An impulse-time perturbation approach for enhancing the robustness of extra-insensitive input shapers

In this paper, perturbation-based extra-insensitive input shapers (PEI-ISs) are proposed to enhance the robustness of the input shaping technique. The extra-insensitive input shaper (EI-IS) has been known to be more robust than the so-called derivative input shapers such as ZVD, ZVDD, and ZVDDD shapers. However, the robustness of the known EI-IS is restricted by the symmetric property in the sensitivity curve. To address this, the PEI-IS is devised by multiplying a series of input shapers in the Laplace domain, of which the impulse times are slightly perturbed from those of the zero vibration (ZV) shaper. For a single-hump case, a closed-form solution to the PEI-IS is provided. For two- and three-hump cases, the approximate solutions are presented. The robustness is evaluated by simulations and assessed by means of the insensitivity. It will be shown that the proposed PEI-IS does improve the robustness and that it can be easily designed.     

Command-induced vibration analysis using input shaping principles

Input shaping is a well-established technique used for reducing the vibratory response of dynamic systems. Analytical tools are available for systems utilizing input shaping. These tools aid in performance analysis by providing intuitive and computationally simple methods for determining key system attributes, such as the residual vibration in response to a command. This paper describes methods whereby arbitrary reference commands may be interpreted as input-shaped commands. This capability allows input shaping analysis tools to be used on systems without input shapers. Experimental results obtained from an industrial 10-ton bridge crane validate the theoretical developments.     

Adaptive input shaping for manoeuvring flexible structures using an algebraic identification technique

Input shaping is an efficient feedforward control technique which has motivated a great number of contributions in recent years. Such a technique generates command signals with which manoeuvre flexible structures without exciting their vibration modes. This paper presents a novel adaptive input shaper based on an algebraic non-asymptotic identification. The main characteristic of the algebraic identification in comparison with other identification methods is the short time needed to obtain the system parameters without defining initial conditions. Thus, the proposed adaptive control can update the input shaper during each manoeuvre when large uncertainties are present. Simulations illustrate the performance of the proposed method.     

Adaptive input shaping for maneuvering flexible structures

In the control of flexible structures many methods are used to reduce residual vibration due to the excitation of flexible modes. Input shaping, a feed-forward method, typically convolves the input with a sequence of impulses that are independent of the system maneuver. While reducing the residual vibration, input shaping extends the duration of the maneuver command by the length of the input shaper. This paper explores the idea of adaptive input shaping which allows a fast input shaper to be used while providing robustness to parameter uncertainty by tuning the shaper to the flexible mode frequency. The adaptive input shaping method presented can adapt between maneuvers or during maneuvers. Analysis yields a large range of convergence that is verified by simulation and shows this method to be less complex than other adaptive approaches.     

Designing feedforward command shapers with multi-objective genetic optimisation for vibration control of a single-link flexible manipulator

This paper presents investigations into the design of a command-shaping technique using multi-objective genetic optimisation process for vibration control of a single-link flexible manipulator. Conventional design of a command shaper requires a priori knowledge of natural frequencies and associated damping ratios of the system, which may not be available for complex flexible systems. Moreover, command shaping in principle causes delay in system's response while it reduces system vibration and in this manner the amount of vibration reduction and the rise time conflict one another. Furthermore, system performance objectives, such as, reduced overshoot, rise time, settling time, and end-point vibration are found in conflict with one another due to the construction and mode of operation of a flexible manipulator. Conventional methods can hardly provide a solution, for a designer-oriented formulation, satisfying several objectives and associated goals as demanded by a practical application due to the competing nature of those objectives. In such cases, multi-objective optimisation can provide a wide range of solutions, which trade-off these conflicting objectives so as to satisfy associated goals. A multi-modal command shaper consists of impulses of different amplitudes at different time locations, which are convolved with one another and then with the desired reference and then used as reference (for closed loop) or applied to system (for open loop) with the view to reduce vibration of the system, mainly at dominant modes. Multi-objective optimisation technique is used to determine a set of solutions for the amplitudes and corresponding time locations of impulses of a multi-modal command shaper. The effectiveness of the proposed technique is assessed both in the time domain and the frequency domain. Moreover, a comparative assessment of the performance of the technique with the system response with unshaped bang–bang input is presented.     

Dynamic input signal design for the identification of constrained systems

In current model predictive control (MPC) practise, the accuracy of the model from system identification is often the crucial factor for the final success. This makes the input signal design a very important step in MPC applications. Because the identification task should move the outputs within some constraints, a constrained design method is needed. Previous constrained signal design methods are usually based on the steady-state gain matrix of a process. Ignoring the system dynamics makes these designs either too conservative when the dynamics are overdamped or allows them to violate the output constraints in the case of underdamped dynamics. In order to address these problems, a new design method making use of the prior approximate estimate of the system dynamics is proposed in this paper. Furthermore, an iterative method of signal design for identification experiments is proposed, and a criterion is defined to compare the accuracy of two successive dynamic models. An example on a subsystem of the challenging Tennessee Eastman process is used to prove the effectiveness of the proposed method.     

