PI Tracking Control Research Articles

PI Tracking Control of a Nonlinear plant

The tracking control design for nonlinear plants by model inversion, following the Linear Algebra Based methodology, usually assumes a proportional to the error approaching of the process variables to the references evolution as a design criterion for the control. In this paper, by using the well-known properties of the integral action, a PI-like control is assumed, countering constant disturbances and model parameters uncertainty. The application to a simple mass-spring nonlinear system illustrates the procedure.

Fault diagnosis and fault tolerant control for non-Gaussian time-delayed singular stochastic distribution systems

Stochastic distribution control (SDC) is a new branch of stochastic system control that the system output is the probability density function (PDF) of the output. In practice, some algebraic relations exist between the input and the weights of SDC systems, leading to a singular state space model between the weights and the control input which increases the complexity of the system. The ignorance of time delay in practical systems will make the effectiveness of the fault diagnosis (FD) and fault tolerant control (FTC) be reduced. In this paper, the linear B-spline basis functions are used to approximate the output PDF. A FD approach based on the adaptive observer is established to diagnose the size of fault in the singular time-delayed SDC system. With the fault diagnosis information, a fault tolerant controller based on PI tracking control scheme is constructed to make the post-fault PDF still track the given distribution. The post-fault closed-loop stability analysis with the practical fault tolerant controller is carried out based on the Lyapunov stability theorem. Finally, a numerical simulation is provided to demonstrate the effectiveness of the proposed approach.

Decentralized PI tracking control for non-Gaussian large-scale interconnected distribution systems

This paper addresses a novel constrained decentralized shaping control problem for a class of nonlinear large-scale interconnected distribution systems. Such systems are generated by multiple output conditional probability density functions (PDFs) and exist in multi-channel non-Gaussian stochastic processes. Following a decoupled B-spline approximation to the output conditional PDFs, the large-scale interconnected weight systems are introduced to characterize the correlation in different weight vectors and further to describe the dynamic relation between the control input and weight vectors. The decentralized PI controller with delay dependent analysis is designed to ensure the system stability and convergence of the dynamic tracking error to zero. Moreover, the L2−L∞ norm from the disturbance to the controlled output is reduced to a prescribed level and the state constraint requirement can also be guaranteed. The effectiveness of the developed algorithm is verified by simulations of paper making process.

PI tracking control for nonlinear time-varying delay Markov jump systems

This paper considers robust stochastic stability and PI tracking control problem for Markov jump systems with both input delay and an unknown nonlinear function. Based on the traditional PI control strategy, a new controller design scheme is proposed for nonlinear time-delay Markov jump systems which can realize multiple control objectives including robust stochastic stability and tracking performance. By using the Lyapunov stability theory and LMI algorithms, a sufficient condition for the solution to robust stochastic stability and tracking control problem is obtained. Then, the desired controller with PI structure is designed, which ensures the resulting closed-loop system is robust stochastically stable and the system state has favorable tracking performance. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.

Optimal integral force feedback and structured PI tracking control: Application for objective lens positioner

This paper describes a new vibration damping technique based on Integral Force Feedback (IFF). Classical IFF utilizes a force sensor and integral controller to damp the resonance modes of a mechanical system. However, the maximum modal damping depends on the frequency difference between the system’s poles and zeros. If the frequency difference is small, the achievable modal damping may be severely limited. The proposed technique allows an arbitrary damping ratio to be achieved by introducing an additional feed-through term to the control system. This results in an extra degree of freedom that allows the position of the zeros to be modified and the maximum modal damping to be increased. The second contribution of this paper is a structured PI tracking controller that is parameterized to cancel the additional pole introduced by integral force feedback. The parameterized controller has only one tuning parameter and does not suffer from reduced phase margin. The proposed techniques are demonstrated on a piezoelectric objective lens positioner. The results show exceptional tracking and damping performance while maintaining insensitivity to changes in resonance frequency. The maximum bandwidth achievable with a commercial PID controller is 26.1Hz. In contrast, with the proposed damping and tracking controller, the bandwidth is increased to 255Hz.

Linearization and Input-Output Decoupling for Nonlinear Control of Proton Exchange Membrane Fuel Cells

This paper presents a nonlinear control strategy utilizing the linearization and input-output decoupling approach for a nonlinear dynamic model of proton exchange membrane fuel cells (PEMFCs). The multiple-input single-output (MISO) nonlinear model of the PEMFC is derived first. The dynamic model is then transformed into a multiple-input multiple-output (MIMO) square system by adding additional states and outputs so that the linearization and input-output decoupling approach can be directly applied. A PI tracking control is also introduced to the state feedback control law in order to reduce the steady-state errors due to parameter uncertainty. This paper also proposes an adaptive genetic algorithm (AGA) for the multi-objective optimization design of the tracking controller. The comprehensive results of simulation demonstrate that the PEMFC with nonlinear control has better transient and steady-state performance compared to conventional linear techniques.

