Closed-loop Step Response Research Articles

A Novel Data-Driven Method for Simultaneous Performance Assessment and Retuning of PID Controllers

A novel data-driven method for simultaneous performance assessment and retuning PID controllers is presented in this study. The PID tuning problem is cast as a convex approximation problem of a reference model, which makes the resulting closed-loop step response resemble that of a predefined reference model. The proposed data-driven method only requires the current PID controller parameters and a set of closed-loop data with set point changes, while the process model is neither necessary to be known a priori nor to be identified directly. The controller effort limitation, which is closely related to variations of controller actions, is an important concern for controller design. To evaluate PID controller performance subject to control effort limitations, a trade-off curve displaying the integrated squared error against the total squared variation of controller actions is obtained, which can be calculated in a cost efficient way and serves as a useful tool for performance assessment and retuning of PID co...

Closed-loop step response for tuning PID-fractional-order-filter controllers

Analytical methods are usually applied for tuning fractional controllers. The present paper proposes an empirical method for tuning a new type of fractional controller known as PID-Fractional-Order-Filter (FOF-PID). Indeed, the setpoint overshoot method, initially introduced by Shamsuzzoha and Skogestad, has been adapted for tuning FOF-PID controller. Based on simulations for a range of first order with time delay processes, correlations have been derived to obtain PID-FOF controller parameters similar to those obtained by the Internal Model Control (IMC) tuning rule. The setpoint overshoot method requires only one closed-loop step response experiment using a proportional controller (P-controller). To highlight the potential of this method, simulation results have been compared with those obtained with the IMC method as well as other pertinent techniques. Various case studies have also been considered. The comparison has revealed that the proposed tuning method performs as good as the IMC. Moreover, it might offer a number of advantages over the IMC tuning rule. For instance, the parameters of the fractional controller are directly obtained from the setpoint closed-loop response data without the need of any model of the plant to be controlled.

Fractional Order PI Controller Design for Time Delay Systems

This paper aims to look into the fractional PI controller design for a closed loop system having a plant with time-delay. The ultimate frequency of the system is found using a relay auto tuning test and then the parameters of a PI controller are estimated using this frequency in the Ziegler-Nichols (Z-N) tuning formula. These parameters are then used for a fractional order PI controller and the effect of varying the fractional integrator order (λ) of the PI controller on the closed loop step response is examined. Finally, for a given example, the table that includes specifications of the control system for different λ values has been obtained and according to the desired specifications, optimum fractional order PI controller is designed. The presented results are illustrated with some examples.

Multiloop and Prediction Based Controller Design for Sugarcane Crushing Mill Process

In the present work a sugarcane crushing mill is presented as a MIMO system with high multivariable interaction.A linear model of the plant is taken with flap position and turbine speed as manipulated variables and mill torque and buffer chute height as controlled variables.The multiloop PI controller has been designed for this plant by first investigating the RGA and the value of Niederlinski index of this plant.The decoupling of this system is done and the respective open loop and closed loop step responses are observed and compared with those of the composite MIMO system. Also the performance of multiloop controller is compared with controller designed using model predictive control system strategy for this plant.

Robust PID Controller Design for Performance Based on Ultimate Plant Parameters

The paper deals with a new robust 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 ηmax and settling time ts of the closed-loop step response. An extension of this method is proposed which enables to design PID controller guaranteeing robust stability and nominal performance for the uncertain plant modeled using unstructured uncertainty. Fulfillment of performance specification is guaranteed for the nominal model as well as for the worst-case one. The main advantage of the proposed method is a direct integration of performance requirements in the design procedure. Effectiveness of the proposed robust PID design method is verified by simulations and experiments on the real plant.

Step Response Identification of a Quadcopter UAV Using Frequency-sampling Filters

This paper presents an approach to identify a quadcopter's closed-loop step response for evaluation of control performance. The first step in the proposed approach is data acquisition using a relay feedback experiment and the second step is step response estimation using frequency sampling filters. The proposed approach provides engineers with an intuitive way to more preciously evaluate the designed controllers and to obtain better controller tuning parameters. To validate this approach, experiments are conducted on a quadcopter test-bed and comparisons are made between the estimated step response and the step response from testing.

Synthesis of Controllers for MIMO Systems with Time Response Specifications

This paper proposes the design of fixed low order controllers for Multi Input Multi Output (MIMO) decoupled systems. The simplified decoupling is used as a decoupling system technique due to its advantages compared to other decoupling methods. The main objective of the proposed controllers is to satisfy some desired closed loop step response performances such as the settling time and the overshoot. The controller design is formulated as an optimization problem which is non convex and it takes in account the desired closed loop performances. Therefore, classical methods used to solve the non convex optimization problem can generate a local solution and the resulting control law is not optimal. Thus, the thought is to use a global optimization method in order to obtain an optimal solution which will guarantee the desired time response specifications. In this work the Generalized Geometric Programming (GGP) is exploited as a global optimization method. The key idea of this method consists in transforming an optimization problem, initially, non convex to a convex one by some mathematical transformations. Simulation results and a comparison study between the presented approach and a Proportional Integral (PI) controller are given in order to shed light the efficiency of the proposed controllers.

