Linear PI Controller Research Articles

APPLICATION OF RESET CONTROL TO A BATCH REACTOR IN THE PRECIOUS GROUP METALS INDUSTRY

Application of reset control to the temperature control loop of an exothermic batch reactor in the Precious Group Metals industry is investigated in this paper. Through modelling and simulation of the process temperature response to cooling, a comparison is drawn between the existing PI controller, an optimized linear PI controller, an optimized linear PI controller with lead, and a reset controller. The simulations confirm the ability of reset control to significantly reduce temperature overshoot as well as decrease the settling time in this process control loop. In addition, the simulations uncover the necessity of applying a non-zero initial condition to the reset controller in this specific control application. The main purpose of the paper is to demonstrate the potential for novel application of reset control with non-zero initial conditions to an existing industrial process in the hydrometallurgical industry. In the literature actual industrial applications of reset control appear to be scarce, and the application of a non-zero initial condition to the reset controller may well be unique. The paper also highlights some typical practical issues, including effects of dead time and noise, which are involved with the application of theoretical control solutions in an industrial environment.

Linear and Nonlinear Control Techniques for a Three-Phase Three-Level NPC Boost Rectifier

This paper deals with three control techniques for a three-phase three-level neutral-point-clamped (NPC) boost rectifier to study their relative performance. Linear, nonlinear, and nonlinear model reference adaptive control (MRAC) methods are developed to control power factor (PF) and regulate output and neutral point voltages. These controllers are designed in Simulink and implemented in real time using the DS1104 DSP of dSPACE for validation on a 1.2-kW prototype of an NPC boost rectifier operating at 1.92 kHz. The performance of boost converter with three control methods has been investigated respectively in steady state in terms of line-current harmonic distortion, efficiency, and PF and during transients such as load steps, utility disturbances, reactive power control, and dc-bus voltage tracking behavior. The linear PI controllers are characterized by reduced complexity but poor performance, whereas the nonlinear control technique has improved the converter performance significantly, while nonlinear MRAC exhibits much better performance in a wide operating range

Solidification and control of a liquid metal column

In this paper, two different 1D mechanistic models for the solidification of a pure substance are presented. The first model is based on the two-domain approach, resulting in 2 partial differential equations (PDEs) and one ordinary differential equation (ODE) with 2 boundary conditions, 2 interface conditions, and one initial condition: the Stefan problem. In the second model, the metal column is considered as one-domain, and one PDE is valid for the whole domain. The result is one PDE with two boundary conditions. The models are implemented in MATLAB, and the ODE solver ode23s is used for solving the systems of equations. The models are developed in order to simulate and control the dynamic response of the solidification rate. The control scheme is based on a linear PI controller.

NEUROFUZZY NETWORK-BASED ADAPTIVE NONLINEAR PI CONTROLLERS

PI controllers are still among the most popular industrial controllers, as they are relatively easy to install and reasonably robust, and can remove steady-state errors of type 0 processes. However, if the system is highly nonlinear, the performance of the PI controllers may deteriorate rapidly. A popular approach to control nonlinear systems is to switch between several linear PI controllers using fuzzy logic based on the Takagi-Sugeno model. In this paper, B-spline neurofuzzy networks are used to implement such a nonlinear controller. Neurofuzzy networks are chosen to implement the nonlinear PI controller for their abilities to approximate nonlinear functions and be trained online using experimental data. Design guidelines and training of the proposed controller are presented. The implementation of the proposed controller is presented, and its performance is demonstrated using a two-tank water level control rig and a continuous stirred-tank reactor process, and compared with PI controllers tuned using existing techniques.

Comparison of Fuzzy Logic Based DC Voltage Control Strategies for a Three Phase Parallel Active Filter

Abstract This paper is on the performance compazison of vazious PI type Fuzzy Logic Controllers for a three phase, three-wired Pazallel Active Filter (PAF) system, consisting of an Insulated Gate Bipolar Transistor (IGBT) based current controlled PWM Voltage Source Inverter. As a novelty in PAF applications, a Self Tuning Fuzzy Logic Controller is developed in order to improve the dynamic behavior of the system. The performance of the self tuning fuzzy control is compared with that of two Mamdani type fuzzy PI controllers with symmetric and asymmetric triangulaz membership functions, as well a classical linear PI controller. Simulations aze performed to evaluate the system performance in terms of maximum overshoot (Tm), rise time (tr), and settling time (ts) of the do capacitor voltage to the 2% of the reference do voltage. The results show that the self tuning fuzzy control improves the dynamic behavior of the PAF, while maintaining the improved Total Harmonic Distortion in the ac source current (THDias)...

