Nonlinear Gain Scheduling Research Articles

Energy saving in batch distillation for separation of ternary zeotropic mixture integrated with vapor recompression scheme: dynamics and control

Abstract In this work, tight composition control and in parallel the operation is integrated with vapor recompression scheme (VRC) is proposed to achieve energy savings and maximum product at a specified high purity for the separation of ternary zeotropic mixture in batch distillation. Firstly, the model representing a ternary system of hexanol/octanol/decanol has been simulated to analyze the open-loop and close-loop dynamics of the process. Secondly, the open-loop and closed-loop operations are integrated with single stage VRC scheme to achieve energy savings. Single stage VRC is operated at very high compression ratio (CR) due to the large temperature difference of the top and bottom streams in batch distillation column. To further improve the thermodynamic efficiency of single stage VRC, double stage compression without intercoolers between the stages of VRC is proposed. Two control schemes have been implemented for constant composition, namely proportional integral (PI) controller and nonlinear gain scheduling proportional integral (GSPI) with and without VRC in closed-loop. The results shows that double stage VRC with GSPI algorithm provides better performance than conventional in terms of energy, product amount and Integral Square Error (ISE).

Decentralized neuro-fuzzy controllers of nonlinear quadruple tank system

This paper presented two decentralized neuro-fuzzy controllers to control the level in lower two tanks in nonlinear quadruple tank system (QTS). The controllers are designed based on adaptive neuro-fuzzy inference system technique. The relation between inputs/outputs was proved using relative gain array, and then, we can divide the quadruple tank system into two subsystems and control each of them separately. The first controller is a neuro-fuzzy inverse nonlinear (NFIN) model, which predicts the voltage required to control the level to track the referred one. So, the voltage was fed to neuro-fuzzy forward nonlinear model (NFFN) to obtain the desired level. The second is neuro-fuzzy nonlinear gain scheduling PI controller, which is designed to control the nonlinear QTS at any operating point. The results show that the NFIN controller has a more accurate tracking level and less computational time in both minimum and non-minimum phases.

Intelligent supervision approach based on multilayer neural PCA and nonlinear gain scheduling

This paper is mainly aimed at developing an off-line supervision approach geared to complex processes. This approach consists of two parts: the first part is the fault detection and isolation and the second one is the process control. The first part is devoted to the implementation of the multilayer neural PCA which combines the advantage of data reduction provided by the principal component analysis and the power of neural network linearization. The transition to control is conditioned by the absence of faults in the process; if there is a defect, it must be isolated by identifying the defected variables. The second part rests on the combination of two control tools: both the gain scheduling and the feedback linearization yield a new approach called nonlinear gain scheduling. To have our work validated, we applied it to a photovoltaic system and it gave effective results.

A LMI Approach to Tracking Control of Nonlinear Polynomial Systems

This paper presents a tracking control approach for a class of nonlinear non-minimum phase systems. This control approach is the combination between an input-output feedback linearization technique and a gain scheduling method to obtain a tracking control structure. The latter is mainly based on the Linear Matrix Inequalities method which allows us to estimate and to enlarge the domain of attraction around operating points. The nonlinear system is represented locally by variation polynomial models. The polynomial models are then used to design a family of feedback controllers. We propose a nonlinear gain scheduling procedure for the problem of guaranteed transition from an actual operating point to a desired one along the reference trajectory. The theoretical results are applied to a non-minimum phase continuously stirred tank reactor in order to illustrate the effectiveness of the proposed approach

Nonlinear gain-scheduling output-feedback control for polynomial nonlinear systems subject to actuator saturation

This paper investigates nonlinear gain-scheduling control approaches for a class of polynomial nonlinear systems, containing an output-dependent vector field with input saturation. Using the polytopic differential inclusion and norm-bounded differential inclusion (NDI) of saturation and dead-zone functions, the nonlinear plants are transformed into systems with measurable parameters. For the polytopic differential inclusion description, a quasi-linear parameter varying (quasi-LPV) output-feedback controller will be sought for saturation control. On the other hand, the NDI model leads to a nonlinear fractional transformation (NFT) output-feedback controller for saturated nonlinear systems. The quasi-LPV and NFT output-feedback control synthesis conditions are derived in the forms of output-dependent matrix inequalities. They can be reformulated as sum-of-squares (SOS) optimisations and solved efficiently using SOS programming. The proposed nonlinear gain-scheduling saturation control approaches will be demonstrated using the Van der Pol equation.

