A singularity-free motion control algorithm for robot manipulators—a hybrid system approach

This paper presents the design and implementation of a singularity-free tracking algorithm for robot manipulators using a hybrid system approach. A hybrid robot motion controller is designed to ensure feasible robot motion in the neighborhood of kinematic singularities. The hybrid control system has a two-layered hierarchical structure, a discrete layer and a continuous layer. The robot workspace is partitioned into subspaces based on the singular configurations of the robot. Switching between continuous controllers is involved when the robot travels across the subspaces. With the hybrid controller, the robot can work at the vicinity of singular configurations, but also can go through and stay at the singular configurations. The stability of the hybrid system is investigated using multiple Lyapunov function theory. Experimental results have demonstrated the advantages of the hybrid robot motion control method.     

Optimal control of a nonlinear fed-batch fermentation process using model predictive approach

Bioprocesses are involved in producing different pharmaceutical products. Complicated dynamics, nonlinearity and non-stationarity make controlling them a very delicate task. The main control goal is to get a pure product with a high concentration, which commonly is achieved by regulating temperature or pH at certain levels. This paper discusses model predictive control (MPC) based on a detailed unstructured model for penicillin production in a fed-batch fermentor. The novel approach used here is to use the inverse of penicillin concentration as a cost function instead of a common quadratic regulating one in an optimization block. The result of applying the obtained controller has been displayed and compared with the results of an auto-tuned PID controller used in previous works. Moreover, to avoid high computational cost, the nonlinear model is substituted with neuro-fuzzy piecewise linear models obtained from a method called locally linear model tree (LoLiMoT).     

Design and evaluation of a model predictive vehicle control algorithm for automated driving using a vehicle traffic simulator

This paper describes the design and evaluation of a model predictive control algorithm for automated driving on a motorway using a vehicle traffic simulator. For the development of a highly automated driving control algorithm, motion planning is necessary to satisfy driving condition in various road traffic situations. There are two key issues in motion planning of automated driving vehicles. One of the key issues is how to handle potentially dangerous situations that could occur in order to guarantee the safety of vehicles. The second key issue is how to guarantee the disturbance rejection of the controller under model uncertainties and external disturbances. To improve safety with respect to the future behaviors of subject vehicles, not the current states but rather the predicted behaviors of surrounding vehicles should be considered. The desired driving mode and a safe driving envelope are determined based on the probabilistic prediction of surrounding vehicles behaviors over a finite prediction horizon. To obtain the desired steering angle and longitudinal acceleration for maintaining the subject vehicle in the safe driving envelope during a finite prediction horizon, a motion planning controller is designed based on an model predictive control (MPC) approach. The developed control algorithm has been successfully implemented on a vehicle electronic control unit (ECU). The proposed control algorithm has been evaluated on a real-time vehicle traffic simulator. The throttle, brake, and steering control inputs and the controlled vehicle behavior have been compared to those of manual driving.     

A geometric process repair model for a two-component system with shock damage interaction

In this article, the repair-replacement problem for a two-component system with shock damage interaction and one repairman is studied. Assume that component 1 will be replaced as soon as it fails, and each failure of component 1 will induce a random shock to component 2. The shock damages may be accumulative, and whenever the total shock damage equals or exceeds a given threshold Δ, component 2 fails and the system breaks down. Component 2 is repairable, and it follows a geometric process repair. Under these assumptions, we consider a replacement policy N based on the number of failures of component 2. Our problem is to determine an optimal replacement policy N* such that the average cost rate (i.e. the long-run average cost per unit time) is minimised. The explicit expression of the average cost rate is derived by the renewal reward theorem, and the optimal replacement policy can be determined analytically or numerically. The existence and uniqueness of the optimal replacement policy N* is also proved under some mild conditions. Finally, two appropriate numerical examples are provided to show the effectiveness and applicability of the theoretic results in this article.     

Optimal maintenance planning for sustainable energy efficiency lighting retrofit projects by a control system approach

The energy savings achieved by implementing energy efficiency (EE) lighting retrofit projects are sometimes not sustainable and vanish rapidly given that lamp population decays as time goes by if without proper maintenance activities. Scope of maintenance activities refers to replacements of failed lamps due to nonrepairable lamp burnouts. Full replacements of all the failed lamps during each maintenance interval contribute to a tight project budget due to the expense for the lamp failure inspections, as well as the procurement and installation of new lamps. Since neither “no maintenance” nor “full maintenance” is preferable to the EE lighting project developers (PDs), we propose to design an optimal maintenance plan that optimises the number of replacements of the failed lamps, such that the EE lighting project achieves sustainable performance in terms of energy savings whereas the PDs obtain their maximum benefits in the sense of cost–benefit ratio. This optimal maintenance planning (OMP) problem is aptly formulated as an optimal control problem under control system framework, and solved by a model predictive control (MPC) approach. An optimal maintenance plan for an EE lighting retrofit project is designed as a case study to illustrate the effectiveness of the proposed control system approach.     