Linear PI control of batch exothermic reactors with temperature measurement

AbstractA wide variety of speciality materials and fine chemicals such as plastics, pharmaceutical and microelectronics components are produced in batch reactors. The nonlinear, transient and finite‐time features of the batch reactors give rise to complex process and control design problems. In particular, the safe operation of exothermic reactors depends on the adequate functioning of a temperature tracking controller, and to a good extent, the same is true for the attainment of a suitable compromise between productivity and product quality attributes. While the stabilization problem of continuous exothermic chemical reactors has been recently addressed with rigorous asymptotic‐stability methods, the same kind of studies have not yet been performed for the finite‐time batch reactor case. In this paper, the problem of designing a temperature tracking controller for an exothermic batch reactor, with n species and m reactions, is addressed under the following premises: (i) only the reactor temperature is measured, (ii) the (typically uncertain) reaction rate and heat exchange nonlinear functions are unknown, (iii) the controller must be linear and easy to tune, and (iv) the closed‐loop reactor motion must be stable in a suitable sense. The combination of industrial‐oriented inventory control concepts in conjunction with singular perturbation results yields a linear controller with a combined feedforward‐PI feedback structure, antireset windup scheme, and conventional‐like tuning rules. The controller: (i) tracks, arbitrarily fast and close, a prescribed temperature trajectory, with admissibly deviated concentration motions, and (ii) quickly recovers the behaviour of an exact model‐based nonlinear I/O linearizing controller. The proposed design is put in perspective with the geometric and IMC nonlinear control approaches. Copyright © 2005 John Wiley & Sons, Ltd.

Nonlinear Function Controller: A Simple Alternative to Fuzzy Logic Controller for a Power Electronic Converter

Recently, there has been an increase in the application of fuzzy logic controllers (FLCs) for control of power electronic converters. Due to the FLCs' complex algorithm, their realization often calls for a compromise between cost and performance. In this paper, it is shown that the rule table of most of the two-input FLCs used with power converters can be approximated into a single nonlinearity. This allows the controller to be easily realized using simple, fast, and inexpensive analog circuits. The simplified nonlinear function controller (NLFC) developed in this manner is shown to be equivalent in performance to the original FLC through simulations. The NLFC concept is then applied to PI-FLC, a type of FLC popular in power converter control applications. This results in the PI-FLC being replaced by a simple nonlinear PI controller (NPIC). Using this simplification, the design of NPICs to obtain good dynamic performance in power converters is explained. An example design of NPIC for controlling a dc-dc boost power converter is presented. Experimental results are also presented to demonstrate the superior dynamic performance of the converter with NPIC versus that of a linear-PI controller.

Nonlinear control of bioreactors with input multiplicities—an experimental work

The phrase input multiplicities means that an input variable with more than one value produces the same output value as if there were a single input-single output process. With input multiplicities, the value of the process gain changes as the manipulated variable changes, and beyond a certain input value, the sign of the gain also changes. A conventional PI controller for processes with input multiplicities may give unstable, less economical, or oscillatory responses. In the present work, control problems of a continuous bioreactor exhibiting two input multiplicities in the dilution rate on productivity were experimentally analyzed. A regulatory problem for the evaluation of controllers was taken up, i.e. a step change was made in the feed substrate concentration from 20 to 25 g/l at steady state conduction at lower (0.09386 h(-1)) and higher (0.2278 h(-1)) dilution rates for the same productivity of 2.9 g/l h. The nonlinear PI controller gave a more stable and fast response at both input dilution rates. The linear PI controller designed for a lower input dilution rate was stable, with some oscillations at the lower dilution rate, but the response was unstable at a higher dilution rate due to the input multiplicity behaviour of the process. Thus, nonlinear PI controller performance was found to be superior to that of the linear controller, and earlier reported theoretical results have been validated by the present experimental work.

