Control design for nonlinear process models using linear robust control methods: An FCCU example

One of the well-known methods for improving the lateral stability of a vehicle is to utilize an active steering controller. Common active steering systems use feedback signals from a yaw rate sensor and side-slip angle estimation. However, in some driving conditions, skilled drivers can prevent vehicle rollover using the steering angle of the vehicle. Hence, the effect of an active front-steering controller on the roll angle of the vehicle is studied in this paper. For this study, a three-degree-of-freedom linear model of a vehicle which has the lateral motion, the yaw motion and the roll motion as the degrees of freedom is derived. The effectiveness of the active steering controller on the roll stability of the vehicle is examined by simulations in a wide range of longitudinal velocities of the vehicle using a linear quadratic regulator controller. The results obtained indicate that the active steering controller increases the roll stability of the vehicle only at low vehicle speeds and also that consideration of the roll degree of freedom in the design of the active steering controller is not effective at high vehicle speeds. Therefore a two-degree-of-freedom bicycle model is sufficient for active steering controller design. Another part of this paper is dedicated to designing a practical active steering controller for a vehicle with time-varying and uncertain parameters. In fact, designing a controller which guarantees the stability of the vehicle with simultaneous uncertainties in the cornering stiffnesses of the tyres and in the time-varying velocity is the main goal of this paper. Another important advantage of the proposed controller is its simplicity and static structure. In fact, this controller design is carried out offline and can be implemented for use in a real vehicle. This simple and powerful controller is a robust linear quadratic regulator controller. For designing a robust linear quadratic regulator controller, a polytopic model of the two-degree-of-freedom vehicle is obtained, which considers the uncertainty in the parameters. In addition, a linear matrix inequality is used to design a linear quadratic regulator controller for an uncertain or parameter-varying system. Finally, the performance of the designed robust linear quadratic regulator controller was studied by simulating the vehicle responses in some manoeuvres. A sport utility vehicle model is used for simulation purposes. This non-linear vehicle model has eight degrees of freedom and its tyres are assumed to be both linear and non-linear. The performance of the robust linear quadratic regulator controller was studied for vehicles with both linear and non-linear Pacejka tyres. The proposed controller guarantees robust stability of the closed-loop system in the presence of 50% variation in the vehicle speed and 20% uncertainty in the stiffnesses of the tyres.

Robust controller design methodology for multivariable chemical processes: Structured perturbations

This paper presents a model reduction and control approach for a class of active flow control problem. Computational fluid dynamics (CFD) has been used extensively to study fluid dynamic systems. It is a powerful tool to gain insight and understanding, but it is also extremely computationally intensive and thus unsuitable for control design and iteration. Various model reduction schemes have been proposed in the past to approximate the Navier-Stokes equation with a low-dimensional model. There are essentially two approaches: input/output model identification and modal decomposition based on snapshots of high-dimensional states such as proper orthogonal decomposition (POD). The former captures mostly the local behavior near a steady state and the latter is highly dependent on the snapshots of the flow state used to extract the projection. This paper presents a novel model reduction approach that attempts to combine the attractive features of the two approaches. The local behavior is first obtained through the identification of a linear (or semi-linear) time invariant model using the input/output data. To capture the large nonlinear structure, we project the difference between CFD response and the linear identified model response onto a set of POD basis. This trajectory is fit to a nonlinear dynamical model to augment the input/output linear model. The resulting linear+nonlinear model is used to design a feedback control law. The difference between the predicted trajectory and CFD simulated trajectory under this control law is further used to refine the POD basis, until a good match is obtained. The proposed method is applied to 2D compressible flow example with outlet flow rate control for a contraction section. Preliminary results for lift control of a 2D airfoil is also included.

Identification of MIMO Volterra Series and Application to FCC Unit

Design and implementation of multi-variable [formula omitted] robust control for the underground coal gasification project Thar

Doubly fed induction generators (DFIGs) are the most popular for application in varying speed wind turbines. This is because of their reduced converter sizes and ability to operate within 30% of their rated speeds. In addition, it also allows for decoupled control of the active and reactive powers. This study provides insight into the application and performance of linear robust control strategies for the operation of the DFIG at different steady states in addition to faulty phenomenon such as grid voltage distortion. To do this, the study explores the designs of loop shaping control, H ∞ control, μ control and linear parameter varying (lpv) control. The four controllers are applied separately with similar conditions in a Matlab & Simulink environment and the results compared. It is noted that though all the comtrollers are robust and promising for stability and tracking, the H ∞ control results into the best performance.

The designs of two linear control systems approach to stabilize the balance of an unmanned bicycle system are presented. Both approaches are based on the use of a reaction wheel or flywheel to balance the bicycle. The two linear control approaches, based on the linearization of a nonlinear model obtained using Lagrange formalism, are the classic linear controllers, PID and State Feedback control. The performance of both controllers is verified by digital simulation and real-time experimental results.