A survey on non-linear gain scheduling design control for continuous and discrete time systems

Recently published researches on trajectory tracking methods are reviewed, and suggestions for further control aims are offered. Both methods for handling reduced tracking error and approaches for treating the case of periodical output trajectories in the case of continuous and discrete non-linear systems are discussed. Computational algorithm aspects are emphasised throughout. The main contribution of this paper is the development of a theoretical framework for different strategies of non-linear gain scheduling control. We demonstrate that one can achieve an accurate trajectory tracking in both cases of discrete and continuous system modelling. The discussion is investigated via the study of a continuous stirred-tank reactor (CSTR) as a second order non-linear model. Finally, interesting conclusions are so derived.

Gain Scheduling Control of a Gravimetric Blender with Vibrant Duct

Blender and feeder are very important devices in a polymer processing plant. The accuracy in delivering the polymer to the plastification unit is a fundamental property for the quality of the final product. To maximize accuracy and precision gravimetric feeder are the best available solution, which measure the weight of the hopper and the feeder. In these devices, it is possible to estimate the delivered flow based on a loss-in-weight method and to design closed loop control systems to regulate the polymer flow. Specifically, in this work vibrating duct feeder are considered which show a peculiar nonlinear dynamics due to the vibrating element. Then, a nonlinear gain scheduling controller has been designed using an implementation which guarantee satisfaction of the so called linearization property.

The Technology to Embed the Predictive Control Algorithm into Configuration Control Software at the DCS Level

The development work and proposes the technique to embed the predictive control algorithm into configuration control software at the DCS level. The thesis presents the technique and its application scheme to control CFBB super-heated steam temperature in a thermal power plant. The control scheme includes that the description of controlled plant characters, conventional control scheme analysis and improved control scheme design. It integrates feed-back and feed-forward DMC with DMC-PID cascade control and nonlinear gain-scheduling compensation for actuator. Satisfactory industrial application results show that such a control scheme has enhanced robustness to the complex process, and better control performance has been obtained.

A novel fuzzy framework for nonlinear system control

Nonlinear PID and gain scheduling controls have attracted much research interests in recent years. These control strategies can accommodate some nonlinear characteristics by allowing the gains varied or rescheduled as a function of system states. In this paper, a novel fuzzy framework is developed to transfer this type of nonlinear controller to its fuzzy domain representation. It is proved that the resulting fuzzy controller is functionally exactly identical to the original control system. One of the benefits of the suggested approach is that it provides a well-defined prototype for the design of fuzzy control system. The resulting linguistic representation can facilitate investigation in linguistic terms into how the controller operates, whereas expert knowledge can be effectively implemented to improve control performance. The viability of the proposed mapping technique is demonstrated by using simulations corresponding to a flexible-link robot.

Humanoid Walking Robot: Modeling, Inverse Dynamics, and Gain Scheduling Control

This article presents reference-model-based control design for a 10 degree-of-freedom bipedal walking robot, using nonlinear gain scheduling. The main goal is to show concentrated mass models can be used for prediction of the required joint torques for a bipedal walking robot. Relatively complicated architecture, high DOF, and balancing requirements make the control task of these robots difficult. Although linear control techniques can be used to control bipedal robots, nonlinear control is necessary for better performance. The emphasis of this work is to show that the reference model can be a bipedal walking model with concentrated mass at the center of gravity, which removes the problems related to design of a pseudo-inverse system. Another significance of this approach is the reduced calculation requirements due to the simplified procedure of nominal joint torques calculation. Kinematic and dynamic analysis is discussed including results for joint torques and ground force necessary to implement a prescribed walking motion. This analysis is accompanied by a comparison with experimental data. An inverse plant and a tracking error linearization-based controller design approach is described. We propose a novel combination of a nonlinear gain scheduling with a concentrated mass model for the MIMO bipedal robot system.

An application of [formula omitted] nonlinear control and gain scheduling to erbium doped fiber amplifiers

This paper presents an application of control theory towards suppressing cross-gain modulation effects in erbium doped fiber amplifiers (EDFAs). These effects arise due to sudden input power changes at network reconfiguration or system faults. An extended nonlinear model of the EDFA is derived, including amplified spontaneous emission (ASE). Two novel EDFA control applications are developed and compared: one based on L 2 nonlinear control and the other based on optimized gain scheduling. The design of each control law is subject to realistic physical constraints as encountered in industrial application.

