An inverse-model approach to multivariable norm optimal iterative learning control with auxiliary optimisation

Motivated by the commonly encountered problem in which tracking is only required at selected intermediate points within the time interval, a general optimisation-based iterative learning control (ILC) algorithm is derived that ensures convergence of tracking errors to zero whilst simultaneously minimising a specified quadratic objective function of the input signals and chosen auxiliary (state) variables. In practice, the proposed solutions enable a repeated tracking task to be accurately completed whilst simultaneously reducing undesirable effects such as payload spillage, vibration tendencies and actuator wear. The theory is developed using the well-known norm optimal ILC (NOILC) framework, using general linear, functional operators between real Hilbert spaces. Solutions are derived using feedforward action, convergence is proved and robustness bounds are presented using both norm bounds and positivity conditions. Algorithms are specified for both continuous and discrete-time state-space representations, with the latter including application to multi-rate sampled systems. Experimental results using a robotic manipulator confirm the practical utility of the algorithms and the closeness with which observed results match theoretical predictions.     

Multivariable norm optimal and parameter optimal iterative learning control: a unified formulation

This article investigates the two paradigms of norm optimal iterative learning control (NOILC) and parameter optimal iterative learning control (POILC) for multivariable (MIMO) ?-input, m-output linear discrete-time systems. The main result is a proof that, despite their algebraic and conceptual differences, they can be unified using linear quadratic multi-parameter optimisation techniques. In particular, whilst POILC has been naturally regarded as an approximation to NOILC, it is shown that the NOILC control law can be generated from a suitable choice of control law parameterisation and objective function in a multi-parameter MIMO POILC problem. The form of this equivalence is used to propose a new general approach to the construction of POILC problems for MIMO systems that approximates the solution of a given NOILC problem. An infinite number of such approximations exist. This great diversity is illustrated by the derivation of new convergent algorithms based on time interval and gradient partition that extend previously published work.     

Accelerated norm-optimal iterative learning control algorithms using successive projection

This article proposes a novel technique for accelerating the convergence of the previously published norm-optimal iterative learning control (NOILC) methodology. The basis of the results is a formal proof of an observation made by D.H. Owens, namely that the NOILC algorithm is equivalent to a successive projection algorithm between linear varieties in a suitable product Hilbert space. This leads to two proposed accelerated algorithms together with well-defined convergence properties. The results show that the proposed accelerated algorithms are capable of ensuring monotonic error norm reductions and can outperform NOILC by more rapid reductions in error norm from iteration to iteration. In particular, examples indicate that the approach can improve the performance of NOILC for the problematic case of non-minimum phase systems. Realisation of the algorithms is discussed and numerical simulations are provided for comparative purposes and to demonstrate the numerical performance and effectiveness of the proposed methods.     

多输入预报自校正前馈控制器及其在高频焊管焊接过程控制中的应用

本文针对高频焊管焊接过程的控制,提出了一种适用于具有多种扰动对象的多输入预报自校正前馈控制器,其特点是综合了广义最小方差控制的最优性、极点配置控制的鲁棒性和多输入前馈控制的抗扰性等优点。该控制器采用间接算法实现,在线选择二次型性能指标中加权项。它不仅可以消除可测干扰的影响,消除稳态跟踪误差,而且即使用于非最小相位系统也具有全局收敛特性。理论分析和仿真实验表明,提出的控制器具有良好的控制性能,可以适应焊接过程环境的变化,从而获得满意的控温效果。     

Discrete‐time repetitive controller for time‐delay systems with disturbance observer

