Tracking control of a two-wheeled mobile robot using input–output linearization

This paper discusses the tracking control of two-wheeled mobile robots that have more outputs than inputs. If the number of inputs and the number of outputs are not the same, the inverse of the decoupling matrix in the input–output linearization does not exist. Therefore, a modified input–output linearization method is proposed, to solve the problem by means of a generalized inverse that provides a least-squares solution. The experimental results show that the tracking of posture, position and orientation (the 3-output case) has advantages over position tracking (the 2-output case) from the viewpoint of input power efficiency, because smoother responses can be obtained by considering the orientation.     

Robust input–output linearisation using uncertainty and disturbance estimation

This article proposes a new approach to robustify an input–output linearisation controller. The robustification is achieved by estimating the uncertainties and external unmeasurable disturbances using a novel uncertainty and disturbance estimator. A significant feature of the proposed approach is that it does not need any information about the uncertainties. The stability of the system and the estimator is established. Effectiveness of the proposed approach is demonstrated through application to the wing rock motion control problem.     

Dynamics and input–output feedback linearization control of a wheeled mobile cable-driven parallel robot

In comparison to the conventional parallel robots, cable-driven parallel robots (CDPRs) have generally superior features such as simple production technology, low energy consumption, large workspace, high payload to moving weight ratio, and also low cost. On the other hand, a wheeled mobile robot (WMR) which is capable of covering a vast area can be used when no specific space is designated for the stationary accessories of a robot. In this paper, the integration of a CDPR with a WMR is proposed to overcome some of the issues related to each of these robots. The kinematic equations of the robot are presented. To derive the dynamic equations, Gibbs–Appel (G–A) formulation is used, which in contrary to the Lagrange formulation benefits from advantages of quasi-velocities over generalized coordinates as well as not requiring Lagrange multipliers. The dynamic equations of the two parts are coupled, and the interacting effects are observable from the governing equations. By considering non-holonomic wheels for the robot, internal dynamics appears in the equations. However, based on some conditions, the equations are input–output linearizable via a static feedback. The platform trajectory is designed based on the given end-effector trajectory. The effectiveness of the controller is shown through simulations and experimental tests.     

Predictor–observer-based control of systems with multiple input/output delays

This paper deals with the control of single-input–single-output linear time-delayed systems, when there are different delays in the output/input transfer function. The process can be disturbed and unstable. A new control structure is proposed, solving the problem in several steps. First, by using a stable predictor/observer the plant is stabilized, regardless the delays. On the stable plant, the multidelay plant model is considered as a single delay plant with additional disturbances. The problem of disturbance rejection is solved by using a disturbance observer approach. Finally, output tracking is achieved by a two degrees of freedom controller.     

Stability and performance analysis of linear positive systems with delays using input–output methods

It is known that input–output approaches based on scaled small-gain theorems with constant D-scalings and integral linear constraints are non-conservative for the analysis of some classes of linear positive systems interconnected with uncertain linear operators. This dramatically contrasts with the case of general linear systems with delays where input–output approaches provide, in general, sufficient conditions only. Using these results, we provide simple alternative proofs for many of the existing results on the stability of linear positive systems with discrete/distributed/neutral time-invariant/-varying delays and linear difference equations. In particular, we give a simple proof for the characterisation of diagonal Riccati stability for systems with discrete-delays and generalise this equation to other types of delay systems. The fact that all those results can be reproved in a very simple way demonstrates the importance and the efficiency of the input–output framework for the analysis of linear positive systems. The approach is also used to derive performance results evaluated in terms of the L ₁-, L ₂- and L _∞-gains. It is also flexible enough to be used for design purposes.     

A simple algorithm for training fuzzy systems using input–output data

This paper proposes a simple algorithm for training fuzzy systems from numerical data. The main advantage of the method is the lack of complicated iterative mechanisms and therefore, its implementation is carried out easily. The suggested algorithm employs a fuzzy model with simplified rules, assuming a fuzzy partition of the input space into fuzzy subspaces. The output is inferred by expanding the model into fuzzy basis functions (FBFs), where each FBF corresponds to a certain fuzzy subspace. The number of rules and the respective premise parts (fuzzy subspaces) are determined using the nearest neighbor approach. Then, the optimal consequent parameters are obtained by the least-squares method. Finally, simulations show the validity of the method.     

A linearized input–output representation of flexible multibody systems for control synthesis

In this paper, a linearized input–output representation of flexible multibody systems is proposed in which an arbitrary combination of positions, velocities, accelerations, and forces can be taken as input variables and as output variables. The formulation is based on a nonlinear finite element approach in which a multibody system is modeled as an assembly of rigid body elements interconnected by joint elements such as flexible hinges and beams. The proposed formulation is general in nature and can be applied for prototype modeling and control system analysis of mechatronic systems. Application of the theory is illustrated through a detailed model development of an active vibration isolation system for a metrology frame of a lithography machine.     

Minimal realisation of bilinear and quadratic input–output difference equations in state-space form

This article studies the realisability property of discrete-time bilinear and quadratic input–output (i/o) equations in the classical state-space form. Constraints on the parameters of the i/o model are suggested that lead to realisable models. Using new formulae for computing basis vectors of certain vector spaces of differential one-forms, we present in this article the complete list of the third- and fourth-order realisable i/o bilinear models, and a new realisable subclass of an arbitrary order is suggested. Moreover, we provide the sufficient conditions of the second- and third-order realisable i/o quadratic models, respectively. All the developed theory and algorithms are illustrated by means of several examples.     

