Step Set-point Change Research Articles

Performance assessment of control loops involving unstable systems for set point tracking and disturbance rejection

In this article, a performance assessment method that measures the performances of set point tracking as well as disturbance rejection characteristics of PID controllers designed for unstable processes is proposed. The lower bounds of integral absolute errors (IAEo) are derived from the desired closed loop transfer function subjected to set point changes which may be of step or ramp types. The performance index is developed by considering Direct Synthesis (DS) method for PID controller design. Based on the theoretical bound IAE0, a dimensionless index is elucidated as the ratio between IAE0 and the actual IAE obtained from closed loop response under step set point changes and load variable changes. Considering this IAE based index as the performance measure of PI/PID control loops, the effectiveness of the controller is evaluated and tested on different types of unstable first order or second order plus time delay processes. Simulation studies for both set-point changes and disturbance rejection on various numerical examples are performed to prove the validity of the suggested performance benchmark.

Steady-State Tracking Properties for the Generalized Minimum Variance Controller: A Review, Proportional-Integral-Derivative Tuning, and Applications

The generalized minimum variance (GMV) controller design to deal and eliminate offset can involve the selection of integral and weighting factors with respect to the controlled plant output. This introduces integral control action in a natural form and produces an implicit control design. The implementation of this idea has been explored in few nonlinear applications as well as in the GMV synthesis for the direct adaptive approach and also hybridized to tune a proportional-integral-derivative (PID) controller. The conventional way to ensure set point tracking and regulation is to use an integral control weighting or an incremental plant model. Besides these three linear GMV control designs, this paper brings numerical essays with nonlinear chemical plant models to show the efficiency, stability, and robustness to step set point changes and load disturbance rejection when moving the operating point of the plant around its nonlinear region.

Decentralized Iterative Learning Control to Large-Scale Industrial Processes for Nonrepetitive Trajectory Tracking

In the procedure of steady-state hierarchical optimization with feedback for a large-scale industrial process, it is usual that a sequence of step set-point changes is carried out and used by the decision-making units while searching the eventual optimum. In this case, the real process experiences a form of disturbances around its operating set-point. In order to improve the dynamic performance of transient responses for such a large-scale system driven by the set-point changes, an open-loop proportional integral derivative-type iterative learning control (ILC) strategy is explored in this paper by considering the different magnitudes of the controller's step set-point change sequence. Utilizing the Hausdorff-Young inequality of convolution integral, the convergence of the algorithm is derived in the sense of Lebesgue-P norm. Furthermore, the extended higher order ILC rule is developed, and the convergence is analyzed. Simulation results illustrate that the proposed ILC strategies can remarkably improve the dynamic performance such as decreasing the overshoot, accelerating the transient response, shortening the settling time, etc.

Plantwide Control System Design: Extension to Multiple-Forcing and Multiple-Steady-State Operation

A new approach to designing plantwide control systems that is based on a linear dynamic process model and output optimal control is extended in this paper. The design of a plantwide architecture is split into four stages, and the results from one stage are used as the input to the next. During the design process, transient responses are easily calculated, and they can be used to compare candidate architectures to one another to eliminate architectures with poor dynamic performance. The design methodology is facilitated through a user-friendly software package that makes use of the best currently available algorithms for solving output optimal control problems. In this paper, the design methodology is extended to cover cases where a set of step disturbances and/or step set-point changes is important, as well as to cases where a common control system is required for multiple-steady-state operation. The approach is illustrated on the Tennessee Eastman process.

Design of robust controllers with simple structures for stable, integrating and unstable processes

A method is presented to design a robust controller for a wide range of stable, integrating and unstable process dynamics. The controller with a simple structure can be a PI, PID or higher-order type, whose parameters are determined simply by specifying the desired closed-loop response. However, the design of high-order controllers may result in good performance but very poor robustness, which is not detectable by the conventional indices of gain and phase margins. To avoid this, a robustness index is proposed as a replacement for the gain margin. Optimal controller design is the achievable by minimizing a designated error integral criterion for a load disturbance subject to inequality constraints on phase margin and the new robustness index. By a clever adjustment in control algorithms, the optimal design for a load disturbance can also give a fast response with a desired overshoot for a step set point change.

