Delay systems with meromorphic functions design

Adaptive Pole Positioning in MIMO Linear Systems by Periodic Multirate-Input Controllers

Autotuners represent a combination of a relay feedback identification test and some control design method. In this contribution, models with up to three parameters are estimated by means of a single asymmetrical relay experiment. Then a stable low order transfer function with a time delay term is identified by a relay experiment. Autotuning principles then combine asymmetrical relay feedback tests with a control synthesis. Two algebraic control syntheses then are presented in this paper. The first one is based on the ring of proper and stable rational functions R PS. The second one utilizes a special ring R MS, a set of RQ-meromorphic functions. In both cases, controller parameters are derived through a general solution of a linear Diophantine equation in the appropriate ring. A final controller can be tuned by a scalar real parameter m>0. The presented philosophy covers a generalization of PID controllers and the Smith-like control structure. This contribution deals with the implementation of proposed autotuners and presents some illustrative examples. A Matlab toolbox for automatic design and simulation was developed and various simulations performed and analyzed.

The application of the Smith predictor in the control system with a constant speed actuator is considered. In order to make it possible to use the Smith predictor a PID-controller with autotuning is used, the autotuning provides the control object model using a self-oscillation mode. The control object has a second order transfer function with a transport delay. The performance of the system was analyzed on an experimental workbench with the industrial constant speed actuator and a physical model of the control object. Recommendations are given, how to correct the PID-law parameters in order to improve the system performance.

Design of a Robust Fractional Order Controller for Burning Zone Temperature Control in an Industrial Cement Rotary Kiln

The object of research in the work is electromechanical systems, a characteristic feature of which is the presence of significant power dependence in the mathematical description. Because of this, problems arise when choosing the structure and parameters of controllers. In particular, in a DC motor with series excitation, a switched reluctance motor and electromagnetic retarders, saturation of the magnetic system in static and dynamic modes can occur. The apparatus of fractional-integral calculus used in the work allows us to describe such nonlinear objects with high accuracy by linear transfer functions of fractional order. So, when approximating the anchor circuit of a DC motor with series excitation by a fractional transfer function, the smallest standard error was obtained. The combination of a conventional PID controller with fractional integral components of the order of 0.35 and 1.35 ensured the best quality of the transient process - the current reaches the set value as quickly as possible without overshoot. Secondly, the switched reluctance motor, in the model of which it is necessary to take into account the power dependences, is described by the aperiodic function of the order of 0.7 when describing the transient processes of the speed during a voltage jump. From the family of controllers studied, the traditional PI controller with additional fractional-integral components of the order of 0.7 and 1.7 ensured the astaticism of the speed loop of the order of 1.7 and the smallest overshoot. Thirdly, the electromagnetic retarders of the driving wheels of a car, used to tune the internal combustion engine, are also most accurately described after testing by the fractional transfer function. Using the PIDIγIµ controller, which ensured closed loop astaticism of the order of 1.63, stabilization of the rotation speed of two wheels without out-of-phase oscillations and the accurate development of a triangular tachogram were achieved. Thus, thanks to the apparatus of fractional-integral calculus, a more accurate identification of object parameters is provided, the mathematical description is reduced to linear transfer functions of fractional order. And in closed systems it is possible to ensure astaticism of fractional order 1.3–1.7 and to achieve a better quality of transient processes than using classical methods.

Fiber optical parametric oscillators are laser sources with multiple longitudinal modes arising from their cavity length reaching several tens of meters. To reduce the noise due to multimode beating, the spacing between neighboring modes is increased using a Smith predictor internal control scheme. The Smith predictor utilizes a model of the dynamic behaviour of the system to deal with pure time delay and eliminate the effect of the delay in the overall closed-loop system. Applying the smith predictor, the system can be made to operate in a single-longitudinal mode, removing the excess modes. In this paper a linear model for operation of parametric oscillator is proposed and based on that transfer function of Smith predictor enhanced parametric oscillator is established. Numerical analysis of resulting transfer function will lead us toward single-longitudinal mode operation.

This chapter examines the proportional integral derivative (PID) controller design. It introduces the idea of disturbance estimation that leads to an equivalent PI control system. The mathematical model used in the chapter is a first order model. For systems with higher order transfer functions, approximation is required. To design a PID controller using the estimation based approach, a second order transfer function is considered. The chapter presents the MATLAB tutorial for the implementation of disturbance observer‐based PID controller. This implementation contains the anti‐windup mechanism when the control signal reaches its maximum or minimum values. The embedded PID controller via estimation is used in the simulation studies within the Simulink environment. The chapter also explains resonant controller design and implementation with anti‐windup mechanism using the disturbance estimation approach. It presents an example to illustrate the disturbance observer‐based resonant controller design.

A Dead Time Compensator Based on Linear Algebra (DTCLA)

In this paper we have introduced as a model in the adaptive Internal Model Control (IMC) structure a fractional order system to obtain a fractional adaptive IMC scheme. We have shown that this adaptive control scheme always provides theoretical guarantees of stability when a stable fractional order transfer function is used as an IMC parameter and that the use of this fractional IMC parameter can improve the performances of the control system along with its robustness against noises. A comparative simulation example is given to illustrate the efficiency of the proposed fractional order adaptive control scheme. Copyright © 2010 John Wiley & Sons, Ltd.

