Control Of Non-minimum Phase Systems Research Articles

Sliding mode control with the reduced-order switching function: an SCB approach

In this paper, the method to design the reduced-order switching function for an uncertain linear system in special coordinate basis (SCB) form is proposed. The sliding mode control with this method guarantees the asymptotic stability of all the states of system in presence of matched disturbance. The proposed design method is applicable to the system with unstable internal dynamics as well. This method enables the option of designing the control law with reduced-order states that are involved in the design of switching function. Also, a high performance sliding mode step-tracking control for non-minimum phase systems using reduced-order nonlinear switching function is proposed. The method is also extended to multiple-input and multiple-output (MIMO) systems. An effectiveness of sliding mode control with reduced-order switching function is shown through numerical examples.

Centralised Multi-input Multi-output Controllers for Non-minimum Phase Systems

In the present work, the method of designing the centralised controllers for the minimum phase multivariable systems proposed by Vijay Kumar et al. is extended to non-minimum phase systems. The controller is designed based on the direct synthesis method. Inverse of process transfer function matrix in the direct synthesis method is approximated based on relative gain array concept. Maclaurin's series is applied to reduce it to a standard proportional and integral form. The method is further improved by using equivalent transfer function matrix derived from relative normalised gain array and relative average residence time array as process inverse transfer function matrix. Effective transfer function is the equivalent transfer function of gij(s) when all other loops are closed. The desired closed-loop transfer function should contain the process right half plane zero. Quadruple tank process with non-minimum phase behaviour is considered to analyse the performance of the proposed centralised controllers. The performance of centralised controllers is compared with a recently proposed decentralised controller.

Fictitious Reference Iterative Tuning of Internal Model Controllers for Non-Minimum Phase Systems: A Laguerre Expansion Approach

Fictitious reference iterative tuning (FRIT) is one of the effective data-driven tuning methods for parameters of a controller with only one-shot experiment. This paper applies FRIT to internal mod...

Dual adaptive control for non-minimum phase systems with functional uncertainties

A dual control for a nonlinear system with non-minimum phase based on the bicriterial approach is proposed and discussed. A particular class of the nonlinear input/output recursive model is composed of linear and nonlinear blocks, the latter being implemented with a multi-layered perceptron neural network. The unknown parameters of the model are estimated in real-time by the extended Kalman filter. The chosen nonlinear model with the affine structure in inputs together with the certainty equivalence principle utilization allow to obtain an analytical solution to control based on generalised minimum variance method. Behaviour of the system based on the enforcement of the certainty equivalence can negatively be affected, especially in a presence of disturbances and functional uncertainties. For that, the control action is enhanced about dual property based on the bicriterial approach that uses two separate criteria to introduce one of the opposing aspects between estimation and control.

Adaptive Inverse Control of Hydro Electric Unit Based on Wavelet Neural Networks

Due to the nonlinear, time-variable and non-minimum phase character of hydro electric unit system integrated with water, motor and power, a new adaptive inverse control method of hydro electric unit based on the function approximation ability of the wavelet analysis and the learning characteristic of neural network is presented. The algorithm and formulas and method of adaptive inverse control is studied. It approximates the model and its inversion of hydro electric unit by wavelet neural networks(WNN), and then through constructing an aim function of broad sense, which is effective to the nonlinear non-minimum phase system. Theory and simulation to for hydro electric unit system demonstrate that the control strategy can more effective improve the dynamic and stationary performance than those based on neural networks. It gives a new approach in control for hydro electric unit system besides offer a beneficial reference to the control of non-minimum phase systems.

An adaptive-dynamic sliding mode controller for non-minimum phase systems

This paper presents a new algorithm for designing dynamic sliding-mode controllers. The proposed controller is based on dynamic sliding manifolds to circumvent the difficulties associated with the conventional sliding mode controllers in the face of non-minimum phase systems. Unlike previous works, a proper and easy to implement algorithm is presented for designing the dynamic sliding manifold which facilitates the design of the controller. The output tracking problem in nonlinear non-minimum phase systems with matched and unmatched disturbances and matched nonlinearities is addressed. Then, the performance of the dynamic sliding mode controller is significantly improved by combining the given dynamic sliding manifold with online parameter adaptation. Simulations results are presented to demonstrate the effectiveness of the proposed sliding mode controller in terms of performance, robustness and stability.

Model Identification and Feedforward Control for Non-minimum Phase Systems

High precision control has received a great attention. Nowadays, as the machines are used for precise operations in manufacturing field, fast and precision control is required. This paper presents model identification using Matlab System Identification Toolbox from open loop input-output experimental data of a linear servo system. Two different models are obtained by varying the sampling time of the experiments by 40ms and 50ms. Different sampling time changes the position of non-stable zero of the transfer function. The identified models are tested using pole-placement feedback controller. The system is further improved by introducing feedforward Zero Phase Error Tracking Control (ZPETC) to control the position tracking of non-minimum phase system. The variations of system performances for both systems are analyzed through simulation and real-time experiment. The results verify that conventional ZPETC is more effective for system that has non-stable zero far from the unit circle.

