Closed-loop Step Response Research Articles

Pisot-Number-Based Discrete-Time Controllers With Integer State Matrices to Ensure Monotonic Closed-Loop Step Responses

Pisot-Number-Based Discrete-Time Controllers With Integer State Matrices to Ensure Monotonic Closed-Loop Step Responses

New fractional-order LADRC scheme based on a novel filtered-Bode’s ideal transfer function for integer-order systems

In this paper, a new Fractional-Order Linear Active Disturbance Rejection Control scheme (FO-LADRC) is proposed to enhance the robustness against loop gain variations of the standard Active Disturbance Rejection Control (ADRC) in the case of uncertain integer-order systems. A new filtered Bode’s ideal transfer function (F-BITF) is proposed to be used as a reference model in the design approach of the proposed control scheme to ensure the dynamic behavior of the closed-loop BITF to the controlled system. A Fractional-order Extended State Observer (F-ESO) is used in the proposed FO-LADRC structure to approximate the system to be controlled by a filtered fractional-order integrator. The fractional order of the F-ESO is a design parameter to tune to achieve the desired overshoot of the closed-loop step response. For the tuning of FO-LADRC structure, an analytical method is proposed. The performance of the proposed FO-LADRC and the Chen’s et al. FO-ADRC structures are evaluated thorough numerical simulation, and then validated in practice in the case of a Cart-Pendulum. Both the simulation and the experimental results show that the proposed FO-LADRC is able to achieve the desired dynamics of the F-BITF and guarantee the robustness with respect to the controller gain variation and the system parameter uncertainties. The comparative study conducted also reveals that the proposed control scheme is more robust than that of Chen.

Robust Fractional Order Flow Control in an Oil Pipeline

The robust fractional order oil flow control in an oil pipeline is addressed in this paper. An experimental identification based on a step like input was developed which yielded a second order transfer function with a zero and a time varying time delay. Controllers are subsequently designed with nominal phase margin and zero steady state error of the closed-loop step response specifications, plus robust damping expressed in terms of a maximum allowed variation of the phase margin of ±10% around the nominal value. We have considered integer and fractional order controllers. Rules to tune the parameters of these controllers have been obtained and a condition to get minimum phase closed-loop systems has been derived. We have shown that PI controllers verifying the three design conditions often yield undesired nonminimum phase closed-loop systems. This is avoided using the proposed fractional order controllers. Simulations carried out in this paper illustrate these results.

Selection of PID controller design plane for time-delay systems using genetic algorithm

The design of a Proportional-Integral-Derivative (PID) controller with proportional, integral, and derivative, gain, k p , k i , and k d , respectively, for a time-delay system, is quite common, particularly in the k i - k d plane, for a fixed k p or in the k p - k i plane, for a fixed k d . These design methods have been widely reported in the literature, however, the process of investigating the effects of using any of these design planes on system performance has not been given serious attention hence the need for this study. The stability region in the k i - k d and k p - k i design plane for a fixed value of k p and k d respectively were determined. For every determined stability region, the optimum value of controller gains in the plane was determined using a genetic algorithm (GA) with the integral of time multiplied by absolute error (ITAE) used as the objective function. The optimum value of the fixed gains was graphically determined by plotting the minimum of ITAE (Min-ITAE) for each stability region against the fixed gains. The overall optimum controller gains are the fixed gain that gives minimum of Min-ITAE (Min (Min-ITAE)) and the gains that resulted in Min-ITAE that yielded the Min (Min-ITAE). Using the determined overall optimum controller gains, the system closed-loop step response was plotted for the two design planes and the time domain performance measures (TDPMs) were determined. Based on TDPMs obtained for examples 1, 2, and 3, the k i -k d design plane yielded a faster response while the k p - k i design plane yielded a response that closely tracks the input irrespective of the system type and order. The study will enable control system designers to select the design plane that will give the best system performance right from the start of controller design without involving trial and error once the system transfer function and design specifications are known.