Proportional stabilization and closed-loop identification of an unstable fractional order process

This paper deals with proportional stabilization and closed-loop step response identification of the fractional order counterparts of the unstable first order plus dead time (FOPDT) processes. At first, the necessary and sufficient condition for stabilizability of such processes by proportional controllers is found. Then, by assuming that a process of this kind has been stabilized by a proportional controller and the step response data of the closed-loop system is available, an algorithm is proposed for estimating the order and the parameters of an unstable fractional order model by using the mentioned data.

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.

Infinite-Dimensional Pole-Optimization Control Design for Flexible Structures Using the Transfer Matrix Method

This paper presents an approach to control design for flexible structures based on the transfer matrix method (TMM). The approach optimizes the closed-loop pole locations while working directly on the infinite-dimensional TMM model. The approach avoids spatial discretization, eliminating the possibility of modal spillover. The design strategy is based on an iterative process of optimizing the closed-loop pole locations using a Nelder-Mead simplex algorithm and then performing hardware-in-the-loop experiments to see how the pole locations are affecting the closed-loop step response. The evolution of the cost function used to optimized the pole locations is discussed. Contour plots (three dimensional Bode plots) in the complex s-plane are used to visualize the pole locations. A computationally efficient methodology for finding the closed-loop pole locations during the optimization is presented. The technique is applied to a single-flexible-link robot and experimental results show that the optimization procedure improves upon an initial, Bode-based compensator design, leading to a lower settling time.

High Performance Continuously Variable Transmission Control Through Robust Control-Relevant Model Validation

Optimal operation of continuously variable transmissions (CVTs) is essential to meet tightening emission and fuel consumption requirements. This is achieved by accurately tracking a prescribed transmission ratio reference and simultaneously optimizing the internal efficiency of the CVT. To reduce the power losses in a CVT, the absolute pressure levels are lowered, which increases the sensitivity to torque disturbances and increases the importance of disturbance feedforwards. This requires a high performance feedback controller for the hydraulic actuation system in a CVT. The aim of this paper is to develop a multivariable feedback controller for the hydraulic actuation system that is robust with respect to the varying system dynamics that are induced by the varying operating conditions, including transmission ratio changes. Hereto, new connections between system identification and robust control are exploited to achieve high performance. As a result, the varying system dynamics are directly evaluated in terms of closed-loop performance objectives. Subsequent robust control design reveals an increase of the control performance of almost a factor two in terms of the criterion value. This leads to improved simulated and measured closed-loop step responses, including a decrease in settling time from 0.4 s to 0.2 s. Finally, the designed robust controller is successfully validated in a standardized driving cycle experiment.

Relationship of lambda and overshoot of step response for a direct synthesis PI controller

The direct synthesis (DS) tuning method is a model-based method for a feedback controller. The main principle of this method is to obtain the controller settings based on a predetermined desired closed loop response. The main advantage is that there is only one parameter to be adjusted, which is lambda (λ), the speed of the desired closed loop response. There are several guidelines available for selecting λ in order to ensure that the closed loop step response matches the desired response. In this paper, a guideline that relates λ and overshoot is proposed and it worked well over a wide range of R varying from 0.05 to 2. For a fair comparison of DS-tuned controllers with different λ guidelines, both performance and robustness for a unit step change in the set point are considered. It was found that the DS-tuned controller with this proposed guideline performed better and the gain margin (GM) and phase margin (PM) lie between 2≤GM≤5 and 30º≤PM≤75º, respectively. Besides, its overshoot changed less with a ±25% process model mismatch, except for τ mismatch.

Simultaneous automatic tuning of cascade control systems from closed-loop step response data

This study presents a novel automatic tuning method for cascade control systems in which both primary and secondary controllers are tuned simultaneously using a single closed-loop step test. The proposed technique identifies the required process information with the help of B-spline series representation for the step responses. The two proportional–integral–derivative (PID) controllers are then tuned using an internal model control (IMC) approach. Considering the rationale of cascade control, the secondary controller is designed for faster disturbance attenuation. Without requiring an additional experiment, the primary controller is designed based on an identified process model that accurately accounts for inner loop dynamics. Finally, this study includes robustness considerations in the controller tuning process, and develops explicit guidelines for the selection of the IMC tuning parameters, completing the automatic tuning procedure for cascade control systems. The proposed method is robust to measurement noise because of the filtering property of the B-splines, and can provide superior control performance for both set-point tracking and disturbance rejection. Simulation examples demonstrate the effectiveness of the proposed automatic tuning method.