A novel discrete‐time repetitive controller design for time‐delay systems subject to a periodic reference and exogenous periodic disturbances is presented. The main idea behind the proposed approach is to take advantage of the plant delay in the controller design, and not to compensate for the effect of this delay. To facilitate this concept, we introduce an appropriate time‐delay and a compensator in a positive feedback connection with the plant, such that a generator for periodic signals is constructed. Then a proportional controller is used to stabilize the closed‐loop system. The tracking control capability is thus guaranteed according to the internal model principle (IMP). In addition, to attenuate external periodic disturbances, a disturbance observer (DO) is developed to simultaneously achieve reference tracking and disturbance rejection. The possible fractional delay due to the digital discretization is handled by using a fractional delay filter approximation. The proposed controller has a simple structure, in which only a proportional parameter and a low‐pass filter are required to be chosen. The closed‐loop stability conditions and a robustness analysis under model uncertainties are studied. Numerical simulations and practical experiments on a servo motor system are conducted to verify the feasibility and simplicity of the proposed controller. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

高阶参数优化迭代学习控制算法

针对线性时不变离散系统的跟踪问题提出一种高阶参数优化迭代学习控制算法.该算法通过建立考虑了多次迭代误差影响的参数优化目标函数,求解得出优化后的时变学习增益参数.从理论上证明了:对于线性离散时不变系统,该算法在被控对象不满足正定性的松弛条件下仍可保证跟踪误差单调收敛于零.同时,采用之前多次迭代信息的高阶算法具有更好的收敛性和鲁棒性.最后利用一个仿真实例验证了算法的有效性.     

Optimal LQ feedforward tracking with preview: Practical design for rigid body motion control

For reference-tracking motion control, preview-based linear quadratic (LQ) design methods provide an effective means to balance tracking performance with available actuation capacity. This paper considers a control structure for which the optimal feedforward controller is independent of the feedback controller. In this way, explicit implementation formulas for feedforward controllers are derived that can be applied to a range of rigid-body motion systems. Key aspects of the optimal LQ solutions are identified, particularly how the choice of design weightings affect steady-state error for polynomial tracking. A redesign procedure for finite preview-time is proposed that preserves exact polynomial tracking properties and control bandwidth of the optimal solutions. Comparative experimental results are presented for a motor-driven linear motion stage.     

Bi-Objective Optimal Control Modification Adaptive Control for Systems with Input Uncertainty

This paper presents a new model-reference adaptive control method based on a bi-objective optimal control formulation for systems with input uncertainty. A parallel predictor model is constructed to relate the predictor error to the estimation error of the control effectiveness matrix. In this work, we develop an optimal control modification adaptive control approach that seeks to minimize a bi-objective linear quadratic cost function of both the tracking error norm and the predictor error norm simultaneously. The resulting adaptive laws for the parametric uncertainty and control effectiveness uncertainty are dependent on both the tracking error and the predictor error, while the adaptive laws for the feedback gain and command feedforward gain are only dependent on the tracking error. The optimal control modification term provides robustness to the adaptive laws naturally from the optimal control framework. Simulations demonstrate the effectiveness of the proposed adaptive control approach.      

Global consensus of second-order unknown multi-agent systems: A distributed fuzzy iterative learning scheme

This article focuses on global fuzzy consensus control of unknown second-order nonlinear multi-agent systems based on adaptive iterative learning scheme. In order to achieve global consensus, a replacement idea is introduced, where fuzzy systems are used as feedforward compensators to model unknown nonlinear dynamics relying on tracking signals. Considering that the network communication is distributed, a kind of hybrid control protocol is designed to avoid the complete dependence on the tracking signals. In addition, considering the complexity of the external environment, this article extends the above distributed protocol to the case of unknown control directions to study global consensus. Finally, the feasibility of the proposed protocols is verified by Matlab numerical simulations.     

Multivariable integral linear quadratic Gaussian robust control of islanded microgrid to mitigate voltage oscillation for improving transient response

A novel robust integral linear quadratic Gaussian (ILQG) controller is presented in this paper to control the voltage of islanded microgrid and improves its transient response. Microgrid is a small grid that consists of number of distributed generator units, power‐electronic components with inductor‐capacitor (LC) filters and loads. The loads are parametrically uncertain and unknown that produces the voltage or power oscillation. The ILQG controller is capable to compensate for the voltage oscillation and exhibits the tracking of grid voltage against the different load dynamics. The design of ILQG controller is carried out by augmenting the plant dynamics with an integrator. The robustness of the ILQG controller is studied by considering a number of uncertainties within the plant model. The performance of ILQG controller is compared with linear quadratic regulator (LQR) and linear quadratic Gaussian (LQG) controller in terms of rise time, settling time, bandwidth and tracking error. The comparison results ensure the high bandwidth and tracking performance of ILQG controller as compared to other controllers.     