A Simple Closed-Loop Test Based Control of Boost Converter Using Internal Model Control and Direct Synthesis Approach

In this article, a simple controller design method for output voltage control of dc–dc boost converter (BC) has been proposed. A simple closed-loop step test with proportional gain <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k_{0}$ </tex-math></inline-formula> is performed. BC open-loop transfer function is obtained from the closed-loop step response test data, which does not require information of BC circuit parameters. Furthermore, the controller is designed from the open-loop model of the BC through the internal model control (IMC) scheme and direct synthesis (DS) approach. The robust stability analysis of both the control schemes has been carried out. The proposed modeling technique and controller design methods have been validated in the experimental setup. Both the controller design techniques work satisfactorily. Superior transient performance of the IMC scheme in comparison to the DS scheme has been observed.

Optimal design of combined cooling, heating and power multi-energy system based on load tracking performance evaluation of adjustable equipment

• Configuration method considering tracking ability is proposed for multi-energy system. • Tracking ability index is presented based on the closed-loop step response of device. • Relationship between tracking ability and economic cost is revealed by optimization. • Preference on tracking ability improves load following performance of the system. The load tracking performance of combined cooling, heating and power multi-energy system (CCHP-MES) is greatly dependent on the system design, including system structure optimization and equipment capacity configuration. Conventional CCHP-MES design approach only considers the economic, environmental and efficiency performance, while the dynamic load tracking performance is underestimated. For this reason, this paper proposes a novel tracking ability index in the capacity configuration optimization of the CCHP-MES by comparing the closed-loop dynamic differences of the involved adjustable equipment. The rise time and overshoot of the equipment output are selected as dynamic characteristics evaluation parameters, and their product can reflect the load following performance quality of the CCHP-IES. The tracking ability index is then embedded into the capacity configuration optimization objective of the CCHP-MES, and a novel MES configuration model is proposed with integrated consideration of the economic benefits and transient load tracking ability. Case studies using typical electrical, thermal, cooling loads and renewable power data verify the efficacy of the optimization model in the planning and design of the CCHP-MES. Considering the load tracking ability of the MES in the configuration will significantly improve the load following performance of the CCHP-MES at the expense of the increased capital investment.

Discrete-time SISO LTI Systems with Monotonic Closed-loop Step Responses: Analysis and Control Based on Impulse Response Models

An explicit relation between the open- and closed-loop system responses is established directly in the time domain by means of Bell polynomials. This relation is used to derive necessary and sufficient conditions on the open-loop impulse response that guarantees that its closed-loop impulse response under unity feedback is non-negative in a given time range. Based on these conditions, a new design technique for PID controllers is presented that guarantees a monotonic closed-loop step response over a desired time interval. The results hold for any (possibly infinite-dimensional) discrete-time LTI system with a known impulse response. Numerical examples are provided to assess the contribution.

Robustness Improvement of the Fractional-Order LADRC Scheme for Integer High-Order System

This article deals with a novel fractional-order active disturbance rejection control (FADRC) scheme to handle a general integer-order system. The proposed control structure enhances the robustness and performance of the classical active disturbance rejection control, especially for the open-loop gain variation. Based on the Bode's ideal transfer function, an analytical design of a state-feedback control is proposed. The integer-order model of the system to be controlled is first transformed to a noninteger-order one, where the introduced fractional order is a design parameter, which imposes the overshoot of the closed-loop step response. In addition, because the model of the system is transformed to a cascade of integer- and fractional-order integrator (the model is noncommensurate), a commensurate fractional-order extended state observer is proposed to estimate the generalized disturbance. To improve the robustness of the proposed FADRC scheme, an analytical design method of a noncommensurate state-feedback control is proposed. The proposed design method is based on the Bode's ideal transfer function cascaded with an integer-order filter. The proposed FADRC scheme is applied for a pendulum-cart test bed, and the effectiveness and robustness of the proposed control are examined by experiments.

