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.     

Comparison of input signals in subspace identification of multivariable ill-conditioned systems

Ill-conditioned processes often produce data of low quality for model identification in general, and for subspace identification in particular, because data vectors of different outputs are typically close to collinearity, being aligned in the “strong” direction. One of the solutions suggested in the literature is the use of appropriate input signals, usually called “rotated” inputs, which must excite sufficiently the process in the “weak” direction. In this paper open-loop (uncorrelated and rotated) random signals are compared against inputs generated in closed-loop operation, with the aim of finding the most appropriate ones to be used in multivariable subspace identification of ill-conditioned processes. Two multivariable ill-conditioned processes are investigated and as a result it is found that closed-loop identification gives superior models, both in the sense of lower error in the frequency response and in terms of higher performance when used to build a model predictive control system.     

A concurrent design of input shaping technique and a robust control for high-speed/high-precision control of a chip mounter

Input Shaping Technique (IST) and Time Delay Control (TDC), a robust feedback control law, were combined to achieve fast and precise point-to-point motion of a chip mounter. TDC was used as a feedback control to overcome disturbances and parameter variations, an IST was used to suppress the residual vibration induced in the closed loop system. TDC was designed first for the machine, and a discrete version of IST was designed on the basis of the closed-loop dynamics. In the design of TDC, a better set of gains was available thanks to the use of IST than TDC alone; in the design of IST, too, a better design was possible than IST alone. As the result of the concurrent design and synergy of the two methods, point-to-point motion could be achieved with no overshoot, the settling time of about 0.05 s and few steady-state errors to position commands of 1.5 mm. This result is far better than a conventional PID control or TDC alone could achieve, thereby showing the effectiveness of the concurrent design.     

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.     

Control system design and input shape for orientation of spherical wheel motor

This paper presents control system design of a multi degrees-of-freedom (DOF) spherical wheel motor (SWM) in a class of ball-joint-like direct drive actuators to control orientation of the shaft. Three controllers (model based open-loop (OL), two closed-loop (CL) controllers) based on a push-pull torque model have been developed from rotor dynamics and magnetic field model referred to here as Distributed Multipole (DMP) model which provides accurate torque computation. The model based OL controller along with three control input shapes has been examined for the inclination control. Their results offer physical intuition, practical effectiveness, and also demonstrate the accuracy of magnetic field and torque computation. Then, two feedback controllers, a PD controller with and without the observer, have been developed for regulating its rotor inclination and experimentally evaluated against the OL controller. Finally, the performance on each controller has been compared to show the effect of the controllers on transient response. The experimental results verify control system design and demonstrate the motion capability of the SWM. While the experimental results illustrate the ability to control, they also reveal constraints and limitations of the controllers and provide insights for future design of control systems for the SWM.     

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.     

一类具有输入饱和的组合系统的半全局分散镇定

研究具有输入饱和组合系统在分散线性状态反馈控制作用下半全局镇定问题。首先给出饱和函数和M矩阵的定义和性质；然后指出所研究的问题是寻找一个分散状态反馈，使得第i阶闭环子系统和完全闭环系统在给定条件下一致渐近稳定；进而运用M矩阵理论，给出了比较简单的具有输入饱和对称组合系统分散半全局镇定的充分条件。     

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.     

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.     

Robust H-infinity control for discrete-time T-S fuzzy systems with input delay

Delay-dependent robust H-infinity control for discrete-time Takagi-Sugeno (T-S) fuzzy systems with interval time-varying input delay is considered.By constructing a new Lyapunov-Krasovskii functional and using convex combination method,a delay-dependent condition is established,under which the resulted closed-loop systems via a fuzzy state feedback are robust asymptotically stable with given H-infinity norm bound.Then,an iterative algorithm based on the modified SLPMM algorithm is proposed to solve the fuzz...     

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.     

Optimal control of linear systems with large and variable input delays

This paper proposes an optimal control law for linear systems affected by input delays. Specifically we prove that when the delay functions are known it is possible to generate the optimal control for arbitrarily large delay values by using a DDE without distributed terms. The solution can be seen as a chain of predictors whose size depends on the maximum delay.