Optimal design for robust control of uncertain flexible joint manipulators: a fuzzy dynamical system approach

A novel fuzzy dynamical system approach to the control design of flexible joint manipulators with mismatched uncertainty is proposed. Uncertainties of the system are assumed to lie within prescribed fuzzy sets. The desired system performance includes a deterministic phase and a fuzzy phase. First, by creatively implanting a fictitious control, a robust control scheme is constructed to render the system uniformly bounded and uniformly ultimately bounded. Both the manipulator modelling and control scheme are deterministic and not IF-THEN heuristic rules-based. Next, a fuzzy-based performance index is proposed. An optimal design problem for a control design parameter is formulated as a constrained optimisation problem. The global solution to this problem can be obtained from solving two quartic equations. The fuzzy dynamical system approach is systematic and is able to assure the deterministic performance as well as to minimise the fuzzy performance index.     

Path-based approach to integrated planning and control for robotic systems: A path-based approach provides an analytical integration of robot planning and control. As a result, the task level control can be achieved, and the system is capable of coping with unexpected or uncertain events

Our newly developed event-based planning and control theory is applied to robotic systems. It Introduces a suitable action or motion reference variable other than time, but directly related to the desired and measurable systems output, called event. Here the event is the length of the path tracked by a robot. It enables the construction of an integrated planning and control system where planning becomes a real-time closed-loop process. The path-based integration planning and control scheme is exemplified by a single-arm tracking problem. Time and energy optimal motion plans combined with nonlinear feedback control are derived in closed form. To the best of our knowledge, this closed-form solution was not obtained before. The equivalence of path-based and time-based representations of nonlinear feedback control is shown, and an overall system stability criterion has also been obtained. The application of event-based integrated planning and control provides the robotic systems the capability to cope with unexpected and uncertain events in real time, without the need for replanning. The theoretical results are illustrated and verified by experiments.     

Coupling geometric analysis and viability theory for system exploration: Application to a living food system

This paper addresses the issue of studying a food complex system in a reverse engineering manner with the aim of identifying the set of all possible actions that makes it reach a quality target with respect to manufacturing constraints. Once the set of actions is identified, several criteria can be considered to identify interesting trajectories and control policies. A viability approach, coupling the viability theory and a geometric approach of robustness, is proposed to study complex dynamical systems. It can be implemented for several types of systems, from linear to non linear or hybrid systems. The proposed framework was adapted to a living food system: a ripening model of Camembert cheese to identify the set of states and actions (capture basin) from which it is possible to reach a predefined quality target. Within the set of viable trajectories, particular trajectories that improve the Camembert cheese ripening process are identified using the proposed approach. The results are applied at a pilot scale and are discussed in this paper.     

Optimal control design for time-varying catalytic reactors: a Riccati equation-based approach

The linear quadratic (LQ) optimal control problem is studied for a partial differential equation model of a time-varying catalytic reactor. First, the dynamical properties of the linearised model are studied. Next, an LQ-control feedback is computed by using the corresponding operator Riccati differential equation, whose solution can be obtained via a related matrix Riccati partial differential equation. Finally, the designed controller is applied to the non-linear reactor system and tested numerically.     

Distributed guaranteed cost control for aperiodic sampled-data networked interconnected systems: a switched system approach

This paper investigates the distributed guaranteed cost control problem for a class of networked interconnected control systems (NICSs) under aperiodic sampling. The NICSs with missing data and time-varying delay are modelled as an aperiodic sampled-data switched system with uncertainties. Then, sufficient conditions ensuring the exponential stability and guaranteed cost quadratic performance are presented by using the average dwell time approach. The distributed state feedback controller is designed by solving a set of LMIs. Finally, a simulation example is given to verify the effectiveness of the proposed method.     

