Controller Tuning Rules Research Articles

Optimal Nash tuning rules for robust PID controllers

In this paper, we propose tuning rules for one degree-of-freedom proportional-integral-derivative controllers, by considering important aspects such as the trade-off in the performance in the servo and regulation operation modes and the control system robustness by constraining the maximum sensitivity peak. The different conflicting objectives are dealt with by using a multi-objective optimization algorithm to generate the trade-off optimal solutions. In this context, a simple tuning rule is determined by using the Nash solutions as a multi-criteria decision making technique. The Nash criteria is shown to provide convenient trade-off solutions for the controller tuning problem. Illustrative simulation examples show the effectiveness of the method.

Unbounded regulators with variable gains for a direct-drive robot manipulator

This paper addresses the position-control problem with variable gains for robot manipulators. We present a new regulator based on a hyperbolic-sine structure with tuning rules for control gains. It is demonstrated that the equilibrium point of the closed-loop system is globally, asymptotically stable according to Lyapunov theory. By using a similar methodology, this concept can be extended to other unbounded controllers such as PD and PID. In order to show the usefulness of the proposed scheme and with the purpose of validating its asymptotical stability property, an experimental comparison involving constant gains controllers, for example: simple PD, PID and hyperbolic-tangent schemes vs variable-gains hyperbolic-sine and PD control schemes, was performed by using a three degree-of-freedom, direct-drive robot manipulator.

Improved PID controller tuning rules for performance degradation/robustness increase trade-off

Definitely, robustness is an important feature that any control system must take into account, especially considering that the design is usually based on low-order linear models that represent the whole controlled process. The problem is that to include such characteristic implies a degradation in the system’s performance. With regard to the previous statement, this paper is concerned with the design of the closed-loop control system, to take into account the system performance to load-disturbance and to set-point changes and its robustness to variation of the controlled process characteristics. The aim is to achieve a good balance between the multiple trade-offs. Here, a PID control design is provided that looks for a robustness increase, allowing some degradation in the system’s combined performance. The proposed approach is complementary to the work presented by Arrieta and Vilanova (Simple PID tuning rules with guaranteed $$M_s$$ robustness achievement, in 18th IFAC world congress, 2011; Ind Eng Chem Res 51(6):2666–2674, 2012. doi: 10.1021/ie201655c ); Arrieta et al. (Performance Degradation Driven PID controller design, in PID12, IFAC conference on advances in PID control, 2012).

Maximum sensitivity based analytical tuning rules for PID controllers for unstable dead time processes

In this paper, maximum sensitivity and internal model control (IMC) based proportional-integral-derivative (PID) controllers are designed for unstable first-order plus-dead-time (UFOPDT) processes. The designed controller parameters are functions of the UFOPDT model parameters and the IMC closed loop tuning parameter. The tuning parameter plays a vital role and determines the closed loop performance and robustness of the designed controller. Systematic guidelines are provided for selection of this tuning parameter based on maximum sensitivity. Analytical tuning rules are developed for the controller parameters for different time delay to time constant ratios with desired level of robustness. These controller settings allow the operator to deal with the closed-loop control system performance-robustness trade-off by specifying the robustness level (maximum sensitivity). Simulation studies have been carried out on various UFOPDT processes to explain the advantages of the proposed analysis.

Low-order feedback-feedforward controller for dead-time processes with measurable disturbances

This paper presents simple tuning rules for low-order feedback and feedforward controllers based on an approximation of the filtered Smith predictor with closed-loop feedforward compensation. An analytical development is introduced to control stable first-order plus dead time processes affected by measurable disturbances that cannot be completely removed from the process output due to dead-time effects. Simulation results for the pH control of a tubular photobioreactor and the steam pressure control of an industrial boiler are given to show the effectiveness of the proposed method.

Unbounded regulators with variable gains for a direct-drive robot manipulator

This paper addresses the position-control problem with variable gains for robot manipulators. We present a new regulator based on a hyperbolic-sine structure with tuning rules for control gains. It is demonstrated that the equilibrium point of the closed-loop system is globally, asymptotically stable according to Lyapunov theory. By using a similar methodology, this concept can be extended to other unbounded controllers such as PD and PID. In order to show the usefulness of the proposed scheme and with the purpose of validating its asymptotical stability property, an experimental comparison involving constant gains controllers, for example: simple PD, PID and hyperbolic-tangent schemes vs variable-gains hyperbolic-sine and PD control schemes, was performed by using a three degree-of-freedom, direct-drive robot manipulator.

New tuning rules for PID controllers based on IMC with minimum IAE for inverse response processes

In this paper new tuning rules for Proportional Integral Derivative (PID) are presented, which are based on Internal Model Control (IMC). This set of equations minimizes the performance index, in this case, the Integral Absolute Error (IAE). Furthermore, a correlation is proposed in order to calculate the tuning parameter of the method, where a holding oscillation response is obtained regarding changes in the set point. This value represents a stability limit for the IMC method. The overall development is then applied to an Inverse Response System of second order and with dead time.