Extension of Reference Signals in Iterative Learning Control for Non-Minimum Phase Systems

This paper proposes to extend the given reference signal in the iterative learning control context so that the resultant signal has the non-minimum phase zero structure as the given plant. This extension enables preventing control inputs exponentially increasing. The extending signals can be synthesiszed by solving a linear equation. The effectiveness of the proposed method is examined by using a numerical example.

Enhanced feedforward control of non-minimum phase systems for tracking predefined trajectory

This article proposes a novel feedforward controller for non-minimum phase systems by utilising the preview information of the desired trajectory. The performance of the proposed controller is analysed theoretically and verified through the simulation, including comparison with the optimal zero phase error tracking controller and the preview-based stable inversion. The simulation results show that the proposed controller can gain outstanding performance even if the preview time of the desired trajectory is limited.

The Parameterization of all Stabilizing Modified Repetitive Controllers for Multiple-Input/Multiple-Output Plants with the Specified Input-Output Frequency Characteristic

In this paper, we examine the parameterization of all stabilizing modified repetitive controllers for multiple-input/multiple-output plants with the specified input-output frequency characteristic. The parameterization of all stabilizing modified repetitive controllers for non-minimum phase systems was solved by Yamada et al. However, when we design a stabilizing modified repetitive controller using the parameterization by Yamada et al., the input-output frequency characteristic of the control system cannot be settled so easily. The input-output frequency characteristic of the control systems is required to be easily settled. This problem is solved by obtaining the parameterization of all stabilizing modified repetitive controllers with the specified input-output frequency characteristic. However, no paper has proposed the parameterization of all stabilizing modified repetitive controllers for multiple-input/multiple-output plants with the specified input-output frequency characteristic. In this paper, we propose the parameterization of all stabilizing modified repetitive controllers for multiple-input/multiple-output plants with the specified input-output frequency characteristic.

On the equivalence between stable inversion for nonminimum phase systems and reciprocal transfer functions defined by the two-sided Laplace transform

In this paper, the two-sided Laplace transform, a classical but not very common mathematical tool, is revived to express the stable inversion for linear nonminimum phase systems that was recently proposed from the viewpoint of state-space representations. It is demonstrated that those two different expressions for the stable inversion are mathematically equivalent. Simple examples are presented to illustrate the two-sided Laplace transform as a direct and intuitive approach to stable inversion. The two-sided Laplace transform approach is also applied to the development of an iterative learning control for nonminimum phase systems that needs neither a precise inversion model nor Fourier-Transform computations, but instead requires only measuring the system response with time reversals.

Galerkin method and approximate tracking in a non-minimum phase bilinear system

The tracking control of non-minimum phase systems is nowadays an open and challenging field, because a general theory is still not available. This article proposes an indirect control strategy in which a key role is played by the inverse problem that arises and their approximate solutions. These are obtained with the Galerkin method, a standard functional analysis tool. A detailed study of the effect on the output caused by the use of an approximate input is performed. Error bounds are also provided. The technique is motivated through its implementation in basic, DC-to-DC nonlinear power converters that are intended to be used as DC-to-AC voltage sources.

目標信号に漸近的に追従し有界な入力で達成可能な出力のパラメトリゼーション

This paper deals with trajectory tracking control for non-minimum phase systems. We first consider to characterize output such that it tracks to a given reference signal asymptotically and that the corresponding input is bounded. In particular, we parameterize the error signals between the reference and the achievable output by using Q-parameters in the frequency domain. Since the parameterized set consists of rational functions which are analytic in the closed right half plane, we can solve easily the problem to minimize theL2norm of the error and the analytic solution of the optimal error is obtained. The optimal output is the projection of the reference to the space of achievable outputs. By using the parameterization, the simultaneous optimization of the error and the input deviation from the steady state input can be also solved. The effectiveness of the proposed method is examined by numerical examples.

Perfect Tracking Control of Nonminimum Phase Systems in Magnetic Levitation System

In this paper, we study the problem of perfect tracking control of nonminimum phase systems in magnetic levitation system. Generally, perfect tracking control schemes cannot be applied to nonminimum phase plants because of unstable pole-zero cancellations. Although the method of state matching using multirate feedforward control to realize perfect tracking control have been proposed, the oscillation restraint and the feasibility in nonminimum phase system cannot be satisfied at same time. We propose a method using the difference of state variables to generate a smooth desired state variable trajectory in the discrete-time systems. The techniques we proposed are applicable to nonminimum phase discrete-time systems and the oscillations between the sampling points are well restrained. We will show that the structure of the proposed perfect tracking controller is very simple and clear. Finally, computer simulations and experiment results based on magnetic levitation apparatus are presented.

Optimal design of PI/PD controller for non-minimum phase system

It is still an open problem to eliminate the undershoot caused by zeros in the right-half plane of non-minimum phase systems (NMPS). In this paper, a two-stage PI/PD controller is investigated on the basis of particle swarm optimization (PSO) to decrease peak overshoot, maximum undershoot, settling time and rise time of non-minimum phase (NMP) system simultaneously. PSO is a global stochastic evolutionary algorithm. It tries to find optimal regions of complex searching space through the interaction of particles in the population. The predominance of the algorithm is its excellent performance and simple implementation. Numerical simulation results illustrate the efficiency of the proposed controller compared with a genetic algorithm -simulated annealing (GA-SA) PID controller in point of improvement of performances of a step response, like fast settling time, small undershoot and small overshoot.