Complex Nonlinear Behavior in the Full-Scale High-Impact Polystyrene Process

In this work, the open-loop nonlinear bifurcation analysis of the high-impact polystyrene process is carried out and used for optimal design, operation, and control analysis. The process can be described by a set of seven continuous stirred tank reactors (CSTRs) connected in series. Process design was carried out using an optimization approach; the nominal optimal operating point is open-loop unstable and agrees with typical industrial operating conditions. For the seven CSTRs cascade, as much as 398 steady states were found, but only 11 are considered as industrially feasible; 9 of them are open-loop unstable. Both input and output multiplicities were found, and implications on optimal grade transitions and process control are discussed. A simple cascade control system was used to demonstrate that linear PI controllers add patterns of nonlinear behavior previously not present in the process.

On Some Low-Cost Tracking Controllers for Mobile Robots

The article addresses the problem of developing low-cost controllers used in tracking control for mobile robots. A simplified dynamic model that can well characterize the wheeled mobile robots with two degrees of freedom is first proposed. The control system structure involved contains two control loops for controlling the forward velocity and the angle between the heading direction and the x-axis. The reference trajectory of the robot is obtained by employing the artificial potential field method used in obstacle avoidance, accompanied by some simple computations in terms of the tracking errors for the x- and y-axes and of the maximum accepted values for these errors. In addition, the authors present development methodologies for three types of tracking controllers: the PI controllers, a version of PI-fuzzy controllers, and a version of sliding mode-PI controllers, based on the Extended Symmetrical Optimum method applied to the basic linear PI controllers and by adding nonlinear features of fuzzy- or sliding mode-type for obtaining control system performance enhancement. Simulation results are provided to validate the proposed dynamic model and navigation controllers.

SENSITIVITY ANALYSIS OF LOW COST FUZZY CONTROLLED SERVO SYSTEMS

The paper performs the sensitivity analysis with respect to the parametric variations of the controlled plant in the case of low cost fuzzy control systems dedicated to servo systems, with focus on solving the tracking control problem for a class of wheeled mobile robots with two degrees of freedom used in mining technologies. A new development method for Takagi-Sugeno PI-fuzzy controllers is proposed, based on applying the Extended Symmetrical Optimum method to the basic linear PI controllers in a cascaded control system structure. Original sensitivity models are derived. The approaches are validated by a case study.

Sensitivity Analysis of a Class of Fuzzy Controlled Mobile Robots

The paper deals with the sensitivity analysis of fuzzy control systems solving the tracking control problem for a class of wheeled mobile robots with two degrees of freedom. There is proposed a development method for PI-fuzzy controllers based on the application of the Extended Symmetrical Optimum method to the basic linear PI controllers. A cascaded control system structure is considered employing the off-line generation of the reference inputs by means of the artificial potential field method for obstacle avoidance. Digital simulation results for a case study validate the theoretical approaches.

New External Neuro-Controller for Series Capacitive Reactance Compensator in a Power Network

The controllable capacitive reactance can be used as the input variable for the external controller of a series capacitive reactance compensator (SCRC) to improve the damping of low-frequency oscillations of the rotor angle and active power in a power system. Conventional linear PI controllers are tuned for best performance at one specific operating point of the nonlinear power system. At other operating point its performance degrades. Nonlinear optimal neuro-controllers are able to overcome this degradation. In this paper, the dual heuristic dynamic programming (DHP) optimization algorithm is applied to design an external nonlinear optimal neuro-controller for the SCRC. Simulation studies using PSCAD/EMTDC/spl reg/ software are presented.

NONLINEAR PI CONTROLLER FOR pH PROCESS

The control of pH is one of the most difficult challenges in the process industry because of the severe nonlinearities and high precision required in manipulating the flow rate. The Wiener model, which consists of a linear dynamic element followed by a nonlinear static element, is used for representing such nonlinear processes. Piecewise continuous polynomials are used for mapping the nonlinear static gain accurately. A nonlinear PI controller was designed based on the Wiener model. Simulation results on the nonlinear mathematical model are presented to highlight the superior performance of the Wiener model based nonlinear PI controller in comparison to that of the local linear PI controller. The performance of the nonlinear PI controller was further improved upon by using the method of inequalities to obtain a single set of PI controller settings that takes into account the parametric variations in the linear dynamic element at different operating points. Simulation and experimental results are presented to support the work.