Monitoring and Assessment of Control Performance for Single Loop Systems

The single loop control system with controller of general structure or with PI/PID structure is studied. The control task of the system is to track step set-point changes or reject the intermittent step output disturbances. Performance of a simple feedback system is assessed with its IAE value (J) and its rise time (tr) observed from the response of the system to a step set-point change. Assume that the dynamics of open loop processes can be represented by models of first order or second order plus dead time (i.e., FOPDT or SOPDT). On the basis of these models, the optimal IAEs and the associated rise times are computed. The performance of a system is assessed by comparing its current IAE to the optimal IAEs. An index is thus defined for this quantitative assessment. To be free of a process model for assessment, envelopes of optimal IAE and the rise time are prepared. A method to estimate the step response for set-point tracking by making use of the response of the system to dither inputs is presented. By...

A robust self-tuning scheme for PI- and PD-type fuzzy controllers

Proposes a simple but robust model independent self-tuning scheme for fuzzy logic controllers (FLCs). Here, the output scaling factor (SF) is adjusted online by fuzzy rules according to the current trend of the controlled process. The rule-base for tuning the output SF is defined on error (e) and change of error (/spl Delta/e) of the controlled variable using the most natural and unbiased membership functions (MFs). The proposed self-tuning technique is applied to both PI- and PD-type FLCs to conduct simulation analysis for a wide range of different linear and nonlinear second-order processes including a marginally stable system where even the well known Ziegler-Nichols tuned conventional PI or PID controllers fail to provide an acceptable performance due to excessively large overshoot. Performances of the proposed self-tuning FLCs are compared with those of their corresponding conventional FLCs in terms of several performance measures such as peak overshoot, settling time, rise time, integral absolute error and integral-of-time-multiplied absolute error, in addition to the responses due to step set-point change and load disturbance and, in each case, the proposed scheme shows a remarkably improved performance over its conventional counterpart.

A Self-Tuning Fuzzy PD Controller

In this article we present a self-tuning PD-type fuzzy logic controller (FLC). The output scaling factor (SF) of the proposed controller is modified on-line by an updating factor (α) according to the process trend. The value of a is determined from a rule-base defined on error (e) and change of error (Δe) of the controlled variable. The proposed self-tuning FLC is designed using a very simple control rule-base and the most natural and unbiased membership functions (MFs) (symmetric triangles with equal base and 50% overlap with neighbouring MFs). The effectiveness of the scheme is established through simulation experiments on various types of second order processes such as (i) marginally stable, (ii) non-linear and (iii) non-minimum phase-pole (unstable) systems with different values of dead time. Performance of the proposed self-tuning FLC is compared with that of its conventional counterpart with respect to both step set-point change and load disturbance using several performance indices. In each case the proposed controller shows remarkably improved performance over the conventional one.

A CLOSED-LOOP REACTION-CURVE METHOD FOR CONTROLLER TUNING

This article proposes a closed-loop, reaction-curve method to provide a procedure for establishing controller settings on the classical three-mode (P1D) controllers. It uses the partial extreme data available during the early period of step set-point change under porportional control mode to determine the ultimate period and the ultimate gain of the open-loop process. The resulting ultimate data are critical for subsequent controller settings according to Ziegler-Nichols rules. Simulation examples and test on a pilot-scale stirred-tank reactor demonstrate that the method can provide adequate critical process data, and that it is applicable to processes that are underdamped, characterized by large dead-times, open-loop unstable or with inverse-response.

Tuning of a D.C. Motor Position Servo Controller Using Tutsim

This paper discusses the use of the TUTSIM microcomputer package for simulating a d.c. motor servo positioner. The use of TUTSIM and its commands for tuning a proportional-derivative controller is illustrated for this simple example while examining the response to a step set-point change.

Design and Application of a Time-Optimum Controller for a Class of Nonlinear Processes

A procedure was developed to extend time-optimum control of linear processes to a class of nonlinear processes consisting of a second-order overdamped linear process followed by a nomemory nonlinearity. Bang-bang control was combined with a proportional-integral-derivation (PID) controller to achieve time-optimum control for set-point changes and good regulator operation for minor disturbances. This dual-mode controller was implemented with a small digital computer. The settling time for step set-point changes with dual-mode control was compared to that with PID control alone. A factor of 2 improvement was achieved through time-optimum control. The dualmode control was successfully applied to an actual nonlinear process.