Level luffing control system for crawler cranes

A level luffing control system for crawler cranes has been developed. By using this system, an operator can safely keep suspended loads level at elevated spots or on sites where visual operation is impossible. This system consists of a microcomputer-based controller, sensors (boom angle, rope length, boom lever pressure, engine speed) and hydraulic actuators. The control algorithm is the combination of feedback and feedforward control. Nonlinear compensation and gain scheduling by engine speed are also added. The effect of this algorithm was verified by numerical simulations and experimental tests. We could keep the suspended load level in the accuracy within 0.15 m by only boom operation. And the system has been put to practical use.

Design of a gain scheduling controller for knee-joint angle control by using functional electrical stimulation

A gain scheduling approach to the feedback control of the knee-joint movement in paraplegic patients, who have recovered partial functionality of muscles through functional electrical stimulation (FES), is studied. Since it was not possible to perform stimulation sessions on the patient during the work development, collected experimental data have been used to tune a known physiological model of the musculo-skeletal system involved FES, which is here adopted as a "virtual patient," i.e., as the system to control. So, a nonlinear black box model is developed, by using I/O data set obtained from the physiological model simulator. With reference to such a black box model a nonlinear gain scheduling controller is designed, by using the knee-joint position as a scheduling variable and by properly interpolating different linear quadratic regulators. It is proven that the linearization property holds for the proposed controller. Furthermore, the performance of such a controller are analyzed through closed-loop simulations, where the physiological model simulator is used to represent the knee-joint dynamics. The proposed controller shows good tracking and robustness properties on the full range of extension of the knee joint angle and simulation show that the presented strategy could perform better than any proposed linear approach to this problem.

Typical Takagi–Sugeno PI and PD fuzzy controllers: analytical structures and stability analysis

In the first part of this paper, we investigate explicit structure of the typical Takagi–Sugeno (TS) fuzzy PI and PD controllers. By typical, we mean the use of at least three trapezoidal or triangular input fuzzy sets for each input variable, fuzzy rules with linear consequent, Zadeh fuzzy logic AND operator and the centroid defuzzifier. This configuration covers many TS fuzzy controllers in the literature. We mathematically prove these fuzzy controllers to be nonlinear PI (or PD) controllers with proportional-gain and integral-gain (or derivative-gain) changing with output of the controlled system. We reveal these fuzzy controllers to be inherently nonlinear gain scheduling PI (or PD) controllers with different variable gains in different regions of input space. The gains constantly change even in the same region, and switch continuously and smoothly between adjacent regions. The explicit structural expressions of the fuzzy controllers are derived and their characteristics, including the bounds and geometrical shape of the gain variation, are studied. In the second part of the paper, we apply the Small Gain Theorem to the derived structures of the fuzzy controllers and establish a sufficient global BIBO stability criterion for nonlinear systems controlled by the fuzzy controllers. Local stability is also examined.

The Local Solvability of a Hamilton--Jacobi--Bellman PDE around a Nonhyperbolic Critical Point

We show the existence of a local solution to a Hamilton--Jacobi--Bellman (HJB) PDE around a critical point where the corresponding Hamiltonian ODE is not hyperbolic, i.e., it has eigenvalues on the imaginary axis. Such problems arise in nonlinear regulation, disturbance rejection, gain scheduling, and linear parameter varying control. The proof is based on an extension of the center manifold theorem due to Aulbach, Flockerzi, and Knobloch. The method is easily extended to the Hamilton--Jacobi--Isaacs (HJI) PDE. Software is available on the web to compute local approximtate solutions of HJB and HJI PDEs.

Nonlinear Process Control by a Combination of Exact Linearization and Gain Scheduling Trajectory Control

Exact linearization and gain scheduling are two different well-known approaches to the design of nonlinear process control systems. The basic idea of the design approach presented in this paper is to combine these techniques for open loop stable nonlinear systems to get a resulting control structure which makes use of the advantages and overcomes some of the disadvantages of both concepts. In a first step, a nominal nonlinear state feedback controller is computed to linearize the input/output map of the process model and to specify a nominal closed loop trajectory. A simulation of the process model is used to calculate the required state variables. Subsequently we design a nonlinear gain scheduling trajectory controller by approximately linearizing the process model not for a number of operating points as in the standard gain scheduling approach but around the nominal trajectory generated by the nonlinear state feedback controller. The linear approximation of the trajectory control loop meets the specifications of the respective linear design. The gain scheduling trajectory controller forces the process output to keep up with the nominal trajectory in case of modelling errors and disturbances. A neutralization process in a stirred tank is used as an example to demonstrate the performance of the resulting nonlinear control structure.