Robust ripple-free deadbeat control design

This paper deals with the design of ripple-free deadbeat controllers with performance or performance robustness optimized over controllers within a prescribed settling time. The performance objective of interest is the minimization of the maximum absolute tracking error. This leads to consider linfinity optimization problems. On the contrary, the optimization of the performance robustness leads to consider l1 optimization problems. An example is provided to illustrate the results.     

最小拍无波纹直流电机控制系统仿真研究

在单位阶跃、单位速度和单位加速度3种典型输入下对直流电机的最小拍无波纹控制进行了研究.Matlab仿真结果表明,最小拍无波纹控制,输出能较快的跟随输入,且跟随后能基本消除静差.最小拍无波纹控制应用在直流电机控制系统中,能够使电机的转速在最少个采样周期内跟随期望转速,使系统达到无静差的稳态,表明了最小拍无波纹控制能实现较高的控制品质.     

Parametrization of all ripple-free deadbeat controllers

This paper is concerned with deadbeat control in sampled-data systems. Deadbeat control achieves finite-time settling (deadbeat settling) at sampling instants, but there may exist error called ripple “between” sampling instants even after the response is settled “at” sampling instants. The objective of this paper is to give a parametrization of all ripple-free deadbeat controllers (controllers which achieve deadbeat settling without ripple) in sampled-data systems. It is also shown that the following holds in general: minimum-time deadbeat control causes ripple when the pulse transfer function to be controlled has stable zeros.     

On output deadbeat control of discrete-time multivariable systems

A necessary extension to the output deadbeat control algorithm of M.R. Marrani et al. (see ibid., vol.AC-34; p.644-8 (1989)) is presented. This extension is shown to provide particular theoretical insights when dealing with the case of a system with multiple stable transmission zeros. It is numerically straightforward to implement. Once the zeros have been calculated, the state zero directions can be determined independently. This method has particular advantages when dealing with the case of a plant with multiple stable transmission zeros     

Design of ripple-free multivariable robust servomechanisms

The application of standard robust servomechanism theory to sampled data systems guarantees asymptotic tracking at sampling instances and between sampling instants, the output will normally contain ripple. In this note, the robust servomechanism theory is extended to sampled-data systems and a technique is proposed for ripple-free tracking of sinusoids and polynomials. It is shown that a continuous internal model is necessary and sufficient to provide ripple-free response.     

Multipurpose deadbeat controllers for multivariable systems

A simple and direct deadbeat control design algorithm for discrete-time multivariable systems is introduced. Our brief was to synthesize a realizable controller to achieve the following objectives: (1) input-output decoupling, (2) deadbeat tracking of any prespecified class of changeable deterministic reference signals and (3) changeable deterministic disturbances rejection where the changeable reference signals and disturbances can be different at each channel. Since the internal stability requirement is satisfied, our design algorithm can easily handle both unstable and non-minimum phase systems. Some constraints on the transfer function are also derived to make sure that the derived controller is realizable. Since all solutions can be described in parametric form, some of the performance criteria can be combined.     

Optimal ripple-free deadbeat control using an integral of time squared error (ITSE) index

This paper describes an optimal ripple-free deadbeat control strategy for single-input–single-output (SISO) linear sampled data plants. The cost function to be minimized is a linear combination of a time-weighted cumulative term that penalizes the tracking error, that is, an integral of time squared error (ITSE) cost term, and a cumulative term which penalizes the control signal deviations from its steady-state value. The optimization problem turns out to be convex, and closed-form solutions are obtained. An example is included to illustrate our results.     

Recursive solutions to deadbeat observers for time-varying multivariable systems

This paper describes a new construction of the deadbeat observer for the state estimation of linear time-varying multivariable systems. The proposed design methods are computationally attractive because of their simplicity and recursive nature, and are recommendable even for time-invariant multivariable systems.     

Adaptive deadbeat control

An adaptive algorithm is presented to incorporate deadbeat control as a principle design criterion. Since this algorithm does not require the solution of the diophantine equation at each sampling step, it possesses a computational advantage over the existing deadbeat control approaches, and so is suitable for application to adaptive systems. The meeting of the internal stability requirement enables this algorithm to handle easily any stable or unstable, minimum or non-minimum phase system. By selecting the zero assignment of the sensitivity function the system can be made to track a class of changeable reference signals and exhibit a deadbeat response with minimum settling time. Some constraints on the transfer function make sure that the derived controller is realizable. The non-linear saturated system and the lathe system are simulated to illustrate the validity of the proposed design algorithm.     