Cooperative adaptive cruise control (CACC) employs intervehicle wireless communications to safely drive at short intervehicle distances, which improves road throughput. The underlying technical requirement to achieve this benefit is formulated by the notion of string stability, requiring the attenuation of the effects of disturbances in upstream direction. The wireless communication delay, however, significantly compromises string stability. In order to compensate for time delays and thus reduce the minimum string-stable time gap, a Smith predictor can be applied. For application of a Smith predictor, the time delay needs to be in a series connection with the plant to be controlled, which is realized by introducing a master-slave architecture for CACC. As a result, information exchange appears to become bidirectional, while the control scheme still follows the one-vehicle look-ahead strategy. Feasibility of both the master-slave CACC strategy and the Smith predictor is explicitly analyzed. With the proposed control scheme, the minimum string-stable time gap can be significantly decreased, even considering communication delay uncertainty. The results are validated using simulations with a platoon of CACC-equipped vehicles.

Cooperative adaptive cruise control (CACC) employs intervehicle wireless communications to realize short intervehicle distances and, hence, to improve road throughput. However, the vehicle actuator delay and communication delay have a significant effect on the (string) stability properties. Therefore, a Smith predictor has been applied to compensate for the vehicle actuator delay, while utilizing a proportional-derivative controller and a constant time gap spacing policy. The control actuation is conducted on a delay-free vehicle model to follow a preceding vehicle with a desired distance, such that the resulting scheme leads to individual vehicle stability independent of the vehicle actuator delay. Moreover, this approach allows for a smaller minimum string-stable time gap compared to without the compensator, thus taking full advantage of CACC. In addition, the Smith predictor has been adapted to take acceleration disturbances into account. The results are experimentally validated using a platoon of two passenger vehicles, illustrating the practical feasibility of this approach.

To satisfy the stringent requirements of ultra-precision systems for high accuracy and rapid dynamic response, the chatter and system delay of voice coil motor (VCM) under operating conditions have become key bottlenecks restricting overall performance enhancement. To address these challenges, this paper proposes an adaptive convergence rate fractional-order sliding mode control strategy based on a Smith predictor (AFOSMC-SP). The strategy constructs a fractional-order sliding mode controller using an improved Oustaloup method, introduces a novel adaptive reaching law based on a saturation function with dynamic gain, and integrates a Smith predictor to compensate for the current-loop delay in the VCM system. This approach reduces algorithmic complexity and position-tracking error while enabling the adaptive adjustment of the system convergence rate to enhance robustness. In addition, the parameter boundary conditions and the global asymptotic stability of the closed-loop system are analyzed using Lyapunov stability theory. The simulation results show that, compared to conventional sliding mode control methods, the proposed AFOSMC-SP strategy provides superior parameter adaptability, higher tracking accuracy, and stronger suppression of external disturbances.

To overcome the convective time delay issue for active closed-loop flow control, a model based predictive control algorithm is analyzed. From a controls perspective, forms of internal model control or model predictive control can be used to accommodate and minimize the effect of systems with pure time delays. Moreover, the Smith predictor is a commonly employed control technique to negate the pure time delay in a closed-loop system. This form of model predictive control is applied to the asymmetric vortex problem of an axisymmetric forebody (specifically a von Karman ogive with fineness ratio of 3.5). The full-order Navier-Stokes equations are numerically solved on the forebody at a high angle of attack and provide the plant process. Small port and starboard blowing patches are used to introduce fluidic disturbances at the nose of the ogive to augment the global flow state and produce a deterministic vortex state. As the active flow control technique exploits a convective instability, a convective time delay exists. Linear-time-invariant and non-linear time-invariant models are developed from the open-loop dynamics. A Smith predictor is employed within the full order CFD simulation. The results of the predictive control are compared to open-loop and model-free closed-loop behavior. It is shown that the predictive control developed in this paper while very suitable for control of this type of flow, is very sensitive to modeling uncertainties.

An experimental application of time delay compensation techniques to distillation column control

This study describes the use of a biofeedback method for the noninvasive study of baroreflex mechanisms. Five previously untrained healthy male participants learned to control oscillations in heart rate using biofeedback training to modify their heart rate variability at specific frequencies. They were instructed to match computer-generated sinusoidal oscillations with oscillations in heart rate at seven frequencies within the range of 0.01-0.14 Hz. All participants successfully produced high-amplitude target-frequency oscillations in both heart rate and blood pressure. Stable and predictable transfer functions between heart rate and blood pressure were obtained in all participants. The highest oscillation amplitudes were produced in the range of 0.055-0.11 Hz for heart rate and 0.02-0.055 Hz for blood pressure. Transfer functions were calculated among sinusoidal oscillations in the target stimuli, heart rate, blood pressure, and respiration for frequencies at which subjects received training. High and low target-frequency oscillation amplitudes at specific frequencies could be explained by resonance among various oscillatory processes in the cardiovascular system. The exact resonant frequencies differed among individuals. Changes in heart rate oscillations could not be completely explained by changes in breathing. The biofeedback method also allowed us to quantity characteristics of inertia, delay, and speed sensitivity in baroreflex system. We discuss the implications of these findings for using heart rate variability biofeedback as an aid in diagnosing various autonomic and cardiovascular system disorders and as a method for treating these disorders.