust under considerable fluctuations of the plant transfer characteristics, and has very good noise cancellation performance both for narrow-band and wide-band disturbances.

Prosthesis grasp reflex via peripheral nerve control: an in vitro study

Here we present an economical and versatile platform for developing motor control and sensory feedback of a prosthetic hand via in vitro mammalian peripheral nerve activity. In this study, closed-loop control of the grasp function of the prosthetic hand was achieved by stimulation of a peripheral nerve preparation in response to slip sensor data from a robotic hand, forming a rudimentary reflex action. The single degree of freedom grasp was triggered by single unit activity from motor and sensory fibers as a result of stimulation. The work presented here provides a novel, reproducible, economic, and robust platform for experimenting with neural control of prosthetic devices before attempting in vivo implementation.

A robust controller design method for feedback substitution schemes using genetic algorithms

Controllers for feedback substitution schemes demonstrate a trade-off between noise power gain and normalized response time. Using as an example the design of a controller for a radiometric transduction process subjected to arbitrary noise power gain and robustness constraints, a Pareto-front of optimal controller solutions fulfilling a range of time-domain design objectives can be derived. In this work, we consider designs using a loop shaping design procedure (LSDP). The approach uses linear matrix inequalities to specify a range of objectives and a genetic algorithm (GA) to perform a multi-objective optimization for the controller weights (MOGA). A clonal selection algorithm is used to further provide a directed search of the GA towards the Pareto front. We demonstrate that with the proposed methodology, it is possible to design higher order controllers with superior performance in terms of response time, noise power gain and robustness.

Real-time application of a constrained predictive controller based on dynamic neural networks with feedback linearization

This paper describes an experimental application of constrained predictive control and feedback linearisation based on dynamic neural networks. It also verifies experimentally a method for handling input constraints, which are transformed by the feedback linearisation mappings. A performance comparison with a PID controller is also provided. The experimental system consists of a laboratory based single link manipulator arm, which is controlled in real time using MATLAB/SIMULINK together with data acquisition equipment.

Coping with delays for real-time gaze control (The Fall and Rise of the Smiths Regulator)

In this paper we describe how to cope with the delays inherent in a real time control system for a steerable stereo head/eye platform. A purposive and reactive system requires the use of fast vision algorithms to provide the controller with the error signals to drive the platform. The time-critical implementation of these algorithms is necessary, not only to enable short latency reaction to real world events, but also to provide sufficiently high frequency results with small enough delays that controller remain stable. However, even with precise knowledge of that delay, nonlinearities in the plant make modelling of that plant impossible, thus precluding the use of a Smith Regulator. Moreover, the major delay in the system is in the feedback (image capture and vision processing) rather than feed forward (controller) loop. Delays ranging between 40msecs and 80msecs are common for the simple 2D processes, but might extend to several hundred milliseconds for more sophisticated 3D processes. The strategy presented gives precise control over the gaze direction of the cameras despite the lack of a priori knowledge of the delays involved. The resulting controller is shown to have a similar structure to the Smith Regulator, but with essential modifications.

Joint servoing for robust manipulator force control

An experimental and theoretical comparison is made of force control performance with different types of innerloop joint servoing techniques. The problem of disturbance rejection and sensitivity to plant dynamics variations (robustness) is addressed. Position, velocity, strain gauge derived joint torque, and current servos are designed and implemented on a specially instrumented industrial robot, and the end-effector force feedback performances achieved are compared. Joint strain derived torque servoing is found to provide the best overall robust force control performance. Experimental results of the robust hard-on-hard contact achieved with the novel force controller implementation based on joint torque sensing are provided. Conclusions are drawn on the force control performance achievable on a geared robot given the joint servoing technique.

Modal coupling in linear control systems using robust eigenstructure assignment

Eigenvalue assignment methods are used widely in the design of control and state-estimation systems. The corresponding eigenvectors can be selected to ensure robustness. For specific applications, eigenstructure assignment can also be applied to achieve more general performance criteria. In this paper a new output feedback design approach using robust eigenstructure assignment to achieve prescribed mode input and output coupling is described. A minimisation technique is developed to improve both the mode coupling and the robustness of the system, whilst allowing the precision of the eigenvalue placement to be relaxed. An application to the design of an automatic flight control system is demonstrated.

Regularization of descriptor systems by output feedback

Conditions are given under which a descriptor, or generalized state-space system can be regularized by output feedback. It is shown that under these conditions, proportional and derivative output feedback controls can be constructed such that the closed-loop system is regular and has index at most one. This property ensures the solvability of the resulting system of dynamic-algebraic equations. A reduced form is given that allows the system properties as well as the feedback to be determined. The construction procedures used to establish the theory are based only on orthogonal matrix decompositions and can therefore be implemented in a numerically stable way.

Optimal growth strategies when mortality and production rates are size-dependent

Pontryagin's maximum principle from optimal control theory is used to find the optimal allocation of energy between growth and reproduction when lifespan may be finite and the trade-off between growth and reproduction is linear. Analyses of the optimal allocation problem to date have generally yielded bang-bang solutions, i.e. determinate growth: life-histories in which growth is followed by reproduction, with no intermediate phase of simultaneous reproduction and growth. Here we show that an intermediate strategy (indeterminate growth) can be selected for if the rates of production and mortality either both increase or both decrease with increasing body size, this arises as a singular solution to the problem. Our conclusion is that indeterminate growth is optimal in more cases than was previously realized. The relevance of our results to natural situations is discussed.