Input-output Linearization Control Research Articles

Shortest-prediction-horizon non-linear model-predictive control

This article concerns non-linear control of single-input-single-output processes with input constraints and deadtimes. The problem of input-output linearization in continuous time is formulated as a model-predictive control problem, for processes with full-state measurements and for processes with incomplete state measurements and deadtimes. This model-predictive control formulation allows one (i) to establish the connections between model-predictive and input-output linearizing control methods; and (ii) to solve directly the problems of constraint handling and windup in input-output linearizing control. The derived model-predictive control laws have the shortest possible prediction horizon and explicit analytical form, and thus their implementation does not require on-line optimization. Necessary conditions for stability of the closed-loop system under the constrained dynamic control laws are given. The connections between (a) the developed control laws and (b) the model state feedback control and the modified internal model control are established. The application and performance of the derived controllers are demonstrated by numerical simulations of chemical and biochemical reactor examples.

Compactly supported radial basis functions for adaptive process control

Abstract An adaptive nonlinear control strategy based on networks of compactly supported radial basis functions is proposed. The local influence of the basis functions allows efficient on-line adaptation that is performed using a gradient law, and new basis functions are added to the network only when new regions in state space are encountered and the prediction error exceeds a pre-specified tolerance. The approximate model is used to construct an input-output linearizing control law. The adaptive control strategy is applied to a nonlinear chemical reactor model.

A robust nonlinear control design for remotely operated vehicle depth control systems

In this paper, an input-output linearisation controller with an adaptive fuzzy outer loop is applied to the depth control of a nonlinear Remotely Operated Vehicle (ROV). The adaptive fuzzy system is added to increase the robustness as well as add 'intelligence' to conventional input-output controllers. The free control parameters are selected using multi-objective fuzzy genetic algorithm optimisation. Simulation results are presented which demonstrate that the proposed control scheme can enhance the closed-loop system performance by reducing the output tracking errors.

Direct Adaptive Control of Partially Known Nonlinear Systems

A direct adaptive control strategy for minimum-phase nonlinear systems is presented. The major advantage of the proposed method is that controller design is not based on a detailed nonlinear model. The only information required about the plant is the state vector, the relative degree, and the sign of a Lie derivative which appears in the associated input-output linearizing control law. Unknown controller functions are approximated via locally supported radial basis functions that are introduced only in regions of the state space where the closed-loop system actually evolves. Lyapunov stability analysis is used to derive parameter update laws which ensure (under certain assumptions) the state vector remains bounded and the plant output asymptotically tracks the output of a linear reference model. The technique is successfully applied to a nonlinear bioreactor model.

ADAPTIVE INPUT–OUTPUT LINEARIZATION OF A pH NEUTRALIZATION PROCESS

Adaptive non-linear control strategies for a pH neutralization process are developed and evaluated via simulation. A non-adaptive non-linear controller is designed using a modified input–output linearization technique which accounts for the implicit output equation in the reaction invariant model. For simplicity the reaction invariants are assumed to be available for feedback. Because the model exhibits significant time-varying behaviour, the input–output linearizing controller is combined with non-linear parameter estimators which account for unmeasured buffering changes. Simulation results demonstrate that a novel indirect adaptive strategy is most suitable for experimental implementation where the reaction invariants must be estimated and sampling is required. © 1997 by John Wiley & Sons, Ltd.

On induction motors control

This paper deals with the control of induction motors. First we show that field-oriented control can be simplified by considering the modulus square of the flux, namely F=f/sup 2/=/spl phi//sub a//sup 2/+/spl phi//sub b//sup 2/ instead of f. Second, we perform an input-output linearizing control without using any of Lie derivatives.

Input-output linearizing control of constrained nonlinear processes

Abstract An input-output linearization strategy for constrained nonlinear processes is proposed. The system may have constraints on both the manipulated input and the controlled output. The nonlinear control system is comprised of: (i) an input-output linearizing controller that compensates for processes nonlinearities; (ii) a constraint mapping algorithm that transforms the original input constraints into constraints on the manipulated input of the feedback linearized system; (iii) a linear model predictive controller that regulates the resulting constrained linear system; and (iv) a disturbance model that ensures offset-free setpoint tracking. As a result of these features, the approach combines the computational simplicity of input output linearization and the constraint handling capability of model predictive control. Simulation results for a continuous stirred tank reactor demonstrate the superior performance of the proposed strategy as compared to conventional input-output linearizing control and model predictive control techniques.

