Search Results (11)

One of the most important contributions of modern control theory from the 1960s was the separation of the dynamics of state-space controller design from the dynamics of state reconstruction. However, because modern control theory predates the mass spread of digital controllers and was predominantly focused on analog solutions that avoided modeling dead-time elements, it cannot effectively cover all aspects that emerged with the development of programmable devices and embedded systems. The same historical limitations also characterized the development of proportional-integral-derivative (PID) controllers, which began several decades earlier. Although they were used to control time-delayed systems, these solutions, which are most commonly used in practice today, can also be referred to as simplified disturbance observers that allow the avoidance of the the direct use of dead-time models. Using the example of controlling systems with a double integrator plus dead-time model, this article shows a novel controller design that significantly improves control performance compared to conventional PID controllers. The new control structure is a combination of a generalized state-space controller, interpreted as a higher-order derivative controller, and a predictive disturbance observer that uses the inversion of double integrator dynamics and dead-time models. It enables the elimination of the windup effect that is typical for PID control and extends the separation of the dynamics of setpoint tracking from the dynamics of state and disturbance reconstruction to time-delayed processes as well. The novelty of the presented solution offers several orders of magnitude lower amplification of measurement noise compared to traditional PID control. On the other hand, it offers high robustness and a stable transient response despite the unstable internal feedback of processes like the magnetic levitation system. The improvements achieved are so high that they call into question the classical solutions with PID controllers, at least for DIPDT models. In addition to the comparison with PID control, the relationship with traditional state space controllers, which today form the basis of active disturbance rejection control (ADRC), is also discussed and examined for processes including dead time. Full article

This paper deals with the tuning of the parameters of a fractional-order PI controller for the speed control of an electric servo drive in which the torque is set by a torque generator. The controller parameters are tuned using the multiple dominant pole method (MDPM), while the fractional order integrator is approximated by the Oustaloup method. The input parameters required for tuning the controller using MDPM are calculated using the optimization algorithm presented in this paper. This algorithm selects the optimal parameters from a set of points in three-dimensional space, based on the symmetry around a central point. The controller tuning is performed for the normalized control loop model. The obtained optimized normalized fractional order PI controller can then be applied to a real servo drive with specific parameters. The proposed tuning was also verified experimentally, comparing the obtained closed-loop responses with those of the integer-order PI controller. Both simulation and experimental results showed a significant reduction in the integral of the absolute error at the disturbance step compared to a control loop using an integer-order PI controller. This results in a faster output response to load torque steps and a smaller control error in a real servo drive. Full article

The proposed practice-oriented controller design (POCD) aims at stabilizing the system, reconstructing and compensating for disturbances while achieving fast and smooth step responses. This is achieved through a simple approach to process identification and controller tuning that takes into account control signal constraints and measurement noise. The proposed method utilizes POCD by eliminating the influence of the unstable zero dynamics of the inverse-response processes, which limits the achievable performance. It extends the previous work on PI and PID controllers to higher-order (HO) automatic reset controllers (ARCs) with low-pass filters. It is also extended according to POCD requirements while maintaining the simplified process model. The final result is an extremely simple design for a constrained controller that provides sufficiently smooth and robust responses to a wide family of HO-ARCs with odd derivatives, designed using integral plus dead time (IPDT) models and tuned by the multiple real dominant pole method (MRDP) and the circle criterion of absolute stability. The proposed design can be considered as a generalization of the Ziegler and Nichols step response method for inverse response processes and HO-ARCs. Full article

The new modular approach to constrained control of higher-order processes with dominant first-order dynamics using generalized controllers with automatic resets (ARCs) is addressed. The controller design is based on the multiple real dominant pole (MRDP) method for the integrator plus dead time (IPDT) process models. The controller output constraints are taken into account by inserting the smallest numerator time constant of the controller transfer function into the positive feedback loop representing the automatic reset (integral) term. In the series realization of the proportional–integral–derivative–acceleration (PIDA) controller (and other controllers with even derivative degree), the time constant mentioned is complex, so only the real part of the time constant has been used so far. Other possible conversions of a complex number to a real number, such as the absolute value (modulus), can be covered by introducing a tuning parameter that modifies the calculated real time constant and generalizes the mentioned conversion when designing controllers with constraints. In this article, the impact of the tuning parameter on the overall dynamics of the control loop is studied by simulation. In addition, an evaluation of the stability of the closed-loop control system is performed using the circle criterion in the frequency domain. The analysis has shown that the approximation of the complex zero by its real part and modulus leads to a near optimal response to the set point tracking. The disturbance rejection can be significantly improved by increasing the tuning parameter by nearly 50%. In general, the tuning parameter can be used to find a compromise between servo and regulatory control. The robustness and applicability of the proposed controller is evaluated using a time-delayed process with first-order dominant dynamics when the actual transfer function is much more complicated than the IPDT model. A comparison of the proposed MRDP-PIDA controller with series PI, PID and PIDA controllers based on a modified SIMC method has shown that the MRDP-PIDA controller performs better than the SIMC method, although the SIMC uses a more complex process model. Full article