PI predictive fuzzy controllers for electrical drive speed control: methods and software for stable development

The paper presents two structures of PI predictive fuzzy controllers (PI-P-FCs) with first- and second-order prediction. The PI-P-FCs are meant for the speed control of electrical drives with variable inertia used in several industrial applications. The new development method for these PI-P-FCs is based on guaranteeing a desired domain for the “phase margin” of the fuzzy control systems (FCSs) with PI-P-FCs when they are considered to be equivalent to the linear control systems with linear (conventional) PI controllers. It is also proposed a stability analysis method for the FCSs with PI-P-FCs employing Popov’s hyperstability theory and a discrete-time state space mathematical model of the controlled plant. A software tool for the stability analysis of the FCSs, developed in the Matlab and Simulink environment, is presented.

A GLC CONTROLLER FOR THE CONTROL OF THE METHYL METHACRYLATE POLYMERIZATION

To produce a certain polymer with desired properties, some of polymerization variables should be controlled. In this paper, a oil bath was designed and constructed for the heating and cooling of the reactor. Then, a mechanistic model was developed for the solution polymerization of methyl methacrylate in a batch reactor. This model is highly non-linear. A Globally Linearizing Control (GLC) strategy was applied to control the reactor temperature. A linear PI controller was designed to eliminate the error. The controller performance was viable and the previously developed GLC method is suitable for the oil heating system.

LINEARIZATION OF FORCE/STROKE CHARACTERISTIC OF SWITCHING SOLENOID USING FUZZY-LOGIC-CONTROLLER

In this paper, the static force/stroke characteristic of switching solenoid is linearized by using the traditional PIcontroller as well as the fuzzy-logic-controller. The major aim is to develop a proportional switching solenoid having the advantage of lower cost as compared with a usual proportional solenoid. Besides, two different methods to implement the linearization are adopted. One is the employment of a force sensor to generate the actual feedback force signal, and the other is the utilization of the numerically estimated pseudo-force as the feedback signal. Experimental results prove that the nonlinear fuzzy-logic-controller is superior to the conventional linear PI-controller concerning the compensation of the high nonlinearity near the end-position of the plunger.

Model‐based synthesis of nonlinear PI and PID controllers

AbstractPI and PID controllers continue to be popular methods in industrial applications. It is well known that linear PI and PID controllers result from the application of model‐based controller design methods to linear first‐ and second‐order systems. It is shown that nonlinear PI and PID controllers result from the application of nonlinear controller design methods to nonlinear first‐ and second‐order systems. As a result, the controllers resulting from nonlinear model‐based control theory are put in a convenient form, more amenable to industrial implementation. Additionally, the quantities used in the controller are useful for monitoring the process and quantifying modeling error. Chemical engineering examples are used to illustrate the resulting control laws. A simulation example further demonstrates the performance of the nonlinear controllers, as well as their useful process monitoring quantities.

High performance nonlinear MIMO field weakening controller of a separately excited dc motor

Abstract This paper presents a novel technique for field weakening implementation of separately excited dc motors. A constant power field weakening controller, which is based on nonlinear load adaptive multi-input multi-output (MIMO) linearization technique, is proposed and developed for achieving speed tracking. Due to the effects of decoupling and linearization, it allows the controller to be implemented and operated at any desired field weakening point of operation. To demonstrate the effectiveness of the proposed controller, the results of computer simulations are presented for a specific motor. The performance of this proposed controller is compared with that of the traditional linear PI controllers. The results show that the proposed controller provides the globally higher speed control performance, while the motor is operated over a wide dynamic regime of field weakening, even under the presence of load torque disturbance.

Exponentially stable non-linear control for speed regulation of induction motor with field-oriented PI-controller

On the basis of a novel dynamic model obtained under a special non-linear co-ordinate transform on a d–q-axis model (w.r.t. the stationary reference frame) of an induction motor, a simple but effective control law for speed regulation is proposed in this paper. This controller is designed using the concept of the field orientation and the property of linear PI-controller, and is shown to be robust with respect to variation of system parameters and load structure. To be rigorous, a Lyapunov theorem with a simple iterative criterion derived in this paper proves the local exponential stability of the system around any desired speed. Numerical simulations are also given to show the effectiveness of the presented control law. Copyright © 2000 John Wiley & Sons, Ltd.