Output deadbeat controllers with stability for discrete-time multivariable linear systems

This short paper Treats the problem of designing output deadbeat controllers having the property that the control input to the system converges to zero as time goes to infinity, for discrete-time multivariable linear systems. Two configurations of controllers are considered: one is of state feedback; the other is a dynamic controller using an observer. The existence of such controllers is examined, and the methods are presented for designing such controllers when they exist. The controller using a state feedback obtained in this paper is optimal in the sense that the controller settles the output in zero for any initial state in the minimum number of steps. On the other hand, the dynamic controller is not optimal in that sense, but it minimizest, wheretis defined as an integer such that the controller drives the output to zero in no more thantsteps for any set of initial conditions of the system and the observer.     

Optimization of control input for deadbeat control systems

The aim of this paper is to deal with the problem of excessive control magnitude with deadbeat control systems. By the use of the transfer-function factorization approach, all stabilizing deadbeat controls are characterized in terms of control input. A formula is derived for the optimal control that minimizes the control input error for the specified settling time. The design procedure is essentially trade-offs between settling time and control input properties. As the bound of such trade-offs, the limiting value of the optimal performance index, as the settling time goes to infinity, is derived. This limit value plays an important role in fixing the most appropriate settling time.     

Output deadbeat control discrete-time multivariate systems

An algorithm is presented to compute output deadbeat controls for linear multivariable systems. The algorithm, based on quadratic optimization with no cost on control (cheap control), is numerically stable and covers the most general cases. The resulting controls are internally stable and are shown to drive the outputs of the system to zero in minimum time using state feedback. The central part of the algorithm is the construction of the nonunique state-cost matrix. Two alternatives are presented having different complexities and resulting in solutions having different properties     

Continuous-time deadbeat control for sampled-data systems

In this paper, the continuous-time deadbeat control problem for the sampled-data systems is considered. We derived the class of all controllers that achieve the continuous-time deadbeat control     

Ripple-free deadbeat control for sampled-data systems

In this paper the ripple-free deadbeat control problem for sampled-data systems is considered. This control objective is to settle the error to zero for all time after some finite settling time, in other words to eliminate the ripples between the sampling instants in deadbeat control of sampled-data systems. The necessary and sufficient conditions to solve this problem are derived and related to the system type, and a method of constructing the ripple-free deadbeat control system is presented.     

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.     

Ripple-free deadbeat control of SISO discrete systems

The ripple-free deadbeat control problem for arbitrary (not necessarily stable) SISO linear discrete plants and reference signals is treated. It is established that a causal, stabilizing ripple-free deadbeat controller exists if and only if the zeros of the plant and the poles of the reference signal are disjoint, and a complete characterization of all such controllers is obtained. Solutions to two illustrative problems are presented.     

Efficient multiple objective optimal control of dynamic systems with integer controls

In practical optimal control problems both integer control variables and multiple objectives can be present. The current paper proposes a generic and efficient solution strategy for these multiple objective mixed-integer optimal control problems (MO-MIOCPs) based on deterministic approaches. Hereto, alternative scalar multiple objective optimisation techniques as normal boundary intersection and normalised normal constraint are used to convert the original problem into a series of parametric single objective optimisation problems. These single objective mixed-integer optimal control problems are then efficiently solved through direct multiple shooting techniques which exploit convex relaxations of the original problem. Moreover, these relaxations enable to quickly approximate the final solution to any desired accuracy (without the need of solving integer problems). Consequently, the set of Pareto optimal solutions of the MO-MIOCP can be accurately obtained in highly competitive computation times. The proposed method is illustrated on (i) a testdrive case study with a complex car model which includes different gears and conflicting minimum time–minimum fuel consumption objectives, and (ii) a jacketed tubular reactor case study with conflicting conversion, heat recovery and installation costs.     

Simultaneous deadbeat tracking control of two plants

The simultaneous deadbeat-tracking control of two plants is developed. The twodegree-of-freedom parametrized asymptotical-tracking controller and simultaneous stabilization problem are applied to derive the simultaneous deadbeat-tracking control of two plants. The conditions for existence are given and the systematic design algorithm of the two-degee-of-freedom controller is proposed such that the simultaneous deadbeat-tracking control of two plants is attained.     

The design of finite-time optimal multivariable systems

A procedure is described for the solution of the free end-point optimal control problem. The multivariable plant is assumed to be linear and time-invariant, and the quadratic performance criterion, which is measured over a finite interval, contains an end-state weighting term. This is the first presentation of a general solution to this problem in the complex frequency domain. A technique is described by which the optimal time-varying feedback gain matrix can be calculated directly from the s domain results.