Comparison of Performance of Optimized Varela Immune Controller and PID Controller for Control of Time-Delay Process

Varela immune controller is a kind of nonlinear controller, which is said to have good anti-delay capabilities. We compare the performance of simulated annealing optimized improved Varela immune controller and optimized PID controller for controlling a process with very long time delay (approximation of biomass-fired boiler temperature control). The results confirm that Varela immune controller is indeed capable of stabilizing the process while being very robust even to extreme changes in process parameters (time constant and time delay). In addition to that, it is also found out that properly (optimally) tuned PID controller is capable of achieving similar performance. The problem of controller tuning is relevant for both controllers but there are no tuning rules for immune controllers, which might favor the use of conventional PID controller. On the other hand, Varela controller has greater flexibility due to its more complex structure, which might help to adapt it to some special kinds of processes.

Performance indices for feedforward control

In this paper, a performance benchmark for the assessment of two feedforward control architectures for the load disturbance compensation problem is proposed. In particular, two indices are devised so that the advantage of using a feedforward compensator with respect to the use of a feedback controller only is quantified. Furthermore, these metrics will help to make quantitative comparisons among different feedforward control schemes and tuning rules. Analysis and simulation results are given to demonstrate the effectiveness of the proposed approach.

Stability Margin Interpretation of the SIMC Tuning Rule for PI Controllers and its Applications

Model reduction and tuning rules given in the SIMC (Simple Internal Model Control) method are very effective in tuning PI controllers. For some processes with large lead elements, control performances by the SIMC method are somewhat oscillatory or sluggish. To mitigate such drawbacks, additional tuning rules based on the second order plus time delay model with lead term are proposed. Improvements for certain types of models are critical. For such processes, besides the SIMC tuning rule, no PI controller tuning rules that are analytic and given in terms of process parameters are not available. Since the proposed tuning rules are very simple, they can be used in the field, effectively complementing the SIMC method.

Design of internal model control-proportional integral derivative controller with improved filter for disturbance rejection

The internal model control (IMC) proportional integral derivative (PID) controller tuning rules provide an excellent tracking of set-point, but sluggish disturbance rejection, as the conventional IMC filter introduces slow process pole. Disturbance rejection is significant than set-point tracking in many industrial applications. This paper proposes the design of IMC-PID controller, cascaded with lead–lag filter, with an improved IMC filter to provide effective disturbance rejection and robust operation of the first-order processes (FOPs). The simulation study was conducted to show the effectiveness of the proposed method on various structures of the FOPs, calculating the controller parameters, maintaining similar robustness in terms of maximum sensitivity MS. Perturbations were incorporated in the parameters of the plant model simultaneously, for the robustness analysis of the controller. The closed-loop performance was evaluated with the integral error criteria, namely, integral absolute error, integral square error, and integral time absolute error. The proposed IMC filter provided good disturbance rejection. The results of recently published design methods were compared with that obtained from the proposed method, validating the usefulness of the proposed method.

Low-order feedforward controllers: Optimal performance and practical considerations

Feedforward control from measurable disturbances can significantly improve the performance in control loops. However, tuning rules for such controllers are scarce. In this paper design rules for how to choose optimal low-order feedforward controller parameter are presented. The parameters are chosen so that the integrated squared error, when the system is subject to a step disturbance, is minimized. The approach utilizes a controller structure that decouples the feedforward and the feedback controller. The optimal controller can suffer from undesirable high-frequency noise characteristics and tuning methods for how to filter the control signal are also provided. For scenarios where perfect disturbance attenuation in theory is achievable but where noise-filtering is needed, the concept of precompensation is introduced as a way to shift the controller time-delay to compensate for the low-pass filtering.

Robust Predictive PI Controller Tuning

Two decades ago, a predictive PI controller was introduced for regulation of dead time dominated linear time-invariant first-order processes. The introduction involved a simple tuning rule with consideration on easy implementation and good performance. Later, the predictive PI controller has been improved by having an additional low-order filter in the controller structure against high-order modeling uncertainties. Also, several publications have been released with a detailed analysis on performance and robustness in particular with comparison of predictive and conventional PI(D) controllers. However, there have not been tuning rules with a design parameter for fine-tuning performance and dealing with robustness. In this paper, stability and robustness of a predictive PI without an additional filter for any time-invariant system is considered resulting in tuning rules for an optimal performance with a targeted robustness against model mismatch. Consequently, simple controller tuning rules are given for a first-order plus dead time and integrating plus dead time systems.