A fuzzy inference system for pump failure diagnosis to improve maintenance process: The case of a petrochemical industry

Pump operating problems may be either hydraulic or mechanical and there is interdependence between the failure diagnoses of these two categories. Consequently, a correct diagnosis of a pump failure needs to consider many symptoms and hydraulic or mechanical causes. But, due to nonlinear, time-varying behavior and imprecise measurement information of the systems it is difficult to deal with pumps failures with precise mathematical equations, while human operators with the aid of their practical experience can handle these complex situations, with only a set of imprecise linguistic if-then rules and imprecise system state, but this procedure is time consuming and needs the knowledge of human experts and experienced maintenance personnel. The purpose of this study is to provide a correct and timely diagnosis mechanism of pump failures by knowledge acquisition through a fuzzy rule-based inference system which could approximate human reasoning. The proposed fuzzy inference system by: (1) reduction of human error, (2) reduction of repair time (3) creation of expert knowledge which could be used for training (4) reduction of unnecessary expenditures for upgrades and finally, (5) reduction of maintenance costs, will improve the maintenance process. The novelty of this work is the knowledge acquisition (the extraction of linguistic rules) through the interactive impact of the critical failure modes on the both hydraulic and mechanical operating parameters including flow rate, discharge pressure, NPSHR (Net Positive Suction Head Required), BHP (Brake Horse Power), efficiency, vibration and temperature. The proposed approach is tested and applied to a petrochemical industry.     

Impact of a system of material points against an absolutely rigid obstacle: A model for its impulsive action

The impact of a system of elastically linked material points against an absolutely rigid obstacle is analytically described and limit to an elastic homogeneous rod is studied.     

Beyond equidistant sampling for performance and cost: A loop‐shaping approach applied to a motion system

Nonequidistant sampling potentially enhances the performance/cost trade‐off that is present in traditional equidistant sampling schemes. The aim of this paper is to develop a systematic feedback control design approach for systems that go beyond equidistant sampling. A loop‐shaping design framework for such nonequidistantly sampled systems is developed that addresses both stability and performance. The framework only requires frequency response function measurements of the LTI system, whereas it appropriately addresses the linear periodically time‐varying behavior introduced by the nonequidistant sampling. Experimental validation on a motion system demonstrates the superiority of the design framework for nonequidistantly sampled systems compared to traditional designs that rely on equidistant sampling.     

A pseudo‐stochastic approach for optimal decision making under limited information: a case of an aggregate production system

In this study, which is both analytical and numerical, we compute the effective information horizon (EIH), i.e., the minimal time interval over which future information is relevant for optimal control and for measuring the performance of a single part‐type production system. Optimal control modeling and process solving, which consider aspects of decision making with limited forecast, are exemplified by a single part‐type production system. Specifically, the analysis reveals practical situations in which there is both a performance loss as well as feasibility violation when only information expected within the planning horizon is considered. The analysis is carried out by developing a pseudo‐stochastic model. We follow previous “pseudo‐stochastic” approaches that solve stochastic control problems by using deterministic, optimal control methods. However, we model the expected influences of all future events, including those that are beyond the planning horizon, as encapsulated by their density functions and not only by their mean values.     

Optimal control of a deterministic multiclass queuing system for which several queues can be served simultaneously

We consider the optimal control problem of emptying a deterministic single server multiclass queuing system without arrivals. We assume that the server is able to serve several queues simultaneously, each at its own rate, independent of the number of queues being served.We show that the optimal sequence of modes is ordered by the rate of cost decrease. However, queues are not necessarily emptied. We propose a dynamic programming approach for solving the problem, which reduces the multi-parametric QP (mpQP) to a series of problems that can be solved readily.     

Prescribed performance adaptive neural output control for a class of switched nonstrict‐feedback nonlinear time‐delay systems: State‐dependent switching law approach

This paper investigates the tracking problem for a class of uncertain switched nonlinear delayed systems with nonstrict‐feedback form. To address this problem, by introducing a new common Lyapunov function (CLF), an adaptive neural network dynamic surface control is proposed. The state‐dependent switching rule is designed to orchestrate which subsystem is active at each time instance. In order to compensate unknown delay terms, an appropriate Lyapunov‐Krasovskii functional is considered in the constructing of the CLF. In addition, a novel switched neural network–based observer is constructed to estimate system states through the output signal. To maintain the tracking error performance within a predefined bound, a prescribed performance bound approach is employed. It is proved that by the proposed output‐feedback control, all the signals of the closed‐loop system are bounded under the switching law. Moreover, the transient and steady‐state tracking performance is guaranteed by the prescribed performance bound. Finally, the effectiveness of the proposed method is illustrated by two numerical and practical examples.