Model predictive control (MPC) is an advanced control that has found widespread use in industries, particularly in process industries like oil refining and petrochemicals. Although the basic premise behind MPC is easy to comprehend, its inner workings are still generally viewed or regarded as too advanced for actual plant operator understanding. This lack of understanding is exposed when MPC performance deteriorates sometime after commissioning, as is often the case in some commercially operated process plants. Currently operators might have difficulty over reasoning about MPC performance degradation and formulating steps to investigate the cause. A tool is described that aims to make MPC more transparent to the operators. Commonly reported causes of MPC performance degradation are discussed and ways in which the operator can recognise them when they occur are outlined. Issues that are addressed include: making the set of controlled variables to be used for a given set of manipulated variables simpler and clearer; ways to recognise when a MPC controller is performing poorly and to identify the source of performance deterioration. An aim is to determine under what instances the operator can return the MPC performance to previous levels or request for specialist support or simply switch the MPC off. A goal is to avoid the kind of often reported situation where the operator gets worried that the controller is deteriorating and ends up taking knee jerk actions that cause further problems in MPC. At the top of the maintenance tool hierarchy is the trends comparison group, where MPC reference graphical performance trends are compared with actual graphical performance trends counterpart. If any abnormality is observed in these trends, the operator is encouraged to choose an option from a list of preliminary diagnostic questions contained in a group below trends comparison group, which best describes the observed abnormality. Each abnormality is associated with a list of suspected causes. When a suspected cause is chosen from the associated list, the operator is led to the symptoms investigation window, which contains scripts detailing steps for systematic examination of each symptom, with a view to either rejecting or confirming the suspicion. Assisted in the investigation are four background information windows: the virtual plant without MPC window, the virtual plant with MPC window, the transfer function matrix window and steady state gain, relative gain array (RGA) and relative weight array (RWA) window. The windows contain information and guidance that the operator might refer to from time to time during symptom investigation. Development of the maintenance tool is still at the design stage. The key components described have been research implementing MPC on three nonlinear process models, a continuous stirred tank reactor (CSTR), an evaporator process and a fluid catalytic cracking unit (FCCU). Case studies representing different MPC degradation scenarios are simulated, followed by a systematic procedure for diagnosing, isolating and recovering from such degradation, based on assumed operator’s perspective and expert’s technical reasoning. The knowledge gained from the case studies is used to develop an outline of a vision for a data-driven model predictive maintenance tool to help the operator make sensible judgements about performance degradation, the form and direction of diagnosis and fault isolation, and possibly, the recovery procedure.

Constrained nonlinear multivariable control of a fluid catalytic cracking process

It is common practice to use linear plant models and linear controllers in the control systems design. Such approach has simple explanation applying to plants with insignificant nonlinearity or to those, functioning closely to a working point. But linear controllers, indeed with some modification, are used even for plants with significant non-linearities. Because of several reasons the non-linear controllers have not broad application. First, the linear control theory is well developed; while the non-linear control methods are clear for few engineers in practice. Second, there are some technological and economical difficulties to get high quality study of the process to be controlled in order to build detailed (more precise) non-linear plant model. Third, new ideas in the field of the control theory are continuously realized, which expand the span of the linear control systems applications as an alternative to utilizing complicated models at the expense of troubles of theoretical and practical nature.

A two-step controller synthesis method is proposed in this article for a class of uncertain non-linear systems described by piecewise affine differential inclusions. In the first step, a robust linear controller is designed for the linear differential inclusion that describes the dynamics of the non-linear system close to the equilibrium point. In the second step, a stabilising piecewise affine controller is designed that coincides with the linear controller in a region around the equilibrium point. The proposed method has two objectives: global stability and local performance. It thus enables us to use well-known techniques in linear control design for local stability and performance while delivering a global piecewise affine controller that is guaranteed to stabilise the non-linear system. To construct the required theoretical framework, a stability theorem for non-smooth Lyapunov functions is presented and proved. The new method will be applied to two examples.

Mathematical modeling of a pressurizer in a pressurized water reactor for control design

Mission of Unmanned Aerial Vehicle (UAV) “Elang Avionik” is surveillance and aerial photographs. Therefore the flight of UAV must be stable and controlable, and first step activity is dynamic modelling and stability analisys. The problems of UAV system is disturbance, noise of sensor, MIMO and uncertainty dynamic model. For good result using the multivariable robust control, with some step research that is: (1)modeling and stability analysis, (2) design and implementation of PID control system, (3) flight dynamic parameter identification, (4) design and implementation of hardware in the loop simulation, (5) design and implementation of multivariable robust control, (6) test and evaluation of system. Simulation result show that the eigen value in longitudinal is: phugoid mode = –0,061293±0,40526i and non-oscillation mode = –6,1121±4,9253. In lateral directional is:dutch roll mode = –0,91089±5,7994i, spiral mode= –0,036563, and roll subsidence mode = –12,7181. Location of poles system on the left of imaginary axis, the means that the character of system is dynamic stable. But settling time to steady state condition is very long and improved by control system design.
 Key word: State space, Longitudinal, Lateral, Stable static, Stable dynamic

Optimization of the production planning is crucial for the economic success of a petroleum refinery. Nevertheless, it is a difficult task, because of the large scale of the system and the complexity of the processes involved. Part 1 of this series of two papers addresses the formulation of process models for petroleum refinery planning. First, a generic formulation of nonlinear refinery planning model is adopted from the literature. Subsequently, the formulation of nonlinear empirical models for crude distillation units (CDUs) and a fluid catalytic cracking (FCC) unit is addressed. These empirical models were successfully validated using rigorous process simulators. Finally, the results from model validation showed that the accuracy of model predictions is as good as the current empirical process models reported in the literature, while the empirical process models proposed in this work overcome the limitations of both linear and nonlinear empirical models for CDUs and FCC units previously developed by other authors. Part 2 [Ind. Eng. Chem. Res.2011, DOI: 10.1021/ie200304v] involves the implementation of nonlinear empirical process models in the petroleum refinery planning.

Decentralized Control Design for Adaptive Structures with Tension-only Elements