The paper extends the earlier work entitled “Making the PI and PID Controller Tuning Inspired by Ziegler and Nichols Precise and Reliable”, to higher-order controllers and a broader range of experiments. The original series PI and PID controllers, based on automatic reset calculated by filtered controller outputs, are now augmented by higher-order output derivatives. This increases the number of degrees of freedom that can be used to modify the resulting dynamics, accelerates transient responses, and increases robustness to unmodeled dynamics and uncertainties. The fourth order noise attenuation filter used in the original work allows for the addition of an acceleration feedback signal, thus resulting in a series PIDA controller or even a jerk feedback that leads to a PIDAJ series controller. Such a design can further use the original process and filter approximation of the step responses through the integral-plus-dead-time (IPDT) model, while allowing experimentation with disturbance and setpoint step responses of the series PI, PID, PIDA and PIDAJ controllers, and thus, evaluating the role of output derivatives and noise attenuation from a broader perspective. All controllers considered are tuned using the Multiple Real Dominant Pole (MRDP) method, which is complemented by a factorization of the controller transfer functions to achieve the smallest possible time constant for automatic reset. The smallest time constant is chosen to improve the constrained transient response of the considered controller types. The obtained excellent performance and robustness allow the proposed controllers to be applied to a wider range of systems with dominant first-order dynamics. The proposed design is illustrated on a real-time speed control of a stable direct-current (DC) motor, which is approximated (together with a noise attenuation filter) by an IPDT model. The transient responses obtained are nearly time-optimal, with control signal limitations active for most setpoint step responses. Four controllers with different degrees of derivative with generalized automatic reset were used for comparison. It was found that controllers with higher-order derivatives may significantly improve the disturbance performance and virtually eliminate overshoots in the setpoint step responses in constrained velocity control. Full article

This paper discusses optimal design of the series proportional–integral–derivative–accelerative (PIDA) controller for integral-plus-dead-time (IPDT) plants. The article starts with the design of disturbance reconstruction and compensation based on proportional-derivative-accelerative (PDA) stabilizing controllers. It shows that by introducing positive feedback by a low-pass filter from the (limited) output of the stabilizing PDA controller, one gets disturbance observer (DOB) for the reconstruction and compensation of input disturbances. Thereby, the DOB functionality is based on evaluating steady-state controller output. This DOB interpretation is in full agreement with the results of the analysis of the optimal setting of the stabilizing PDA controller and of its expanded PIDA version with positive feedback from the controller output. By using the multiple real dominant pole (MRDP) method, it confirms that the low-pass filter time constant in positive feedback must be much longer than the dominant time constant of the stabilized loop. This paper also shows that the constrained PIDA controller with the MRDP setting leads to transient responses with input and output overshoots. Experimentally, such a constrained series PIDA controller can be shown as equivalent to a constrained MRDP tuned parallel PIDA controller in anti-windup connection using conditional integration. Next, the article explores the possibility of removing overshoots of the output and input of the process achieved for MRDP tuning by interchanging the parameters of the controller transfer function, which was proven as very effective in the case of the series PID controller. It shows that such a modification of the controller can only be implemented approximately, when the factorization of the controller numerator, which gives complex conjugate zeros, will be replaced by a double real zero. Neglecting the imaginary part and specifying the feedback time constant with a smaller approximative time constant results in the removal of overshoots, but the resulting dynamics will not be faster than for the previously mentioned solutions. A significant improvement in the closed-loop performance can finally be achieved by the optimal setting of the constrained series PIDA controller calculated using the performance portrait method. This article also points out the terminologically incorrect designation of the proposed structure as series PIDA controller, because it does not contain any explicit integral action. Instead, it proposes a more thorough revision of the interpretation of controllers based on automatic reset from the controller output, which do not contain any integrator, but at the same time represent the core of the most used industrial automation. In the end, constrained structures using automatic reset of the stabilizing controller output can ensure a higher performance of transient responses than the usually preferred solutions based on parallel controllers with integral action that, in order to respect the control signal limitation, must be supplemented with anti-windup circuitry. The excellent properties of the constrained series PIDA controller are demonstrated by an example of controlling a thermal process and proven by the circle criterion of absolute stability. Full article

The paper discusses the stability and robustness of the proportional-integral (PI), proportional-integral-derivative (PID), and proportional-integral-derivative-accelerative (PIDA) controller for the integral-plus-dead-time (IPDT) plants. To enable the implementation and measurement of noise attenuation, binomial low-pass filters are added to the traditional design of controllers with ideal transfer functions, and the impact of the low-pass filters on the robust stability of the circuit is studied in detail. The proposed controller tuning, which integrates the suboptimal controller and filter design, is based on explicit tuning formulas derived by using the multiple real dominant pole (MRDP) method. It is shown that by combining derivative actions with possibly higher-order low-pass filters, it is possible to either accelerate the transients or increase the closed loop robustness and that the problem of defining the robust stability area should be addressed at the stage of determining the process model. In addition, if wishing to maintain the closed loop robustness of unfiltered PI control, while increasing the degree of the derivative components, one needs to increase the filtering properties of the low-pass filter used accordingly. Simple analytical relations for setting filtered PI, PID, and PIDA controllers with equivalent robustness are derived. Full article