A Novel PID Controller Design Methodology for Specified Performance Using Ultimate Plant Parameters

The paper deals with a new PID controller design method based on integrating requirements on transient performance into the popular frequency-domain Ziegler-Nichols design approach. The developed method provides support to the designer by converting identified ultimate plant parameters into PID controller parameters using variable weights that depend on expected maximum overshoot emax and settling time ts of the closed-loop step response. The weights (α1,α2,α3) of ultimate plant parameters Tc and Kc occurring in tuning rules ΘPID=(P,Ti,Td)=(α1Kc,α2Tc,α3Tc) differ from standard recommendations of the Ziegler-Nichols method (α1Z-N,α2Z-N,α3Z-N)=(0.6,0.5,0.125). Developed PID controller tuning rules are presented in the modified Ziegler-Nichols table.

Simple Analytic Proportional-Integral-Derivative (PID) Controller Tuning Rules for Unstable Processes

Very simple proportional-integral-derivative (PID) controller tuning rules for a wide range of stable processes are available. However, for unstable processes, the design trend is for controllers to be more complex for better performances. Here, the design concept of “simplicity” is extended to unstable processes. Simple desired closed-loop transfer functions for the direct synthesis method and simple approximations of the process time delay are utilized for unstable processes. Very simple tuning rules for PID controllers and set-point filters are obtained, yielding similar or even improved performances over previous more complicated PID controller tuning methods.

Design of non-parametric process-specific optimal tuning rules for PID control of flow loops

The problem of designing optimal process-specific rules for non-parametric tuning is undertaken in the paper. It is shown that producing non-parametric process-specific optimal tuning rules for PID controllers leads to the problem that can be characterized as optimization under uncertainty. This happens due to the fact that tuning rules, unlike tuning constants, are produced not for a particular process or plant model but for a set of models from a certain domain. The novelty of the proposed approach is that the problem of obtaining optimal tuning rules for a flow process is formulated and solved as a problem of optimization of an integral performance criterion parametrized through values that define the domain of available process models. The considered non-parametric tuning assumes the use of the modified relay feedback test (MRFT) recently proposed in the literature. It allows one to tune the PID controller satisfying the requirements to gain or phase margins that is achieved through coordinated selection of tuning rules and test parameters. This approach constitutes a holistic approach to tuning. In the present paper, optimal tuning rules coupled with MRFT, for flow loops, are proposed. Final results are presented in the form of tables containing coefficients of optimal tuning rules for the PI controller, obtained for a number of specified gain margins. The produced non-parametric tuning rules well agree with the practice of loop tuning.

Simple Analytic PID Controller Tuning Rules Revisited

The SIMC method by Skogestad (J. Process Control 2003, 13, 291–309) to tune the PID controller is revisited, and a new method (K-SIMC) is proposed. The proposed K-SIMC method includes modifications of model reduction techniques and suggestions of new tuning rules and set point filters. Effects of such modifications are illustrated through simulations for a wide variety of process models. The proposed modifications permit the SIMC method to be applied with more confidence.

Non-Fragile Tuning of Fractional-Order PD Controllers for IPD-Modelled Processes

This paper deals with introducing non-fragile algebraic tuning rules for fractional-order PD controllers where they are used in controlling processes modeled in Integral Plus Delay (IPD) forms. These tuning rules are obtained based on a recently introduced approach, named as the centroid approach, which results in non-fragile tuning methods. Based on this approach, the centroids of two-dimensional admissible regions or the center of gravity of three-dimensional admissible regions in controller parameter space give non-fragile options for choosing controller parameters.

A SYSTEM FOR DISSOLVED OXYGEN CONTROL IN INDUSTRIAL AERATION TANK

The control system is developed for accurate set-point control of dissolved oxygen concentration in industrial aeration tank based on adaptation of PI controller to time-varying dynamics of the controlled process. The controller adaptation algorithm refers to the process state model-based transfer function that follows changes in process dynamics by updating the function parameters with on-line measurements of process variables, and the controller tuning rules developed for typical structure transfer function models. The control system was investigated via computer simulation of the dissolved oxygen concentration set-point control in an industrial aeration tank under process disturbances and set-point step changes. The control system demonstrates fast adaptation of PI controller parameters and noticeably higher accuracy control compared to that of ordinary fixed gain PI controller. DOI: http://dx.doi.org/10.5755/j01.itc.41.1.921

Kappa-tau type PI tuning rules for specified robust levels

New tuning rules for 2-DoF PI controllers in the spirit of the kappa-tau ones are addressed in this paper. In particular, tuning rules have been devised in order to minimize the integrated absolute error with a constraint on the maximum sensitivity MS. Different tuning rules have been obtained for a batch of plants and for several robustness levels in terms of MS. The setpoint weight is also exploited to improve the setpoint following performance because the PI controller is tuned by optimizing the load disturbance rejection performance. In particular, explicit tuning rules are given in order to select the optimal setpoint weight to minimize the integrated absolute error. Simulation results demonstrate the effectiveness of these methodologies. Some comments relating to industrial practice are offered in this context.