Predictive generic model control for non-linear interval systems with application in arc welding

A control technique is proposed for a class of non-linear systems with parameter intervals. This technique can be considered as a modification of the Generic Model Control (GMC), which specifies the desired derivative of the output as a Proportional- Integral (PI) function of the error between the reference and the output. Specifically, to reduce unnecessary control variations and improve the suitability for the control of non-minimum phase systems, a multistep prediction is incorporated into the GMC, which in its original form is 'nearsighted', to develop a Predictive GMC (PGMC). For non-linear interval systems, interval arithmetic is used to analyse the interval of the input, which can guarantee the system's output stability defined by an output range. The PGMC is then derived for the interval non-linear system and an adaptive factor is proposed to improve the understanding of process dynamics and the performance of the closed-loop system. The resultant algorithm can control a non-linear system with parameter intervals and guarantee that the system's output will meet a specified criterion. A simulation has been done to demonstrate the effectiveness of the PGMC in reducing control signal variations. Also, an arc welding process has been controlled using the interval PGMC algorithm to demonstrate the effectiveness of the full-proposed control technique.

Comparision of Multivariable Controllers for Non-Minimum Phase Systems

A system with one or more right half plane transmission (RHPT) zero is generally called a non-minimum phase system. In this paper, the authors compare two methods of designing multivariable controllers for systems with RHPT zeros. The methods used are decoupled internal model controller and a simple tuning method. In the decoupled IMC method, controller design procedure is developed with the help of a model reduction theorem. Davison has proposed a simple tuning method, which is based on inverse of the steady-state gain matrix [G(0)]. Previously the method was applied to multivariable minimum phase systems only. In the present work the Davison method is applied to systems with multivariable right half plane zero. The decoupled IMC method involves some complex calculations in designing controllers, whereas the Davison method is simple to apply. Simulation results are given for the following 2 × 2 transfer function matrix of the systems: (1) a four-tank system, a benchmark example of multivariable system; (2) a system with individual and multivariable transmission zero at s = 1; and (3) binary distillation column. The performance comparisons are given by the sum of IAE values based on response and interaction both for servo and regulatory problems. The presented simple tuning method gives an improved performance.

Output tracking control of a one-link flexible manipulator via causal inversion

Output tracking control is a challenging problem. This paper introduces a new design procedure for output tracking control of nonminimum phase systems. This new controller achieves stable /spl epsi/-tracking of a reference profile given in real time via a causal inversion approach. In this approach, the nonminimum phase system is first stably inverted on-line to obtain both desired (and stable) state and input trajectories. Then an H/sub /spl infin// optimal controller is used to stabilize the closed-loop system. In contrast to stable inversion, the causal inversion approach does not require precalculation. In contrast to nonlinear regulation, the causal inversion approach avoids the numerical intractability of solving nonlinear PDEs. As an example of the application, a causal inversion-based controller is designed for tip trajectory tracking of a one-link flexible manipulator. Simulation results demonstrate its effectiveness in output tracking.

The Parametrization of All Stabilizing Modified Repetitive Controllers for Non-Minimum Phase Systems

In the present paper, we give the parametrization of all stabilizing modified repetitive controllers for non-minimum phase systems. The basic idea to obtain the parametrization of all modified repetitive controllers for non-minimum phase systems is very simple. If the repetitive controller stabilizes the plant, then the repetitive controller must be included in the class of all stabilizing controllers for the plant. The parametrization of all stabilizing controllers for the plant, which is not necessarily repetitive controllers, are obtained by Youla et al. and Vidyasagar. The parametrization of all stabilizing controllers includes a free parameter, which is stable. That is, stabilizing repetitive controllers for non-minimum phase systems can be designed using the free parameterin the parametrization by Youla et al. and Vidyasagar. Using this idea, we obtain the parametrization of all stabilizing modified repetitive controllers for non-minimum phase systems. Next, a numerical example is illustrated to show the effectiveness of the proposed parametrization.

THE PARAMETRIZATION OF ALL ROBUST STABILIZING REPETITIVE CONTROLLERS

In this paper, we investigate the parameterization of all robust stabilizing repetitive controllers for single-input/single-output continuous time non-minimum phase systems. The repetitive control system is a type of servo mechanism designed for a periodic reference input. When repetitive control design methods are applied to real systems, the influence of uncertainties in the plant must be considered. In some cases, the uncertainties in the plant make the repetitive control system unstable, even though the controller was designed to stabilize the nominal plant. The stability problem with uncertainty is known as the robust stability problem. Several papers to design robust stabilizing repetitive control systems have been published. However the parametrization of all robust stabilizing repetitive controllers has not been considered. In this paper, we propose the parametrization of all robust stabilizing repetitive controllers for non-minimum phase systems. Finally, a numerical example is illustrated to show the effectiveness of the proposed parametrization.