Dynamic allocation for input redundant control systems

In this paper we address control systems with redundant actuators and characterize the concepts of weak and strong input redundancy. Based on this characterization, we propose a dynamic augmentation to a control scheme which performs the plant input allocation with the goal of employing each actuator in a suitable way, based on its magnitude and rate limits. The proposed theory is first developed for redundant plants without saturation and then extended to the case of magnitude saturation first and of magnitude and rate saturation next. Several simulation examples illustrate the proposed technique and show its advantages for practical application.     

A discrete-time approach to impulse-based adaptive input shaping for motion control without residual vibration

Modifying a command or actuation signal by convolving it with a sequence of impulses is a useful technique for eliminating structural vibration in rest-to-rest motion of mechanical systems. This paper describes an adaptive discrete-time version of this approach where amplitude and timing of impulses are tuned during operation to match the system under control. Solutions giving zero residual vibration are formulated in terms of a quadratic cost function and constructed by iterative operations on measured sets of input–output data. The versatility of the approach is demonstrated by simulated test cases involving (1) amplitude optimization of impulses with fixed timings, (2) timing optimization of impulses with fixed amplitudes and (3) combined timing and amplitude optimization. The approach is model-free and directly applicable to multi-mode systems. Moreover, fast adaptation within a single rest-to-rest maneuver can be achieved.     

A fast nonlinear control method for linear systems with input saturation

We present a novel, fast saturating nonlinear feedback law for single input systems with linear dynamics and input saturation. It is fast in the sense that it yields a better performance than a saturating linear control law. The control law is based on implicit soft variable-structure control. A convex optimization procedure for the controller synthesis based on linear matrix inequalities (LMIs) is derived at the price of some conservatism. As an example, we consider the control of a submarine.     

Composite nonlinear feedback control for linear singular systems with input saturation

This paper investigates the composite nonlinear feedback (CNF) control technique for linear singular systems with input saturation. First, a linear feedback control law is designed for the step tracking control problem of linear singular systems subject to input saturation. Then, based on this linear feedback gain, a CNF control law is constructed to improve the transient performance of the closed-loop system. By introducing a generalized Lyapunov equation, this paper develops a design procedure for constructing the CNF control law for linear singular systems with input saturation. After decomposing the closed-loop system into fast subsystem and slow subsystem, it can be shown that the nonlinear part of the CNF control law only relies on slow subsystem. The improvement of transient performance by the proposed design method is demonstrated by an illustrative example.     

Controller design for a class of nonlinear systems with input saturation using convex optimization

In this paper, we propose a new design strategy for nonlinear systems with input saturation. The resulting nonlinear controllers are locally asymptotically stabilizing the origin. The proposed methodology is based on exact feedback linearization which is used to reformulate the nonlinear system as a linear system having state-dependent input saturation. Linear saturating state feedback controllers and soft variable-structure controllers are developed based on this system formulation. The resulting convex optimization problems can be written in terms of linear matrix inequalities and sum of squares conditions for which efficient solvers exist. Polynomial approximation based on Legendre polynomials is used to extend the methodology to a more general class of nonlinear systems. To demonstrate the benefit of this design method, a stabilizing controller for a single link manipulator with flexible joint is developed.     

On reference governor in iterative learning control for dynamic systems with input saturation

Input saturation is inevitable in many engineering applications. Most existing iterative learning control (ILC) algorithms that can deal with input saturation require that the reference signal is realizable within the saturation bound. For engineering systems without precise models, it is hard to verify this requirement. In this note, a “reference governor” (RG) is introduced and is incorporated with the available ILC algorithms (primary ILC algorithms). The role of the RG is to re-design the reference signal so that the modified reference signal is realizable. Two types of the RG are proposed: one modifies the amplitude of the reference signal and the other modifies the frequency. Our main results provide design guidelines for two RGs. Moreover, a design trade-off between the convergence speed and tracking performance is also discussed. A simple simulation result verifies the effectiveness of the proposed methods.     

Identification of multi-input systems: variance analysis and input design issues

This paper examines the identification of multi-input systems. Motivated by an experiment design problem (should one excite the various inputs simultaneously or separately), we examine the effect of an additional input on the variance of the estimated coefficients of parametrized rational transfer function models, with special emphasis on the commonly used FIR, ARX, ARMAX, OE and BJ model structures. We first show that, for model structures that have common parameters in the input-output and noise models (e.g. ARMAX), any additional input contributes to a reduction of the covariance of all parameter estimates. We then show that the accuracy improvement extends beyond the case of common parameters in all transfer functions, and we show exactly which parameter estimates are improved when a new input is added. We also conclude that it is always better to excite all inputs simultaneously.     

