PID Structure Research Articles

Effect of Derivative Algorithm and Tuning Selection on the PID Control of Dead-Time Processes

Many control engineers try to avoid the use of derivative action in operating units. As Isaksson and Graebe have pointed out (in a presentation at Control Systems 2000, Victoria, British Columbia, May 2000), there is an “industrial myth that derivative action does not work.” They claim that some of this is due to the need to adjust the derivative filter constant, in addition to the usual three parameters of PID controllers. Modern distributed control systems offer a variety of choices for the PID algorithm, including both series (interacting) and parallel (ideal). The many PID tuning methods that have been developed over the years have used different algorithms, and some are limited to a narrow range of parameter values (dead times). Most tuning methods require setting three tuning parameters, but some propose setting four parameters. All this complexity presents a confusing picture to the practitioner who is faced with trying to tune a PID controller. This paper presents a quantitative comparison of alternative derivative algorithms and tuning methods for processes with a wide range of dead-time/lag ratios. Results show that, when the correct algorithm is used, the IMC tuning method proposed by Morari and Zafiriou (Robust Process Control; Prentice Hall: New York, 1989) gives good performance for large-dead-time processes. The correct algorithm has a four-parameter, parallel, output-filtered PID structure.

Theory and Applications of the Robust Cross-Coupled Control Design

The cross-coupled control (CCC) has been recognized as an efficient motion controller that reduces contouring errors, but theoretical analysis of it is lacking, and there is no systematic design approach for obtaining a CCC system with guaranteed control performance. Consequently, the compensators C in CCC are commonly implemented in a PID structure and their contouring accuracy is usually degraded in real applications under different operating conditions. In an attempt to overcome the CCC design limitations described above, this paper introduces a robust CCC design based on a novel formulation: the contouring error transfer function (CETF), leading to an equivalent formulation as in the feedback control design problem. Then, methods in robust control design can be readily employed to achieve robust CCC with specified stability margins and guaranteed contouring performance. Furthermore, the proposed design has been verified as being internally stable. All provided experimental results indicate that the proposed robust CCC design consistently renders satisfactory contouring accuracy under different operating conditions.

Multiple model adaptive control for interval systems

We present a multiple model adaptive control(MMAC) for linear interval systems of real coefficient. In order to improve the performance as well as stability, the multiple model adaptive control(MMAC) method is introduced. In this approach, the identification models are parameterized in a finite set which consists in 16 Kharitonov systems and each controller of multiple models is designed by the coefficient diagram method(CDM) with PID structure. The characteristic equation of overall system results in a set of multilinear perturbed polynomials with respect to uncertain parameters. The robust stability of the proposed method are analyzed and the performance is examined by simulations on Narendra's example.

Optimal PID controllers including roll off and schmidt predictor structure

A new evaluation method for controllers recently proposed, has been somewhat modified to handle additional control goals for extended versions of PID controllers. To improve the roll off of the loop gain at high frequencies, an extra low pass filter has been included in the PID structure. When the filter is incorporated in the design, the system behavior does not deteriorate. For plants with significant time delay, a Schmidt predictor may be included. It is however shown that the more complicated predictor structure implies marginal improvements in terms of performance and robustness, compared to an ordinary PID, when both are optimized according to the same criterion.

Analysis of direct action fuzzy PID controller structures

The majority of the research work on fuzzy PID controllers focuses on the conventional two-input PI or PD type controller proposed by Mamdani (1974). However, fuzzy PID controller design is still a complex task due to the involvement of a large number of parameters in defining the fuzzy rule base. This paper investigates different fuzzy PID controller structures, including the Mamdani-type controller. By expressing the fuzzy rules in different forms, each PLD structure is distinctly identified. For purpose of analysis, a linear-like fuzzy controller is defined. A simple analytical procedure is developed to deduce the closed form solution for a three-input fuzzy inference. This solution is used to identify the fuzzy PID action of each structure type in the dissociated form. The solution for single-input-single-output nonlinear fuzzy inferences illustrates the effect of nonlinearity tuning. The design of a fuzzy PID controller is then treated as a two-level tuning problem. The first level tunes the nonlinear PID gains and the second level tunes the linear gains, including scale factors of fuzzy variables. By assigning a minimum number of rules to each type, the linear and nonlinear gains are deduced and explicitly presented. The tuning characteristics of different fuzzy PID structures are evaluated with respect to their functional behaviors. The rule decoupled and one-input rule structures proposed in this paper provide greater flexibility and better functional properties than the conventional fuzzy PHD structures.