Modeling and simulation analysis of oil-free scroll compressor driven by magnetic force

In order to solve the problems of wear, lubrication and complex structure of digital oil-free scroll compressor, an oil-free scroll compressor driven by magnetic force is proposed in this paper. The new scroll compressor is driven by electromagnetic force, without anti-rotation mechanism and motor, which reduces mechanical contact, so as to achieve the goal of low wear and oil-free. Back pressure device provides variable axial magnetic force to reduce the vibration of the compressor and ensure that the compressor works under the optimum force. The mathematical model of back pressure device and driving force is established and verified by finite element method. The results are in good agreement. The closed-loop step response of the new compressor is simulated. The gas force is decomposed and analyzed. The analysis, calculation and simulation results show that the back pressure device and the driving device meet the requirements of the compressor.

Reinforcement Learning based Design of Linear Fixed Structure Controllers

Reinforcement learning has been successfully applied to the problem of tuning PID controllers in several applications. The existing methods often utilize function approximation, such as neural networks, to update the controller parameters at each time-step of the underlying process. In this work, we present a simple finite-difference approach, based on random search, to tuning linear fixed-structure controllers. For clarity and simplicity, we focus on PID controllers. Our algorithm operates on the entire closed-loop step response of the system and iteratively improves the PID gains towards a desired closed-loop response. This allows for embedding stability requirements into the reward function without any modeling procedures.

Fixed-order controller synthesis for monotonic closed-loop responses: a linear programming approach

We consider the problem of synthesizing dynamic controllers to guarantee monotonic closed-loop step responses. Restricting our attention to controllers which yield positive closed-loop systems, we derive synthesis conditions that are linear in the controller parameters. A linear programming formulation that attempts to optimize the decay rate of the closed-loop system while ensuring asymptotic stability and monotonic step response is developed. An alternative approach which guarantees closed-loop stability and a near-monotonic response is also introduced. Several illustrative examples demonstrate the effectiveness of the approach.

Data-driven I-PD Gain Tuning using Closed-loop Step Response Data

Data-driven I-PD Gain Tuning using Closed-loop Step Response Data

Design and Analysis of Three-Stage Amplifier for Driving pF-to-nF Capacitive Load Based on Local Q-Factor Control and Cascode Miller Compensation Techniques

This paper presents a new frequency compensation approach for three-stage amplifiers driving a pF-to-nF capacitive load. Thanks to the cascode Miller compensation, the non-dominant complex pole frequency is extended effectively, and the physical size of the compensation capacitors is also reduced. A local Q-factor control (LQC) loop is introduced to alter the Q-factor adaptively when loading capacitance CL varies significantly. This LQC loop decides how much damping current should be injected into the corresponding parasitic node to control the Q-factor of the complex-pole pair, which affects the frequency peak at the gain plot and the settling time of the proposed amplifier in the closed-loop step response. Additionally, a left-half-plane (LHP) zero is created to increase the phase margin and a feed-forward transconductance stage is paralleled to improve the slew rate (SR). Simulated in 0.13-µm CMOS technology, the amplifier is verified to handle a 4-pF-to-1.5-nF (375× drivability) capacitive load with at least 0.88-MHz gain-bandwidth (GBW) product and 42.3° phase margin (PM), while consuming 24.0-µW quiescent power at 1.0-V nominal supply voltage.

Reference Model Design for Data-driven Controller Parameter Tuning Based on Closed-loop Step Response Data with Manipulated Variable Evaluation

Reference Model Design for Data-driven Controller Parameter Tuning Based on Closed-loop Step Response Data with Manipulated Variable Evaluation

The usage of Lambert W function for identification and speed control of a DC motor

The paper proposes a new method of identifying the linear model of a DC motor. The parameter estimation is based on the closed-loop step response of the DC motor under a proportional controller. For the application of the method, a deliberate delay of the measured speed was introduced. The paper considers the speed regulation of the direct current motor with negligible inductance by applying 1-DOF and 2-DOF, proportional integral retarded controllers. The proportional and integral gain of the PI retarded controllers was received by using a pole placement method on the identified model. The Lambert W function was applied for the identification and in designing the controller with the purpose of finding the rightmost poles of the closed-loop as well as the boundary conditions for selecting the gain of the PI controller. The robustness of the calculated controllers was considered under the effect of an disturbance, uncertainty in each of the DC motor parameters as well as perturbations in time delay.