H∞ output feedback control for large-scale nonlinear systems with time delay in both state and input

The H∞ output feedback control problem for a class of large-scale nonlinear systems with time delay in both state and input is considered in this paper. It is assumed that the interconnected nonlinearities are limited by constant multiplied by unmeasured states, delayed states and external disturbances. Different from existing methods to study the H∞ control of large-scale nonlinear systems, the static gain control technique is utilized to obtain an observer-based output feedback control strategy, which makes the closed-loop system globally asymptotically stable and attenuates the effect of external disturbances. An example is finally carried out to show the feasibility of the proposed control strategy.     

H∞ output feedback control for large-scale nonlinear systems with time delay in both state and input

The H∞ output feedback control problem for a class of large-scale nonlinear systems with time delay in both state and input is considered in this paper. It is a...     

Input–output feedback linearizing control of linear induction motor taking into consideration the end-effects. Part II: Simulation and experimental results

This is the second part of a paper, divided in two parts, dealing with the application of the input–output feedback linearization (FL) control technique to linear induction motors (LIMs).The first part has treated the theoretical formulation of the input–output feedback linearization control technique as to be applied to linear induction motors. This second part describes the set of tests, both in numerical simulations and experiments, performed to assess the validity of the control technique. In particular, it addresses the issues of the sensitivity of the FL control versus the LIM electrical parameters’ variations and the improvements achievable by considering the LIM dynamic end effects in the control formulation.The proposed FL technique has been further compared, under the same closed-loop bandwidths of the flux and speed systems, with the industrial standard in terms of high performance control technique: field oriented control (FOC).     

Robust H∞ dynamic output feedback control for spacecraft rendezvous with poles and input constraint

This paper is concerned with the output feedback control problem for spacecraft rendezvous subject to target angular velocity uncertainty and controller uncertainty, external disturbance and input constraint. A general full-order dynamic output feedback (DOF) controller is proposed. As a stepping-stone, the H_∞ performance requirement, poles and input constraint are analysed separately via linear matrix inequalities (LMIs). Then, with the obtained results, the controller design problem is cast into a convex problem subject to a set of LMI constraints through a critical change of controller variables. Furthermore, when the system states are all available, a reduced sufficient condition of the non-fragile state feedback controller is given. Compared with existing results, the designed controller has overcome the disadvantage of strictly proper DOF controller, where the initial value of the control input is zero. Besides, the constraint on poles placement is relaxed. A numerical simulation is performed to verify the effectiveness of the proposed method.     

Connectivity and the measurement of operational risk: an input–output approach

In this article I propose a framework for the analysis of the interdependencies within a financial institution that is based on the input–output framework originally developed by Leontiev (1941). After discussing the state of the art of operational risk measurement, I briefly review the foundations of input–output analysis and explain how to build an input–output model at the business unit level for a financial institution. I also discuss the suitability of an input–output model in capturing the impact on operational risk losses of the interdependencies within a financial institution and then present, through some numerical examples, how to implement the model within a quantitative framework for the measurement of operational risk. In Ersilia, to establish the relationships that sustain the city's life, the inhabitants stretch strings from the corners of the houses, white or black or gray or black-and-white according to whether they mark a relationship of blood, of trade, authority, agency. When the strings become so numerous that you can no longer pass among them, the inhabitants leave: the houses are dismantled; only the strings and their supports remain. From a mountainside, camping with their household goods, Ersilia's refugees look at the labyrinth of taut strings and poles that rise in the plain. That is the city of Ersilia still, and they are nothing. Italo Calvino, Invisible Cities (1972)     

Modeling of input–output relationships for a plasma spray coating process using soft computing tools

To automate any manufacturing process, its input–output relationships are to be known in both forward and reverse directions. The present work aims to correlate input process parameters with various responses of a plasma spray coating process. Statistical regression analysis had been carried out previously for this process based on the data collected through central composite design of experiments to establish input–output relationships in forward direction. However, the said relationships could not be accurately determined in reverse direction using the obtained regression equations due to the presence of a non-square transformation matrix. Soft computing-based approaches had been developed to model the process in both forward as well as reverse directions. The performances of the developed approaches had been tested on different cases obtained through real experiments. A comparative study had been made of these developed approaches in terms of accuracy in predictions.     

Global robust output regulation control for cascaded nonlinear systems using the internal model principle

This article considers the global robust output regulation problem via output feedback for a class of cascaded nonlinear systems with input-to-state stable inverse dynamics. The system uncertainties depend not only on the measured output but also all the unmeasurable states. By introducing an internal model, the output regulation problem is converted into a stabilisation problem for an appropriately augmented system. The designed dynamic controller could achieve the global asymptotic tracking control for a class of time-varying reference signals for the system output while keeping all other closed-loop signals bounded. It is of interest to note that the developed control approach can be applied to the speed tracking control of the fan speed control system. The simulation results demonstrate its effectiveness.     

An iterative algorithm for simulation error based identification of polynomial input–output models using multi-step prediction

Effective identification of polynomial input–output models for applications requiring long-range prediction or simulation performance relies on both careful model selection and accurate parameter estimation. The simulation error minimisation (SEM) approach has been shown to provide significant advantages in the model selection phase by ruling out candidate models with good short-term prediction capabilities but unsuitable long-term dynamics. However, SEM-based parameter estimation has been generally avoided due to excessive computational effort. This article extends to the nonlinear case a computationally efficient approach for this task, that was previously developed for linear models, based on the iterative estimation of predictors with increasing prediction horizon. Conditions for the applicability of the approach to various model classes are also discussed. Finally, some examples are provided to show the effectiveness and computational convenience of the proposed algorithm for polynomial input–output identification, as well as the improvements achievable by enforcing SEM parameter estimation. A benchmark for nonlinear identification is also analysed, with encouraging results.