Tracking control for sampled‐data systems with uncertain time‐varying sampling intervals and delays

In this paper, a solution to the approximate tracking problem of sampled‐data systems with uncertain, time‐varying sampling intervals and delays is presented. Such time‐varying sampling intervals and delays can typically occur in the field of networked control systems. The uncertain, time‐varying sampling and network delays cause inexact feedforward, which induces a perturbation on the tracking error dynamics, for which a model is presented in this paper. Sufficient conditions for the input‐to‐state stability (ISS) of the tracking error dynamics with respect to this perturbation are given. Hereto, two analysis approaches are developed: a discrete‐time approach and an approach in terms of delay impulsive differential equations. These ISS results provide bounds on the steady‐state tracking error as a function of the plant properties, the control design and the network properties. Moreover, it is shown that feedforward preview can significantly improve the tracking performance and an online extremum seeking (nonlinear programming) algorithm is proposed to online estimate the optimal preview time. The results are illustrated on a mechanical motion control example showing the effectiveness of the proposed strategy and providing insight into the differences and commonalities between the two analysis approaches. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust adaptive feedforward control and achievable tracking for systems with time delays

A feedback/feedforward controller architecture is developed that characterises the achievable reference tracking of real time inputs for both minimum phase and non-minimum phase systems with time delays, when there are no modelling errors or external disturbances. This characterisation is obtained by factoring the plant into its minimum phase, non-minimum phase, and time delay components, which are used to design two feedforward controllers that inject signals into two points of the feedback loop. Design constraints are provided that determine both the types of signals that may be achieved, and the feedforward controllers that will generate that output. Of course, in practice, both modelling errors and external disturbances will be present. In this case, we develop robust analysis tools that both guide the feedback controller design process, and provide rigorous robust tracking performance that guarantees for the overall resulting closed-loop system. Robust methods for designing the feedforward controllers are presented, and numerical examples are provided. The performance of this architecture depends strongly on the choice of design parameters, and the accuracy of the plant model used. Hence, the use of adaptation methods is also considered, and it is shown that they can readily be employed to improve the performance of this control methodology.     

Control of a pneumatic power active lower-limb orthosis with filter-based iterative learning control

A filter-based iterative learning control (FILC) scheme is developed in this paper, which consists in a proportional–derivative (PD) feedback controller and a feedforward filter. Moreover, based on two-dimensional system theory, the stability of the FILC system is proven. The design criteria for a wavelet transform filter (WTF) – chosen as the feedforward filter – and the PD feedback controller are also given. Finally, using a pneumatic power active lower-limb orthosis (PPALO) as the controlled plant, the wavelet-based iterative learning control (WILC) implementation and the orchestration of a trajectory tracking control simulation are given in detail and the overall tracking performance is validated.     

Use of disturbance measurement feedforward in LQG self-tuners

An explicit adaptive regulator with disturbance measurement feedforward is presented, based on a polynomial LQG design. The addition of an optimized feedforward filter to a feedback regulator involves the solution of only one additional linear polynomial equation. The regulator is designed to handle shape-deterministic disturbances, such as steps, ramps and sinusoids, as well as stochastic disturbances. The properties of the off-line solution in the case of unstable disturbance models are explained. Computational aspects, the computational complexity and the robustness against unmodelled dynamics are discussed. It is argued that the use of feedforward can improve not only the disturbance rejection, but also the stability robustness of an LQG feedback regulator     

Longitudinal tunnel ventilation control. Part 1: Modelling and dynamic feedforward control