Self-optimizing control of an LNG liquefaction plant

In this paper we apply self-optimizing control (SOC) to a cascaded LNG liquefaction plant. We first introduce the model, and then define the operational objective, which is to achieve minimal energy consumption while satisfying operational constraints. Four control structures are compared; a “standard” temperature control structure, an SOC structure with two plant measurements, an SOC structure that uses a combination of plant measurements as controlled variable, and an SOC structure where we also include measurements of disturbances in addition to the plant measurements. We find that the SOC structures significantly reduce the average steady-state loss when the operating conditions change. We furthermore find that using more plant measurements in the SOC structure results in lowered losses. In particular, for the disturbances considered, the steady-state loss becomes acceptably low, such that there is no need for a supervisory real-time optimization layer. Finally, it has been found that including disturbance measurements results in somewhat reduced losses, although the improvement was insignificant for the studied case. The effectiveness of the SOC framework is shown by closed-loop step responses to selected disturbances.

Friction characteristics and servo control of a linear peristaltic actuator

Despite presenting several inherent advantages, pneumatic actuators are typically discarded for applications where fine motion control is required. This is mainly caused by friction effects caused by piston and rod seals, namely the discontinuities found in friction forces around zero velocity. These effects are very hard to predict and thus to counteract using conventional control laws. This paper explores the use of a different pneumatic actuation solution, a pneumatic linear peristaltic actuator (PLPA), to overcome this problem. The solution envisaged has several potential advantages over conventional or low-friction actuators. Since literature is scarce on this topic, this paper presents the working principle and the model of a PLPA, along with experimental results of its static and viscous friction forces. These results are compared against the ones obtained with a conventional low-friction actuator. Finally, the paper explores the use of a PLPA and a low-friction actuator for servo control, using a conventional PID-type controller. It is experimentally shown that, contrary to what happens with conventional (even low friction) actuators, the use of an integral action does not lead to a limit cycle. Moreover, zero steady-state control error is obtained in a closed loop step response, showing that the approach proposed in this study potentially leads to a low-cost and simple motion control solution.

A Design Method for an Optimal Pre-filter in FRIT Using Closed-loop Step Response Data

This paper gives a design method for an optimal pre-filter in FRIT using closed-loop step response data by extending the method for VRFT. The paper shows that both the data-driven cost function and the original one have the same second order Taylor expansion with extended parameter descriptions. Finally, a numerical example shows the effectiveness of the proposed method.

Virtual Feedback Reference Tuning Using Closed Loop Step Response Data in Frequency Domain

SUMMARYThe paper gives a controller tuning method using a virtual reference feedback tuning (VRFT) approach in frequency domain. While the original VRFT uses a data‐driven performance index based on input/output data directly, the proposed one derives a frequency domain performance index based on the Fourier transformation of one‐shot experimental input‐output data. The frequency domain performance index enables the optimal prefilter to be straightforwardly designed without using the spectral density of the collected input signal. Hence, the proposed one outperforms the original one when the input and output data are collected from the closed loop step response. The effectiveness of the proposed method is illustrated through a numerical example.

Closed-loop Identification of an Industrial Extrusion Process

This paper deals with the challenging problem of closed-loop identification for multivariable chemical processes and particularly the estimation of an open-loop plant model for a lab-scale industrial twin-screw extruder used in a powder coatings manufacturing line. The aim is to produce a low order efficient model in order to assist the scaling-up and the model-based control design of the manufacturing process. To achieve this goal, a two-stage indirect approach has been deployed which relies on the a-priori knowledge of the controller parameters in order to extract good estimates of the open-loop dynamics of the underlying process. As input excitation signals we have used multiple single variable step tests at various operating conditions (current industrial practice) carried out manually in order to generate the data-set which captures the dynamics of the extrusion process. In order to increase the efforts for obtaining a suitable plant model, we have employed various identification techniques, such as Prediction Error Methods (PEM) and Subspace Identification Methods (SIM) in order to generate candidate closed-loop models that fit to the original input-output process data. Then, a comparison of the estimated models was performed by means of the mean square error and data fitting criteria in order to select the model that best describes the dynamic behaviour of the extrusion process. Model validation based on closed-loop step responses also used as verification of the results.