Nonlinear controllers for an induction motor

Tremendous breakthroughs in the techniques of nonlinear control have been achieved in the last twenty years or so. These methods include the differential-geometric techniques, differential-algebraic methods, variable structure control, back-stepping, etc. This paper specifically considers some of the differential-geometric techniques in terms of their suitability for high-performance induction motor control. It is shown that both dynamic feedback linearization and input-output linearization are applicable to induction motor control, and a comparison of the two is made. The particular effectiveness of the input-output linearization controller is demonstrated with experimental results.

Shortest-Prediction Horizon Nonlinear Model Predictive Control

This article presents a continuous-time formulation of model predictive control. This formulation allows (i) to establish the connections between model predictive control and input-output linearizing control methods and (ii) to address the problems of constraint handling and windup in input-output linearizing control methods. Model predictive control laws with the shortest possible prediction horizon are derived for constrained nonlinear processes with deadtime. They have explicit analytical form, and thus their implementation does not require on-line optimization. Furthermore, in the absence of constraints, they are input-output linearizing.

Observer-based non-linear control of a fed-batch autoinductive fermentation process

Optimal regulatory control of an autoinductive recombinant culture in a fed-batch reactor is considered. End point optimization results in a three-stage process: biomass growth, inducer synthesis and product synthesis. It is shown that in the last stage the substrate concentration should be maintained constant. This is achieved using an input—output linearizing controller accompanied by a novel non-linear state observer for the estimation of unmeasured state variables on the basis of on-line off-gas carbon dioxide concentration measurements. Experimental runs of luminous recombinant E. coli strain in a laboratory fermenter demonstrate the rapid convergence of the observer estimates as well as the effectiveness and robustness of the overall control system.

A normal form approach to approximate input-output linearization for maximum phase nonlinear SISO systems

A control synthesis scheme is presented for nonlinear single-input-single-output systems which have completely unstable (antistable) zero dynamics. The approach is similar in spirit to linear approaches for nonminimum phase systems and involves the derivation of an input-output linearizing controller for a suitably-defined nonlinear minimum phase approximation to the original system. The linearizing controller achieves an approximately linear input-output response and internal stability.

Robust Regulation of Temperature in Reactor−Regenerator Fluid Catalytic Cracking Units

FCC processes involve complex interactive dynamics which are difficult to operate and control as well as poorly known reaction kinetics. This work concerns the synthesis of temperature controllers for FCC units. The problem is addressed first for the case where perfect knowledge of the reaction kinetics is assumed, leading to an input-output linearizing state feedback. However, in most industrial FCC units, perfect knowledge of reaction kinetics and composition measurements is not available. To address the problem of robustness against uncertainties in the reaction kinetics, an adaptive model-based nonlinear controller with simplified reaction models is presented. The adaptive strategy makes use of estimates of uncertainties derived from calorimetric (energy) balances. The resulting controller is similar in form to standard input-output linearizing controllers and can be tuned analogously. Alternatively, the controller can be tuned using a single gain parameter and is computationally efficient. The performance of the closed-loop system and the controller design procedure are shown with simulations.

Nonlinear Controllers for Induction Motors

Tremendous breakthroughs in the techniques of nonlinear control have been achieved in the last twenty years or so. These methods include the differential-geometric techniques, differential-algebraic methods, variable structure control, back-stepping, etc. This paper specifically considers some of the differential-geometric techniques in terms of their suitability for high-performance induction motor control. It is shown that both dynamic feedback linearization and input-output linearization are applicable to induction motor control and a comparison of the two is made. The particular effectiveness of the input-output linearization controller is demonstrated with experimental results.

Adaptive input-output linearizing control of a continuous stirred tank reactor

In this paper, we report the application of two different parameter adaptation schemes used to improve the performance of input-output linearizing control of an exothermic continuous stirred tank reactor (CSTR). The first technique is based on ensuring the stability of the control system in the sense of Lyapunov when there are variations in the parameters appearing linearly in the linearizing control law. The second approach considers recursive least squares for parameter estimation independent of the control system stability. When the reactor is subjected to conditions of extreme parametric sensitivity and unstable operating conditions in the presence of variations in the process parameters, the parameter adaptive approach to linearizing control exhibits satisfactory behavior in terms of offset free regulation and improved performance.

