For First Order Plus Time Delay Research Articles

Robust tilt‐integral‐derivative controller synthesis for first‐order plus time delay and higher‐order systems

ABSTRACTA tilt integrator of the tilt‐integral‐derivative (TID) controller is an integrator to the power of a fraction. The current state of the art of TID controller is difficult to satisfy prespecified frequency‐domain specifications and is not able to build the connection between the frequency‐domain synthesis and time‐domain analysis. To fill the gap in TID control theory, a systematic tuning method of robust TID controller for first order plus time delay (FOPTD) and higher‐order processes is proposed, which is based on combining frequency‐ and time‐domain specifications synthesis. The TID controller parameters , , and optimal fractional order are settled to meet frequency‐domain specifications including phase margin, gain crossover frequency, and flat phase constraint that guarantee systemic stability and robustness. The parameter can be determined under the time‐domain specification including the smallest ITAE that achieves optimal dynamic performance. In addition, the steps of the proposed robust TID controller design process are given in detail, and an example is given to illustrate the corresponding steps. At last, the control and gain variation performances of the obtained TID controller are compared with some other controllers (PID, FOPI, and FOPID). Simulation results for FOPTD and higher‐order systems illustrate the superior robustness as well as the transient performance of the proposed control tuning procedure. To verify the practical usefulness of the outcomes of this paper, some experimental results on temperature control of a Peltier cell are presented.

Development of tuning free SISO PID controllers for First Order Plus Time Delay (FOPTD) and First Order Lag Plus Integral Plus Time Delay model (FOLIPD) systems based on partial model matching and experimental verification

This work aims to introduce a tuning-free PID controller for stable FOPTD and FOLIPD systems. The objective was achieved using a partial model-matching strategy; matching the coefficients of corresponding powers of s of the closed loop response of the model to the desired closed loop transfer function. Closed-loop performance is evaluated by considering a unit step change in the process model and compared the results with other methods reported earlier in the literature. Input and output performances were evaluated using error analyses and total variation. The robustness of the proposed method was assessed via incorporation of uncertainties in the process model parameters. The proposed method was also experimentally validated for FOPTD model using a temperature controlled lab. It was concluded that the method was analytically derived and model based with a key advantage that the resultant PID required no tuning parameter.

Technical note: On the actuator rate limit effect in reaction curves

While actuator rate limit is common and counted in practical engineering, it has not drawn enough attention in control synthesis especially system identification. In this note, it aims to construct a new identification framework for first-order plus time-delay (FOPTD) systems affected by actuator rate limit. It is found that the rate limit can lead to an illusory delay in system reaction curves. Furthermore, necessary quantitative analyses are given to validate that excessively estimated or illusory delay significantly influences estimation accuracy of other parameters and subsequently degrades control performance. Two illustrative examples and experimental results are provided to demonstrate the adverse effect of actuator rate limit on system identification and the effectiveness of the proposed model structure on control performance.

Frequency frame approach on loop shaping of first order plus time delay systems using fractional order PI controller

This study proposes an analytical design method of fractional order proportional integral (FOPI) controllers for first order plus time delay (FOPTD) systems. Suggested technique obtains the general computation equations of controllers for such systems. These equations are used to tune controller parameters to meet specified frequency and phase properties to satisfy the stability of whole system. It is found that the designed controllers not only make the system stable, but also have positive effect on the performance and robustness of the system. Main contribution of the paper lays on this thought. There proposed a concept, “frequency frame” which encloses the curves between phase and gain crossover frequencies in Bode plot. Robustness of the control system can be improved by expanding or constricting the edges of this frame and flattening the curves inside the frame. Thus, any case that leads the system to instability can be avoided. Analytically derived equations are tested with proper examples and the results are shown illustratively. Advantages and disadvantages of the method are comparatively given.