Bilinear controller with PID structure

The motivation for, and the implementation of, a bilinear control strategy having a PID structure is described. Improved consistency is automatically achieved by exploiting the fact that local bilinearisation holds for a wider range about a given operating point than a conventional approach in which local linearity is assumed. In terms of reduced activity of the control variable and tighter tracking of the process variable, the bilinear controller provides improved consistency of performance over a wider operating range. The benefits of employing the bilinear approach, which offers continuous scheduling of gains through an assumed bilinear controller model structure, are highlighted when the controller is applied to a continuously operated high-temperature furnace. Performance is compared to that of an optimally tuned industrial PID controller.

Stability issues of finite-precision controller structures for sampled-data systems

The paper investigates the sensitivity of closed-loop stability with respect to (w.r.t.) finite word length (FWL) effects in the implementation of the digital controller coefficients. Both the shift and delta operators are considered for controller parameterization. Two tractable lower-bound measures of closed-loop stability are studied, and the optimal realization of general FWL controller structures is formulated as a constrained non-linear optimization problem. The emphasis of the paper, however, is on the derivation of a new algorithmic approach for the optimal realization of FWL PID controller structures. It is shown that, for PID structures, the optimization can be decoupled into two unconstrained problems with a maximum of four independent variables. An optimization strategy is developed to provide an efficient computational method for searching the optimal FWL PID controller realization with maximum stability bound and minimum bit-length requirement. Simulation results involving an IFAC benchmark PID controller system are presented to illustrate the effectiveness of the proposed strategy.

PID tuning based on loop-shaping H∞ control

Loop-shaping H∞ controllers are designed for both stable and integrating processes. H∞ controllers for typical industrial processes have a PID structure interpretation. Further, if the precompensator is carefully chosen, the design indicator will be independent of plant constants. This fact leads to the derivation of a direct relation between the controller parameters and the plant constants, and the results can be viewed as new PID tuning rules for stable and integrating processes. The main contribution of the tuning rules is that the PID parameters can be obtained using one design parameter which reflects the trade-off between stability robustness and time domain performance of the closed-loop system, thus making it convenient to choose PID parameters dependent on the uncertainties of the processes.

A novel model-following scheme with simple structure for electrical position servo systems

A novel model-following scheme with a simple structure for electrical position servo systems is proposed. It is quite different from and much simpler than existing model-following control (MFC) schemes. The nominal model of a plant is used as the reference model in this scheme. The common external input to the reference model and to the plant is not fed from the reference command but from a model controller which is designed for the nominal model of the plant to ensure a satisfactory reference output trajectory. The following of the plant to the reference model with the expected output trajectory is guaranteed using a correction signal from an adaptive mechanism which has a simple linear PID structure, taking only the generalized output error as its input. Conditions for asymptotic model-following are first developed rigorously and then implemented. The system design method is described. Simulation and experimental results show that the proposed MFC scheme is effective and robust against both parameter variations and load disturbance of the actual plant. The comparison of the MFC system with position PI and PID control systems illustrates the superiority of the proposed MFC scheme over the conventional PI/PID control scheme.

Tuning PID Controllers for Disturbance Rejection Based on Linear Quadratic Optimal Methods

Structural stability and sensitivity properties of a PID regulator tuned as a linear quadratic optimal controller (LQOC) are presented. The solution of the LQOC control problem gives as a result a PID structure, but only when a resticted class of models for the disturbance and the plant is considered. The concept of robustness is introduced for those models which can not be included in the class of models leading to PID structures. This method gives as a result, a set of simple tuning rules for PID regulators, which can be applied to a wide range of processes and disturbances.

Relationship between deadbeat and pole-placement discrete-time PID controllers

This paper considers PID control in terms of its implementation by means of an ARMA plant model. Two controller actions are considered, namely pole placement and deadbeat, both being applied via a PID structure for the adaptive real-time control of an industrial level system. As well as looking at two controller types separately, a comparison is made between the forms and it is shown how, under certain circumstances, the two forms can be seen to be identical. It is shown how the pole-placement PID form does not in fact realise an action which is equivalent to the deadbeat controller, when all closed-loop poles are chosen to be at the origin of the z-plane.

Investigations on the Stochastically Optimized PID Controller for a Linear Quarter-Car Road Vehicle Model

SUMMARY An active suspension for a linear quarter - car road vehicle model using a PID structured controller is discussed here. The PID parameters are not optimized using the conventional methods but are based on stochastic optimal control methods. The main idea is to obtain a full feedback optimal LQG controller and then to constrain this controller to fit a PID structure using constrained feedback techniques. The overall performance of this active suspension is evaluated here.