The article deals with a computer-supported design of optimal and robust proportional-integral-derivative controllers with two degrees of freedom (2DoF PID) for a double integrator plus dead-time (DIPDT) process model. The particular design steps are discussed in terms of intelligent use of all available information extracted from a database of control tracking and disturbance rejection step responses, assessed by means of speed and shape-related performance measures of the process input and output signals, and denoted as a performance portrait (PP). In the first step, the performance portrait method (PPM) is used as a verifier, for whether the pilot analytical design of the parallel 2DoF PID controller did not omit practically interesting settings and shows that the optimality analysis can easily be extended to the series 2DoF PID controller. This is important as an explicit observer of equivalent input disturbances based on steady-state input values of ultra-local DIPDT models, while the parallel PID controller, allowing faster transient responses, needs an additional low-pass filter when reconstructed equivalent disturbances are required. Next, the design efficiency and conciseness in analyzing the effects of different loop parameters on changing the optimal processes are illustrated by an iterative use of PPM, enabled by the visualization of the dependence between the closed-loop performance and the shapes of the control signals. The main contributions of the paper are the introduction of PPM as an intelligent method for controller tuning that mimics an expert with sufficient experience to select the most appropriate solution based on a database of known solutions. In doing so, the analysis in this paper reveals new, previously undiscovered dimensions of PID control design. Full article

The paper discusses the proportional-integral-derivative (PID) controller from the viewpoint of (a) the analytical tuning of the PID controller for the double integrator plus dead time (DIPDT) model and (b) the numerical tuning using the performance portrait method (PPM). In the first case, the already published tuning with multiple real dominant pole, extended by integrated tuning procedures, which incorporate the inevitable low-pass filters by delay equivalences, is elaborated for modified sets of real poles. By considering several such modified sets of real poles, resulting in several new sets of controller parameters, the design can be better adapted to the requirements of the control tasks solved and to the limitations of the existing control loop hardware. In a noisy and uncertain environment, the balance between speed of setpoint and disturbance responses and acceptable excessive controller effort can thus be improved. The effectiveness of the analytical design can be evaluated using the numerical performance portrait method (PPM). For an already generated performance portrait (PP), it can offer a broad spectrum of controller settings that satisfy various design constraints. However, the results of the analytical design are still important as they facilitate the initial steps in the elaboration of the PPM and in explaining the nature of PID control. The developed controller tuning are compared using a new interpretation of PID controller as an extension of the stabilising PD controller by disturbance observer (DOB). The input disturbances reconstructed by DOB by evaluating the controller output of an integral process model in steady-state, can be estimated by a low-pass filter with a sufficiently long (integral) time constant. All analysed results are in full agreement with the proposed DOB interpretation, which furthermore contributes significantly to the explanation of the problems related to the optimal design of PID controllers. Full article

This paper deals with the design of a DC motor speed control implemented by an embedded controller. The design is simple and brings some important changes to the traditional Ziegler–Nichols tuning. The design also includes a novel anti-windup implementation of the controller and an integrated noise-reduction filter design. The proposed tuning method considers all important aspects of the control, such as pre-processing of the measured signals and filtering (to attenuate the measurement noise), time delays of the process, modeling and identification of the process, and constraints on the control signal. Three important aspects of designing PI and PID controllers for processes with noisy output on Arduino-type embedded computers are considered. First, it deals with the integrated design of the input filter and the controller parameters, since both are interdependent. Secondly, the method of setting the controllers from step responses by Ziegler and Nichols is modified for the case of digital signal processing (without drawing the tangent), while it recommends the suitability of its modification in terms of the use of both integral and static models. Third, the most suitable anti-windup solution for the given controller structure is proposed. In summary, the paper shows that an appropriate design of the embedded controller can achieve excellent closed-loop performance even in a noisy process environment with limited control signals. Full article

The paper investigates and explains a new simple analytical tuning of proportional-integrative-derivative (PID) controllers. In combination with nth order series binomial low-pass filters, they are to be applied to the double-integrator-plus-dead-time (DIPDT) plant models. With respect to the use of derivatives, it should be understood that the design of appropriate filters is not only an implementation problem. Rather, it is also critical for the resulting performance, robustness and noise attenuation. To simplify controller commissioning, integrated tuning procedures (ITPs) based on three different concepts of filter delay equivalences are presented. For simultaneous determination of controller + filter parameters, the design uses the multiple real dominant poles method. The excellent control loop performance in a noisy environment and the specific advantages and disadvantages of the resulting equivalences are discussed. The results show that none of them is globally optimal. Each of them is advantageous only for certain noise levels and the desired degree of their filtering. Full article