Ibrahim Kaya

IMC based automatic tuning method for PID controllers in a Smith predictor configuration

In this paper, a new approach is presented based on relay autotuning of a plant to find parameters for its control using a Smith predictor. A Smith predictor configuration is represented as its equivalent internal model controller (IMC) which provides the parameters of the proportional-integral (PI) or proportional-integral-derivative (PID) controller to be defined in terms of the desired closed-loop time constant, which can be adjusted by the operator, and the parameters of the process model. This means that only one parameter, namely the desired closed-loop time constant, is left for tuning, assuming that the model parameters have been obtained from a relay autotuning. The ISE criterion was used to find the filter parameter, and simple equations were obtained to tune the Smith predictor. The method is very simple and has given improved results when compared with some previous approaches.

Obtaining controller parameters for a new PI-PD Smith predictor using autotuning

Abstract The paper extends a recent work on a modified PI-PD Smith predictor, which leads to significant improvements in the control of processes with large time constants or an integrator or unstable plant transfer functions plus long dead-time for reference inputs and disturbance rejections. Processes with high orders or long time delays are modelled with lower order plant transfer functions with longer time delays. The PI-PD controller is designed so that the delay free part of the system output will follow the response of a first order plant or second order plant, where it is appropriate, assuming a perfect matching between the actual plant and model in both the dynamics and time delay. The provided simple tuning formulae have physically meaningful parameters. Plant model transfer functions and controller settings are identified based on exact analysis from a single relay feedback test using the peak amplitude and frequency of the process output. Examples are given to illustrate the simplicity and superiority of the proposed method compared with some existing ones.

Improving performance using cascade control and a Smith predictor.

Many investigations have been done on tuning proportional-integral-derivative (PID) controllers in single-input single-output (SISO) systems. However, only a few investigations have been carried out on tuning PID controllers in cascade control systems. In this paper, a new approach, namely the use of a Smith predictor in the outer loop of a cascade control system, is investigated. The method can be used in temperature control problems where the secondary part of the process (the inner loop) may have a negligible delay while the primary loop (the outer loop) has a time-delay. Two different approaches, including an autotuning method, to find the controller parameters are proposed. It is shown by some examples that the proposed structure as expected can provide better performance than conventional cascade control, a Smith predictor scheme or single feedback control system.

A new Smith predictor and controller for control of processes with long dead time.

Good control of processes with long dead time is often achieved using a Smith predictor configuration. Typically a PI or PID controller is used; however, it is shown in this paper that for some situations improved set point and disturbance responses can be obtained if a PI-PD controller is used. Several methods are possible for selecting the parameters of the PI-PD controller but when the plant transfer function has no zeros, the use of the standard forms provides a simple algebraic approach, and also reveals why difficulties may be encountered if a PID controller is used. Some examples are given to show the value of the approach presented.

Tuning PI controllers for stable processes with specifications on gain and phase margins

In industrial practice, controller designs are performed based on an approximate model of the actual process. It is essential to design a control system which will exhibit a robust performance because the physical systems can vary with operating conditions and time. Gain and phase margins are well known parameters for evaluating the robustness of a control system. This paper presents a tuning algorithm to design and tune PI controllers for stable processes with a small dead time while meeting specified gain and phase margins. Simulation examples are given to demonstrate that the proposed design method can result, in a closed-loop system, in better performances than existing design methods which are also based on user-specified gain and phase margins.

A PI-PD controller design for control of unstable and integrating processes

A model-based PI-PD controller design, where the PD feedback is used to change the poles of the plant transfer function to more desirable locations for control by a PI controller, is proposed. Several procedures for obtaining the parameters of the PI-PD controller are possible but one of the simplest approaches, which is used in this paper, is to employ integral squared time error standard forms as this enables the design to be completed using simple algebra. Also, an exact method for model extraction of some integrating processes which may or may not have a time delay is presented. The method is compared with several existing methods to control integrating processes and it is shown that the proposed method is superior to existing ones.

Computation of stabilizing PI and PID controllers

In this paper, a simple method for the calculation of stabilizing PI controllers is given. The proposed method is based on plotting the stability boundary locus in the (k/sub p/, k/sub i/)-plane and then computing stabilizing values of the parameters of a PI controller. The technique presented does not require sweeping over the parameters and also does not need linear programming to solve a set of inequalities. Thus is offers several important advantages over existing results obtained in this direction. Beyond stabilization, the method is used to shift all poles to a shifted half plane that guarantees a specified settling time of response. Furthermore, computation of stabilizing PI controllers, which achieve user specified gain and phase margins is studied. It is also shown via an example that the stabilizing region in the (k/sub p/, k/sub i/)-plane is not always a convex set. The proposed method is also used to design PID controllers. The limiting values of the PID controller, which stabilize a given system are obtained in the (k/sub p/, k/sub d/)-plane and (k/sub i/, k/sub d/)-plane. Examples are given to show the benefit of the method presented.

Autotuning of a new PI-PD Smith predictor based on time domain specifications

The paper extends a recent work on a modified PI-PD Smith predictor, which leads to significant improvements in the control of processes with large time constants or an integrator or unstable plant transfer functions plus long dead time for reference inputs and disturbance rejections. Processes with high orders or long time delays are modeled with lower order plant transfer functions with longer time delays. The PI-PD controller is designed so that the delay-free part of the system output will follow the response of a first-order plant or second-order plant, where it is appropriate, assuming a perfect matching between the actual plant and model in both the dynamics and time delay. The provided simple tuning formulas have physically meaningful parameters. Plant model transfer functions and controller settings are identified based on exact analysis from a single relay feedback test using the peak amplitude and frequency of the process output. Examples are given to illustrate the simplicity and superiority of the proposed method compared with some existing ones.

Exact parameter estimation from. relay autotuning under static load disturbances

Obtaining the parameters for PID controllers based on limit cycle information from the process in a relay controlled feedback loop has become an accepted practical procedure. If the form of the plant transfer function is known, exact expressions for the limit cycle frequency and amplitude can be derived in terms of the plant parameters, so that their measurements, assumed error free, can be used to calculate the parameter values. In the literature to date the solutions have only been considered for odd symmetrical limit cycles which will not be the situation when constant disturbances exist. Use of these expressions will lead to errors when the limit cycle is not odd symmetrical. The paper reports on exact parameter estimation for stable and unstable FOPDT or SOPDT plant transfer functions from relay autotuning under static load disturbances where the limit cycles are asymmetrical.

A GRAPHICAL METHOD FOR COMPUTATION OF ALL STABILIZING PI CONTROLLERS

Abstract In this paper, a new method for the calculation of all stabilizing PI controllers is given. The proposed method is based on plotting the stability boundary locus in the ( k p , k i )-plane and then computing the stabilizing values of the parameters of a PI controller. The technique presented does not require sweeping over the parameters and also does not need linear programming to solve a set of inequalities. Thus it offers several important advantages over existing results obtained in this direction. Computation of stabilizing PI controllers which achieve user specified gain and phase margins is also studied. Furthermore, the proposed method is used to compute all the parameters of a PI controller which stabilize a control system with an interval plant family. Examples are given to show the benefits of the method presented.