Closed-Loop Identification of Multivariable Systems, Using B-Spline Series Expansions for Step Responses

Closed-loop identification is vital in improving underperforming controllers. This paper presents a novel closed-loop identification method for multivariable systems from step responses. The full transfer function matrix of an interactive n × n multivariable process is identified through a sequential step change in the setpoint. The proposed method first approximates the closed-loop step responses, using B-spline series expansions. Based on these expansions, a matrix formulation that represents the closed-loop tests is used to obtain the analytical expressions of open-loop transfer functions. Finally, the reduced low-order models are identified based on the frequency response data by a linear least-squares technique. The proposed identification method is simple and applicable to general multivariable control systems, such as decentralized or centralized control. This method is robust to measurement noise due to the filtering property of the B-splines. Simulation examples have demonstrated the effectiveness of the proposed method for a wide range of multivariable systems.

Closed-Loop Identification of Multivariable Systems by Optimization Method

An optimization method is presented for the closed-loop identification of first-order-plus-time-delay (FOPTD) transfer function models of multivariable systems using step responses. A standard least-squares optimization method is used to obtain the parameters of the FOPTD models by matching the closed-loop step responses of the model with those of the actual process. A simple method is proposed to obtain the initial guess values for the transfer function model parameters from the process main and interaction responses. The effects of measurement noise and controller settings on the identified model parameters were also studied. This method was applied to stable FOPTD and higher-order transfer function models of multivariable systems. The proposed method considerably reduces the computational time (by about a factor of 15) for the optimization when compared with the genetic algorithm method reported by Viswanathan et al. (Ind. Eng. Chem. Res. 2001, 40, 2818−2826).

Closed-loop step identification of low-order continuous-time process model with time delay for enhanced controller autotuning

A continuous-time model identification method is proposed based on a closed-loop step response test for obtaining a low-order process model to facilitate control design in industrial engineering practices. By introducing a damping factor to the closed-loop step response for realisation of the Laplace transform, a frequency response estimation algorithm is developed in terms of the closed-loop system configuration used for identification. Correspondingly, two model identification algorithms for obtaining the widely used low-order process models of first-order-plus-dead-time (FOPDT) and second-order-plus-dead-time (SOPDT) are derived analytically respectively. To improve model fitting accuracy over a specified frequency range interested to controller tuning, in particular for identification of a higher order process, another identification algorithm is given based on weighted least-squares fitting of the process frequency response points estimated in the specified frequency range. Using the identified low-order models, a model-based controller design and tuning method is proposed for improving load disturbance rejection. Illustrative examples from the recent literature are used to demonstrate the effectiveness and merits of the proposed identification algorithms and controller tuning method.

Identification and Controller Tuning of Cascade Control Systems Based on Closed-Loop Step Responses

This paper presents a new automatic tuning method for cascade control systems based on a single closed-loop step test. The proposed method identifies the required process information with the help of B-spline series expansions for the step responses. The two PID controllers are then tuned using an internal model control (IMC) approach. The secondary controller is designed for enhanced disturbance rejection, and the primary controller is designed, without requiring an additional test, based on an identified process model that accurately accounts for the inner loop dynamics. The desired levels of system robustness explicitly guide the selection of the IMC tuning parameters. The proposed method is robust to measurement noises because of the filtering property of the B-splines, and can provide satisfactory control performance. Simulation examples confirm the effectiveness of the proposed method.

Easy Tuning of PID Controllers for Specified Performance

The presented method allows achieving maximum overshoot and specified settling time of the closed-loop step response. It provides a simple way to control linear stable SISO systems even if the mathematical model is unknown. Tuning rule parameters are based on one suitably chosen point of the plant frequency response obtained by sine-wave signal with specified excitation frequency, and the required phase margin. The main result provided is construction of empirical charts used to convert time-domain performance specifications (maximum overshoot and settling time) into frequency domain performance measure (phase margin). The method is applicable for systematic shaping of the closed-loop response of the plant. The new approach has been verified on a set of benchmark examples and on a real plant as well.

On-Line Identification of Process Model Based on Swarm Intelligence Technology

On-line identification problem of process model was discussed in this paper, which use warm intelligent technology. An on-line identification method based on HPSO-Rosenbrock parameter estimation algorithm is proposed to solve the problem that traditional identification methods cannot be used in continuous-time systems on closed-loop step response conditions. This identification method is a combined method of a modified PSO and Rosenbrock which can make full use of global search ability of PSO and local search ability of Rosenbrock. Identification results of HPSO-Rosenbrock algorithm were made and compared with the other identification methods. The simulation and compare results show that the on-line identification method proposed in this paper is an approximate unbiased and effective identification method. This method can be successfully applied to closed-loop identification under secious noise and big dead-time object which provides a new idea for system optimization and advanced control.

Frequency Response Estimation for Mechanical Systems Using Closed-Loop Step Response Data

In this paper, a simple scheme to estimate frequency transfer functions of linear time-invariant single-input single-output systems based on closed-loop step response data is investigated. The method uses only a single set of step response data of plants under closed-loop operating conditions. The input and output of a plant are filtered by a simple bandpass filter, and the frequency transfer function of the plant is obtained with the Discrete Fourier Transforms of the filtered input and output signals. The method is applied to a resonant mechanical system and its validity is illustrated through simulations and experiments.