Stabilization and PID tuning algorithms for second-order unstable processes with time-delays (original) (raw)
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Improved analytical PID controller design for the second order unstable process with time delay
Computer Aided Chemical Engineering, 2007
The design of the PID controller cascaded with first order filter has been proposed for the second order unstable time delay processes. The design algorithm is based on the IMC criterion which has single tuning parameter to adjust the performance and robustness of the controller. The setpoint filter is used to diminish the overshoot in servo response. The simulation results of the suggested method are compared with recently published tuning methods to demonstrate the superiority of the proposed method. For the reasonable comparison the controllers are tuned to have the same degree of robustness by the measure of maximum sensitivity (Ms). A guideline is also provided for the ease of the selection of closed-loop time constant (λ).
IOP Conference Series: Materials Science and Engineering, 2017
The presence of unstable dead-time systems in process plants often leads to a daunting challenge in the design of standard PID controllers, which are not only intended to provide close-loop stability but also to give good performance-robustness overall. In this paper, we conduct stability analysis on a double-loop control scheme based on the Routh-Hurwitz stability criteria. We propose to use this unstable double-loop control scheme which employs two P/PID controllers to control first-order or second-order unstable dead-time processes typically found in process industries. Based on the Routh-Hurwitz stability necessary and sufficient criteria, we establish several stability regions which enclose within them the P/PID parameter values that guarantee close-loop stability of the double-loop control scheme. A systematic tuning rule is developed for the purpose of obtaining the optimal P/PID parameter values within the established regions. The effectiveness of the proposed tuning rule is demonstrated using several numerical examples and the result are compared with some wellestablished tuning methods reported in the literature.
Tuning PID Controllers for Time-Delay Processes with Maximizing the Degree of Stability
In this paper, we propose a method of tuning PID controller parameters for first-order plus dead-time processes with the objective of maximizing the degree of stability. Since the presence of dead-time in a feedback loop gives rise to an infinite-dimensional closed-loop system, which has an infinite number of poles and thus the conventional Routh-Hurwitz algebraic criterion of stability cannot be applied to characterize the necessary conditions of the maximum degree of stability. To overcome this difficulty, we make use the theory of D-partition technique. Based on analytically characterizing the D-partition boundaries of the controller parameter space, necessary conditions of the maximum degree of stability are derived. With these derived conditions, the problem of maximizing the degree of stability is converted to a set of parametric optimization problems, whose solutions can be obtained by an existing method. For showing the applicability of the method, a tuning example with graphical illustrations is given.
Tuning of Two-Degree-Of-Freedom Pi / Pid Controller for Second-Order Unstable Processes
2008
⎯ The proportional-integral-derivative (PID) controllers are still widely used in the process industries even though more advanced control techniques have been developed. The main reason is its relatively simple structure, which can be easily understood and implemented in practice. Over the years, there are many formulas derived to tune the PID controllers for stable processes. However, unstable systems are fundamentally and quantifiably, more difficult to control than stable ones. Despite these difficulties, research for unstable process control has been increasingly active. Many different approaches of controller design for unstable processes have been reported in the literature. However, they usually either show excessive overshoot and large settling time or have complicated formulas. Moreover, it is difficult to achieve all goal since control system design involves inherent conflicts and trade-offs. For example, a controller design that minimizes the effect of load disturbances ...
… IEEE Transactions on, 2006
The control of unstable first-order plus dead-time (UFOPDT) processes using proportional-integral (PI) and proportional-integral-differential (PID) type controllers is investigated in this brief. New tuning rules based on the exact satisfaction of gain and phase margin specifications are proposed. The tuning rules are given in the form of iterative algorithms, as well as in the form of accurate, analytical approximations. Moreover, several specific functions, related to the crossover frequencies of the Nyquist plot and to the feasible design specifications for a given process, are derived. These functions, which are particularly useful for the general design of PI-and PID-type controllers for UFOPDT processes are accurately approximated, in order to simplify the tuning procedure. With the proposed approximations, the tuning rules reported in this brief require relatively small computational effort and are particularly useful for online applications.
2007 Mediterranean Conference on Control & Automation, 2007
The control of unstable second order plus deadtime (USOPDT) processes systems using generalized PID type controllers is investigated in this paper. New tuning rules based on the exact satisfaction of gain and phase margin specifications are proposed. The tuning rules are given in the form of iterative algorithms, as well as in the form of accurate analytic approximations, particularly useful for on-line tuning applications. The proposed tuning rules are applied for the control of a gravity-biased one degree of freedom magnetic levitation experimental system with very satisfactory results.
Archives of Control Sciences, 2021
The time delay element present in the PI controller brings dead-time compensation capability and shows improved performance for dead-time processes. However, design of robust time delayed PI controller needs much responsiveness for uncertainty in dead-time processes. Hence in this paper, robustness of time delayed PI controller has been analyzed for First Order plus Dead-Time (FOPDT) process model. The process having dead-time greater than three times of time constant is very sensitive to dead-time variation. A first order filter is introduced to ensure robustness. Furthermore, integral time constant of time delayed PI controller is modified to attain better regulatory performance for the lag-dominant processes. The FOPDT process models are classified into dead-time/lag dominated on the basis of dead-time to time constant ratio. A unified tuning method is developed for processes with a number of dead-time to time constant ratio. Several simulation examples and experimental evaluation are exhibited to show the efficiency of the proposed unified tuning technique. The applicability to the process models other than FOPDT such as high-order, integrating, right half plane zero systems are also demonstrated via simulation examples.
PID controller tuning for the first-order-plus-dead-time process model via Hermite-Biehler theorem
ISA Transactions, 2005
This paper discusses PID stabilization of a first-order-plus-dead-time ͑FOPDT͒ process model using the stability framework of the Hermite-Biehler theorem. The FOPDT model approximates many processes in the chemical and petroleum industries. Using a PID controller and first-order Padé approximation for the transport delay, the Hermite-Biehler theorem allows one to analytically study the stability of the closed-loop system. We derive necessary and sufficient conditions for stability and develop an algorithm for selection of stabilizing feedback gains. The results are given in terms of stability bounds that are functions of plant parameters. Sensitivity and disturbance rejection characteristics of the proposed PID controller are studied. The results are compared with established tuning methods such as Ziegler-Nichols, Cohen-Coon, and internal model control.
IFAC-PapersOnLine, 2018
This paper proposes a method so that all PID controller tuning parameters, which are satisfying stability of any integrating time delay processes, can be calculated by forming the stability boundary loci. Processes having a higher order transfer function must first be modeled by an integrating plus first order plus dead time (IFOPDT) transfer function in order to apply the method. Later, IFOPDT process transfer function and the controller transfer function are converted to normalized forms to obtain the stability boundary locus in 2 , (/)
Optimal PID tuning for second order plus dead time processes
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