Optimal Integral Force Feedback and Structured PI Tracking Control: Application for High Speed Confocal Microscopy.

In this paper, an improvement to Integral Force Feedback (IFF) damping control is proposed. The main limitation of Integral Force Feedback is that the maximum modal damping depends on the system's parameters. Hence, for some system achievable damping is insignificant. The proposed improvement allows any arbitrary damping ratio to be achieved for a system by introducing a new feed-through term in the system. To achieve displacement tracking, one technique is to enclose the system in an integral feedback loop. However, the bandwidth is limited due to the effects of an additional pole in the damping loop. The proposed Structured PI controller is parameterised so that it contains a zero that cancel the additional pole. Experiment was conducted on a commercial objective lens positioner. The results show an exceptional tracking and damping performance and the system's insensitivity to changes in resonance frequency. The maximum bandwidth achievable with a commercial PID controller is 26.1 Hz. In contrast, with the proposed method, the bandwidth is increased to 255 Hz.

Improving the positioning bandwidth of the Integral Resonant Control Scheme through strategic zero placement.

Integral Resonant Control (IRC) is a simple and robust control scheme for vibration damping. Combined with an integral tracking controller, the IRC has been shown to improve the performance of a wide range of nanopositioners. However, the overall improvement in positioning performance is limited by the pole induced by the IRC. Through selective zero placement, the induced pole can be placed near origin. A structured PI tracking controller, where the PI gains are selected to place a zero at a specific location, is used to cancel the pole. This effectively reduces the order of the system by one. For this system, controller gains are derived analytically in order to maximize tracking bandwidth. Simulation results for one axis of a nanopositioner are provided for both standard and modified IRC schemes. Compared to the standard IRC scheme, the modified IRC scheme is found to provide a 55% increase in the ±1 dB bandwidth and a reduction of both maximum and rms tracking errors.

Fault diagnosis and fault tolerant control for the non-Gaussian time-delayed stochastic distribution control system

The purpose of fault diagnosis of stochastic distribution control (SDC) systems is to use the measured input and the system output probability density functions (PDFs) to obtain the fault information of the SDC system. When the target PDF is known, the purpose of fault tolerant control of stochastic distribution control system is to make the output PDF still track the given distribution using the fault tolerant controller. However, in practice, time delay may exist in the data (or image) processing, the modeling and transmission phases. When time delay is not considered, the effectiveness of the fault detection, diagnosis and fault tolerant control of stochastic distribution systems will be reduced. In this paper, the rational square-root B-spline is used to approach the output probability density function. In order to diagnose the fault in the dynamic part of such systems, it is then followed by the novel design of a nonlinear neural network observer-based fault diagnosis algorithm. The time delay term will be deleted in the stability proof of the observation error dynamic system. Based on the fault diagnosis information, a new fault tolerant controller based on PI tracking control is designed to make the post-fault probability density function still track the given distribution, which is dependent of the time delay term. Finally, simulations for the particle distribution control problem are given to show the effectiveness of the proposed approach.

Gain-scheduled PI tracking control on stochastic nonlinear systems with partially known transition probabilities

Abstract This paper studies the problem of continuous gain-scheduled PI tracking control on a class of stochastic nonlinear systems subject to partially known jump probabilities and time-varying delays. First, gradient linearization procedure is used to construct model-based linear stochastic systems in the vicinity of selected operating states. Next, based on stochastic Lyapunov stabilization analysis, sufficient conditions for the existence of a PI tracking control are established for each linear model in terms of linear matrix inequalities. Finally, continuous gain-scheduled approach is employed to design continuous nonlinear PI tracking controllers on the entire nonlinear jump system. Simulation example is given to illustrate the effectiveness of the developed design techniques.

Constrained PI Tracking Control for Output Probability Distributions Based on Two-Step Neural Networks

In this paper, a new method for the control of the shape of the conditional output probability density function (pdf) for general nonlinear dynamic stochastic systems is presented using two-step neural networks (NNs). Following the square-root B-spline NN approximation to the measured output pdf, the problem is transferred into the tracking of dynamic weights. Different from the previous related works, time-delay dynamic NNs with undetermined parameters are employed to identify the nonlinear relationships between the control input and the weighting vectors. In order to achieve the required control objective and satisfy the state constraints due to the property of output pdfs, a constrained PI tracking controller is designed by solving a class of linear matrix inequalities and algebraic equations. With the proposed tracking controller and adaptive projection algorithms, both identification and tracking errors can be made to converge to zero, and the state constraints can also be simultaneously guaranteed. Finally, two simulated examples are given, which effectively demonstrate the use of the proposed control algorithm.