Proportional integral-fractional filter controller design for first order lag plus time delay system

ABSTRACTIn this work, a design approach of proportional integral-fractional filter (PI-FF) controller for first order plus time delay (FOPTD) system is proposed in order to enhance the feedback control system performances characteristics. The controller design method is drawn up such that the transfer function of the overall closed-loop system is equivalent to the transfer function of the general fractional Bagley–Torvik reference model whose behaviour ranges from relaxation to oscillation for different values of the fractional order derivative and the damping ratio-like parameter. The tuning parameters of the PI-FF controller are derived analytically from the FOPTD process model and the general fractional Bagley–Torvik reference model parameters. Illustrative examples were presented to test the effectiveness and the usefulness of the proposed PI-FF controller on the feedback control system performance characteristics enhancement.

Dual SIMC-PI Controller Design for Cascade Implement of Input Resetting Control with Application

Input resetting control (IRC) is an economical and effective approach to achieve good closed-loop behavior for systems with extra inputs. The paper investigates use of the cascade IRC implementation. A SIMC-based controller tuning rule is proposed for first-order plus time delay (FOPTD) processes in the two-input–single-output (TISO) structure. Satisfactory regulatory capacities for both set-point tracking and input resetting are obtained. Both of the controllers are analytically derived with proportional-integral (PI) forms by proposing the equivalent transfer functions. The resulting tuning guideline shows how the adjustable parameters should be changed to balance a trade-off between performance specifications and levels of robustness. Numerical simulations have been carried out to demonstrate the effectiveness of the proposed method. Moreover, the feasibility of implementing the proposed control strategy in practice is verified by a light intensity control experiment.

Simple Proportional Integral Controller Tuning Rules for FOPTD and HOPTD Models Based on Matching Two Asymptotes

Many methods are available to tune proportional integral (PI) controllers for first order plus time delay (FOPTD) models of overdamped processes. The two asymptotes for small and large ratios of time delays over time constants are easily calculated. These two asymptotes can be used to evaluate and provide guidelines for the performance and application ranges of PI controller tuning rules. By matching these two asymptotes, a simple analytic tuning rule is suggested. For some overdamped processes whose transfer functions have large zero terms, half-order plus time delay (HOPTD) models are found to yield better results than the FOPTD models. Applying the technique of matching two asymptotes, a simple analytic PI controller tuning rule has also been proposed for the HOPTD models. To apply these tuning rules to high order processes with known transfer functions, model reduction methods to obtain the FOPTD and HOPTD models are investigated. Simulation results for empirical and full models of processes show the ...

Robust design of Smith predictor for a delay margin based on maximum sensitivity

Using direct synthesis method, the controller in the Smith predictor structure is designed as a proportional-integral (PI) controller for first order plus time delay (FOPTD) model and proportional-integral-derivative (PID) controller for second order plus time delay (SOPTD) model. The tuning parameter in the direct synthesis method is evaluated based on the maximum sensitivity (peak value of the sensitivity function) of the closed loop. Delay margin is recommended as the robustness measure for delay compensators because the delay compensators are more sensitive for delay uncertainties. In this work, a simple analytical formula is developed for selection of the tuning parameter corresponding to the delay margin. Nominal and robust control performances are achieved with the designed controller. Three examples have been considered to show the advantages of the proposed design method.

Design of balanced proportional–integral–derivative controllers based on bilevel optimisation

A bilevel optimisation framework is proposed to find the proportional–integral–derivative (PID) controller with balanced performance in terms of transient response, actuator preservation and robustness. In the lower level problem, the transient performance is optimised so that the balanced controller can be designed with minimal controller output variation in the upper level problem, where the requirement on transient performance is relaxed to a pre-specified extent. The robustness of the system is guaranteed by constraints on the maximum sensitivity in both problems. The trade-off between transient performance and actuator preservation is controlled uniformly for diverse process dynamics by a single parameter, which characterises the uniformness of relaxation in transient performance. By choosing different values of this parameter, tuning rules are provided for first order plus time delay (FOPTD) processes for set point following and load disturbance rejection, respectively. The efficiency of these tuning rules is demonstrated by examples covering the whole plant family set.