High-performance induction motor control via input-output linearization

We have shown that a current-command input-output linearization controller can achieve high-performance motion control, that is, the precise tracking of a fast point-to-point position reference. Specifically, this controller was shown to provide the means of decoupling the speed and flux dynamics in an induction motor. This decoupling of speed and flux was exploited to simultaneously track the position/speed reference and an optimal flux reference. This flux reference was used to obtain the optimal (max/min) motor torque at any given speed without violating voltage and current limits. Experimental results were presented to demonstrate the effectiveness of this scheme. >

Time Delay Compensation for Nonlinear Processes

A new time delay compensation strategy for nonlinear processes is developed and evaluated. Simulation results for a continuous stirred tank reactor demonstrate that the globally linearizing control (GLC) compensation technique can yield poor performance in the presence of unmeasured disturbances and/or plant/model mismatch. A theoretical analysis of a discrete-time version of the GLC predictor indicates that the poor regulatory performance is attributable to ineffective use of the process state variables, which are assumed to be measured. A new discrete-time prediction strategy is developed which provides improved predictions, yet maintains the desirable characteristics of the GLC approach. A continuous-time version of the predictor is combined with an input-output linearizing controller to yield the new time delay compensation strategy. The proposed scheme is computationally efficient and not restricted to open-loop stable processes. Simulation results for the reactor example demonstrate the superior performance and robustness of the proposed compensation strategy as compared to the GLC approach

Design of adaptive linearizing controllers for non-isothermal reactors

This paper deals with the control of the temperature in non-isothermal stirred-tank reactors involving M (M greater-than-or-equal-to 1) chemical reactions. The proposed control algorithm is an input-output linearization controller which accounts for the well-known process nonlinearities. The control scheme is also adaptive in order to deal with the parameter uncertainty: in particular it is shown how to include explicit on-line estimates of the M activation energies within the adaptive linearizing controller. The performance of the control law is illustrated in simulation.

Nonlinear differential-geometric techniques for control of a series DC motor

The problem of controlling a series DC motor using only current measurements is considered. It is shown that both speed and load-torque may be estimated from the current measurements. Two nonlinear feedback laws are considered based on feedback linearization and input-output linearization, respectively. Both of these control laws require knowledge of the speed and load-torque. The speed/torque estimation scheme and the control schemes are valid in the presence of magnetic saturation in the field circuit and when high-speed field-weakening is employed. By neglecting the armature inductance, the estimation is accomplished using nonlinear state-space and output-space transformations to construct an observer with linear error-dynamics whose rate of convergence may be arbitrarily specified. (Such an observer could provide reliability to existing systems in the event of a speed sensor failure.) The feedback-linearization controller involves a nontrivial state-space transformation allowing control of the full state trajectory. An input-output linearization controller with stable internal dynamics is also explicitly constructed. Finally, simulations are given to demonstrate the algorithms. >

Adaptive nonlinear control of a pH neutralization process

An adaptive nonlinear control strategy for a bench-scale pH neutralization system is developed and experimentally evaluated. The pH process exhibits severe nonlinear and time-varying behavior and therefore cannot be adequately controlled with a conventional PI controller. The nonlinear controller design is based on a modified input-output linearization approach which accounts for the implicit output equation in the reaction invariant model. Because the reaction invariants cannot be measured online and the linearized system is unobservable, a nonlinear output feedback controller is developed by combining the input-output linearizing controller with a reduced-order, open-loop observer. The adaptive nonlinear control strategy is obtained by augmenting the non-adaptive controller with an indirect parameter estimation scheme which accounts for unmeasured buffering changes. Experimental tests demonstrate the superior performance of the adaptive nonlinear controller as compared to a non-adaptive nonlinear controller and conventional PI controller.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Adaptive input-output linearizing control of induction motors

A nonlinear adaptive state feedback input-output linearizing control is designed for a fifth-order model of an induction motor which includes both electrical and mechanical dynamics under the assumptions of linear magnetic circuits. The control algorithm contains a nonlinear identification scheme which asymptotically tracks the true values of the load torque and rotor resistance which are assumed to be constant but unknown. Once those parameters are identified, the two control goals of regulating rotor speed and rotor flux amplitude are decoupled, so that power efficiency can be improved without affecting speed regulation. Full state measurements are required.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>