Road tunnels exceeding a certain minimum length are equipped with a ventilation system. In case of a fire it is used to achieve a predefined air flow velocity in the tunnel by adequately controlling the installed jet fans in order to ensure sufficient visibility for persons to safely follow the escape routes. As the dynamics of the air flow in road tunnels strongly depend on the tunnel length, short tunnels with longitudinal ventilation systems pose a challenging control task. In this paper, non-linear dynamic feedforward control is proposed for longitudinal ventilation control in case of an emergency. For this purpose, an analytical non-linear zero-dimensional model of the air flow is feedback linearised. Due to its special properties, which are presented and analysed, two different versions of feedforward control are proposed: One is focused on performance, the other on robustness. Finally, the beneficial behaviour of the presented two-degrees-of-freedom control approach is demonstrated by its application to an Austrian motorway tunnel.     

Comment on ‘ Tolerance analysis using fuzzy sets ’ and ‘ A procedure for multiple aspect decision making ’

The problem of tracking a reference vector variable from a given class is considered for discrete time linear multiple input-output plants. The plant and the reference are both described by an input-output relation and the objective is to track so that a quadratic criterion is minimized. This tracking problem is solved by reformulating it as a regulator problem for an augmented system. The optimal control law is shown to contain both feedback and feedforward terms and it is obtained by applying polynomial matrix techniques. The design procedure consists in spectral factorization and the solution of linear equations in polynomial matrices. The case of unstable references is included and a natural solvability condition is derived in the form of divisibility of polynomial matrices.     

On learning transient,auto-tunings of learnable bandwidth and lead step in iterative learning control

The learning transient and tracking accuracy of phase lead compensation iterative learning control are determined by its three parameters: learning gain, system learnable bandwidth and lead step. Because of the model inaccuracy, the learnable bandwidth is often chosen as a conservative value, which often degrades the learning performance. In this article, the learning transient is analysed and the tuning of learnable bandwidth and lead step are developed to achieve good learning transient and tracking accuracy simultaneously. The attractive properties include that the less dependence on system model and that the tracking error during this process keeps at a very low level. Experimental results on an industrial robot are presented to verify the tuning process.     

Feedforward digital tracking controllers for motion control applications

This paper reviews digital tracking control algorithms for motion control applications. In tracking control, the control objective is to steer the control object along the time-varying desired output. Two design approaches are presented for the case where the desired signal is known in advance, i.e. previewable. One approach is based on the mathematical inverse of a closed-loop system consisting of a controlled plant and a feedback controller. If the mathematical inverse is asymptotically stable, i.e. the closed-loop system does not possess zeros outside the unit circle (unstable zeros), it is an ideal feedforward controller for achieving perfect tracking under the preview assumption. For closed-loop systems with unstable zeros, a cancellation technique for the phase shift induced by unstable zeros is introduced. Another approach is based on linear quadratic optimal control and is known as finite optimal preview control. In this approach, the feedback controller and feedforward controller are determined simultaneously by minimizing a quadratic performance index which involves a tracking error term and a term related to the control effort. Applications of these tracking control algorithms to mechanical systems control are described.     

Convex LPV synthesis of estimators and feedforwards using duality and integral quadratic constraints

A method is presented for synthesizing output estimators and disturbance feedforward controllers for continuous‐time, uncertain, gridded, linear parameter‐varying (LPV) systems. Integral quadratic constraints are used to describe the uncertainty. Since the gridded LPV systems do not have a valid frequency‐domain interpretation, the time domain, dissipation inequality approach is followed. There are 2 main contributions. The first contribution is that a notion of duality is developed for the worst‐case gain analysis of uncertain, gridded LPV systems. This includes notions of dual LPV systems and dual integral quadratic constraints. Furthermore, several technical results are developed to demonstrate that the sufficient conditions for bounding the worst‐case gain of the primal and dual uncertain LPV systems are equivalent. The second contribution is that the convex conditions are derived for the synthesis of robust output estimators for uncertain LPV systems. The estimator synthesis conditions, together with the duality results, enable the convex synthesis of robust disturbance feedforward controllers. The effectiveness of the proposed method is demonstrated using a numerical example.