The identification of nonlinear models for process control using tailored “plant-friendly” input sequences

This paper considers certain practical aspects of the identification of nonlinear empirical models for chemical process dynamics. The primary focus is the identification of second-order Volterra models using input sequences that offer the following three advantages: (1) they are “plant friendly;” (2) they simplify the required computations; (3) they can emphasize certain model parameters over others. To provide a quantitative basis for discussing the first of these advantages, this paper defines a friendliness index f that relates to the number of changes that occur in the sequence. For convenience, this paper also considers an additional nonlinear model structure: the Volterra–Laguerre model. To illustrate the practical utility of the input sequences considered here, second-order Volterra and Volterra–Laguerre models are developed that approximate the dynamics of a first-principles model of methyl methacrylate polymerization.     

Input shaping and time-optimal control of flexible structures

We consider the problem of minimum time input shaping and its relation to the classical time-optimal control problem. We demonstrate that some typical minimum time input shapers are equivalent to the time-optimal control of different, although related, systems. The analytical proofs are based on the optimality criteria stipulated by the Karush-Kuhn-Tucker conditions.     

Neural observer-based adaptive compensation control for nonlinear time-varying delays systems with input constraints

This paper describes a neural network state observer-based adaptive saturation compensation control for a class of time-varying delayed nonlinear systems with input constraints. An advantage of the presented study lies in that the state estimation problem for a class of uncertain systems with time-varying state delays and input saturation nonlinearities is handled by using the NNs learning process strategy, novel type Lyapunov-Krasovskii functional and the adaptive memoryless neural network observer. Furthermore, by utilizing the property of the function tan h²(?/?)/?, NNs compensation technique and backstepping method, an adaptive output feedback controller is constructed which not only efficiently avoids the problem of controller singularity and input saturation, but also can achieve the output tracking. And the proposed approach is obtained free of any restrictive assumptions on the delayed states and Lispchitz condition for the unknown nonlinear functions. The semiglobal uniform ultimate boundedness of all signals of the closed-loop systems and the convergence of tracking error to a small neighborhood are all rigorously proven based on the NN-basis function property, Lyapunov method and sliding model theory. Finally, two examples are simulated to confirm the effectiveness and applicability of the proposed approach.     

Design and validation of a desk-free and posture-independent input device

This study investigates variations in performance, postures and strains on the hand-arm-shoulder musculature during the operation of a wireless mouse, trackpad and a new input device. The device is held between the flexed index and middle fingers with the palm facing sideways. The buttons and wheels are activated by flexion and/or rolling of the thumb. Eleven males and nine females participated in the study. All subjects performed an aiming task to test the pointing and dragging functions. The results of this study reveal that the new pointing device allowed users to adopt more ergonomic postures and has the advantage of reduced muscular loadings of the upper extremities. Mean (SD) muscular activities (%RVC) using the wireless mouse, the trackpad and the new input device were as follows: trapezius: 3.0 (1.7), 4.4 (2.9) and 1.4 (1.0), and extensor carpi ulnaris: 7.3 (4.4), 14.5 (8.4) and 5.6 (3.1), respectively. The device was used in a variety of hand positions, alternatively. The size of the working area was far greater when the new input device was used than when the two conventional analogues were used. Although reasonable performance was not achieved, the results support recommendations concerning the redesign of the device. The ergonomic efforts in the design of the input device are of heuristic value, providing a basis for future development.     

Adaptive tracking control of uncertain MIMO nonlinear systems with input constraints

In this paper, adaptive tracking control is proposed for a class of uncertain multi-input and multi-output nonlinear systems with non-symmetric input constraints. The auxiliary design system is introduced to analyze the effect of input constraints, and its states are used to adaptive tracking control design. The spectral radius of the control coefficient matrix is used to relax the nonsingular assumption of the control coefficient matrix. Subsequently, the constrained adaptive control is presented, where command filters are adopted to implement the emulate of actuator physical constraints on the control law and virtual control laws and avoid the tedious analytic computations of time derivatives of virtual control laws in the backstepping procedure. Under the proposed control techniques, the closed-loop semi-global uniformly ultimate bounded stability is achieved via Lyapunov synthesis. Finally, simulation studies are presented to illustrate the effectiveness of the proposed adaptive tracking control.     

Adaptive low-gain integral control of linear systems with input and output nonlinearities

An adaptive low-gain integral control framework is developed for tracking constant reference signals in a context of finite-dimensional, exponentially stable, single-input, single-output linear systems with positive steady-state gain and subject to locally Lipschitz, monotone input and output nonlinearities of a general nature: the input nonlinearity is required to satisfy an asymptotic growth condition (of sufficient generality to accommodate nonlinearities ranging from saturation to exponential growth) and the output nonlinearity is required to satisfy a sector constraint in those cases wherein the input nonlinearity is unbounded.     

Guaranteed cost LQG control for uncertain systems with a normalized coprime factor uncertainty structure

The paper extends the robust minimax LQG control design methodology to stochastic uncertain systems with a general uncertainty structure, which includes normalized coprime factor uncertainty, passive uncertainty and sector norm-bounded uncertainty as special cases. The derivation of the result uses a special parameter-dependent Girsanov measure transformation. The efficacy of the proposed methodology is illustrated using the problem of frequency locking of an optical cavity which occurs in the area of experimental quantum optics.