An adaptive fuzzy logic power system stabilizer

The paper presents an adaptive fuzzy logic power system stabilizer (PSS) design for damping oscillatory electromechanical modes of oscillations and enhancing the first-swing synchronous stability margins. The novel design utilizes a multivariable damping signal vector consisting of machine speed deviation, rate of speed deviation, and voltage deviation. The design is based on a multizonal PID structure and fuzzy logic variable-gain scheduling to optimize the damping action. The fuzzy logic PSS is proposed for use in parallel with the conventional analog type PSS with added simple switching criteria. The two PSS blocks can be allowed independent, sequential, and/or combined operation with different effective stabilizing weighting. The paper investigates an individual conventional PSS, a rule based fuzzy PSS, and hybrid operation. The parallel operation of a conventional PSS and a fuzzy logic one provides optimal sharing of the damping action under small- as well as large-scale generation-load mismatch or variations in external network topology due to fault or switching conditions.

Tuning a Robust PID Controller as a Linear Quadratic Optimal Controller

Structural, stability and sensitivity properties of a PID controller tuned as a linear quadratic optimal controller (LQOC) are presented. The solution of the LQOC control problem gives as a result a PID structure, only when a restricted class of models for the disturbance and the plant are considered. The concept of robustness is introduced for those models which can not be included in this desired set. This method gives as a result a set of simple tuning rules for PID controllers, which can be applied to a wide range of processes and disturbances.

Auto-Selecting PID Structures Towards Intelligent Controllers in Electrical Servo Drives

This paper proposes a strategy of auto-selecting PID structures for intelligent controllers, particularly in electrical servo drives. After comparing PID structures, a generic control algorithm with weighting factors is derived, where the weighting factors serve to select different structures. Then, a practical rule linking weighting factor values with controller requirements in terms of tracking and maintaining capabilities is proposed. Since controller requirements can be estimated intuitively from the setpoint profile, an appropriate control structure can be automatically selected from evaluation of the desired profile. Finally, computer simulation demonstrates the effectiveness of this auto-selection strategy, in selectively utilising the advantages of various PID structures.

Adaptive PID control of systems with unknown time delay

A new algorithm for the adaptive control of systems with unknown time delay is presented in which the underlying control law has the familiar PID structure. The design is based on a continuous-time approach. This algorithm can be applied to a class of high-order systems which can be modelled by either a second-order system with time delay or a first-order system with time delay. The parameters of the system including time delay are estimated recursively by a derivative-free least-squares algorithm. The controller settings are selected according to a set of analytical formulae derived from mean-square error criteria. The algorithm is tested on simulated examples as well as a laboratory-scale coupled-tank apparatus.

Optimal gain scheduling controller for a diesel engine

A generalized gain scheduling control mechanism based on off-line optimization techniques has been developed for a 2-cylinder, water cooled diesel engine. First, a set of linearized models is obtained for the engine operating at three different speeds and a total of 15 load conditions. From the experimental data analysis, it is concluded that the behavior of the engine can best be characterized by a set of fifth order difference equations with appropriate time delays. Optimal controllers with a PID structure are then synthesized by off-line numerical optimization using these mathematical models to minimize the integral squared error of the engine speed deviation subject to a step speed change command. The designed control system has been implemented and tested on a Petter diesel engine (Model PH2W). Experimental results indicated that the designed optimal control strategy has greatly improved the performance of the original engine in terms of both speed regulation and disturbance rejection. Attempts have also been made to evaluate the fuel efficiency of the engine with respect to controller parameter variations. It is concluded that there exists a strong correlation between controller parameter settings and the engine fuel consumption rate. >

Distributed and Self-Tuning Control System for Diesel Generators

The paper describes a distributed control system for synchronous generating sets. Self-tuning regulators for synchronizing and load sharing are described. Pole placement is used as controller design method and robustness against unknown system dynamics is achieved by proper selection of filters in connection with Least Squaresystem identification. Simplifications leading to a single tuning knob for a controller with PID structure are shown. The methods are tested on a programmable simulator. Measurements on a 1MW MAN B & W diesel generator have given a set of parametersfor the simulator and verified the simulator model.

H∞andH2simple controllers for robotic applications

A new method is discussed which allows one to synthesize continuous-time controllers of lead/lag or PID type that are optimal both in the H∞ and H2 sense (equalizing H2 controllers), for a restricted class of systems well suited for robotic applications. In particular, conditions on the plant are given so that the optimal controller has a lead/lag or PID structure in cascade with an additional low-pass filter. The method is applied to synthesize a PI controller for the velocity control of one joint of an electrically actuated industrial SCARA robot.

多変数離散時間2自由度PID型制御系における適応ゲイン調整法

多変数離散時間2自由度PID型制御系における適応ゲイン調整法