Static Decoupling Research Articles

Design of Multivariable PID Control Using Iterative Linear Programming and Decoupling

The design of multivariable process control systems is specially complicated when there are strong interactions between the different control loops, and even more with multiple time delays. This paper proposes an iterative design method of centralized proportional-integral-derivative (PID) controllers for stable linear systems. The methodology is based on the linear parameterization of equivalent loop transfer functions (ELTFs) for centralized control. These functions capture the dynamics of the other loops and, from a prior design, allow solving the design problem at each iteration with linear programming that shapes the Nyquist plot of the ELTFs in the frequency domain, which also avoids the need for approximations. Two optimizations are proposed: (I) maximizing integral gains by fulfilling linear robustness margins in each ELTF and (II) maximizing linear robustness margins by fulfilling minimum bandwidths in each loop. In both optimizations, static decoupling and decoupling at a frequency close to the bandwidth of each loop are included as constraints, which improves the decoupling performance and the procedure convergence. The effectiveness of the method is verified in three simulation examples (square and non-square) and a lab experimental process. The proposed designs achieve a similar or better response when compared to that achieved by other authors.

Study on Agricultural Machinery-Load-Testing Technology and Equipment Based on Six-Dimensional Force Sensor

Tractor traction power consumption is one of the main causes of energy consumption in agricultural production. Scientific and accurate control of tractor traction power consumption can obviously save energy and reduce consumption. In view of the backward load-testing technology and low measurement accuracy in field work, this study designed an array test equipment, which formed a measurement matrix based on a six-dimensional force sensor to accurately measure tractor hauled load, which could provide a reference signal for intelligent operation. In this paper, the static calibration test was carried out on the six-dimension force sensor, and the linearity, sensitivity, and zero drift were analyzed. The static characteristics of the test unit meet the measurement requirements. A static decoupling model was established. The decoupling errors of each channel were stable at 0.02%FS, 0.02%FS, 0.8%FS, 0.36%FS, 0.018%FS, and 0.06%FS, respectively. Finally, the whole hanging test of the measuring equipment was carried out—the error was 1.24%, −1.2% respectively—to verify the accuracy of the measurement of the sensor device under different working conditions.

Stability Analysis of Two Power Converters Control Algorithms Connected to Micro-Grids with Wide Frequency Variation.

Distributed power generation, micro-grids, and networks working in islanding mode have strong deviations in voltage quantities. These deviations can be divided into amplitude and frequency. Amplitude deviations are well-known and studied, as they are common in small and big grids. However, deviations on the ac mains frequency have not been widely studied. The literature shows control schemes capable of bearing these variations, but no systematic analysis has been performed to ensure stability. As the majority of power converters are designed for big grids, their analysis and design neglect frequency disturbances, therefore those devices allow a very small frequency operating window. For instance, in power converters that need to be synchronized to the grid, the standard deviation does not go beyond 0.5 Hz, and for grid-tied inverters it does not go beyond 1 Hz, whereas variations of around 8 Hz can be expected in micro-grids. This work presents a comprehensive analysis of the control system’s stability, where two different control schemes for a back-to-back static converter topology are implemented and studied under a wide variable grid frequency. Because the behavior of power converters is nonlinear and coupled, dynamic and static decouplers are usually introduced in the controller, being a key element on the scheme according to the findings. The results show that using just a static decoupler does not guarantee stability under frequency variations; meanwhile, when a dynamic decoupler is used, the operating window can be greatly extended. The procedure shown in this paper can also be extended to other control algorithms, making it possible to carefully choose the control system for a variable frequency condition. Simulated and experimental results confirm the theoretical approach.

Multivariable active disturbance rejection control for compression liquid chiller system

The compression liquid chiller system is a strongly nonlinear and multivariable system. How design a suitable control strategy still is a challenging task. This paper proposes a multivariable active disturbance rejection control (ADRC) for a compression liquid chiller system, where the loop coupling is estimated and compensated in real-time by enhanced reduced-order extended state observer (ESO) and static decoupling. Based on the nonlinearity and coupling analyses of the compression liquid chiller system, the reduced-order ESO-based ADRC is developed. Then the stability region of the proposed ADRC is deduced and a practical parameter tuning procedure is summarized in detail. With the application of the proposed ADRC for the compression liquid chiller system, the simulation results illustrate that the proposed control strategy can guarantee satisfactory tracking performance and estimate the loop coupling completely under different operating conditions. The performance of the loop coupling rejection and the fluctuation of the control signal have improved by at least 57.05% and 58.76% under all operating conditions, respectively, compared with the decentralized regular ADRC. The simulation results also show the proposed multivariable ADRC has a promising future for practical systems.

6-DoF Magnetically Levitated Rotary Table With Dynamic Numerical Force and Torque Regulator

Multiaxis motion control over a large travel range is still difficult for magnetic levitation positioning systems because the accuracy of the magnetic force model deteriorates when both translation and rotation of the moving part take place. To overcome this issue, this paper studies a dynamic force and torque regulating method based on the numerical wrench model and validates it with a 6-degree-of-freedom (DoF) magnetically levitated (maglev) rotary table. In each sampling cycle, the current-wrench transformation matrix (CWTM) is determined by the numerical wrench model, and then it is employed to decide the exciting currents for each coil phase by solving the overdetermined equation. A field programmable gate array (FPGA) is used as the processor to meet the real-time requirement of the control system by taking advantage of the fine-grained parallelism in the numerical wrench model. A high level synthesis (HLS) tool, general intellectual property core, a very-high-speed integrated circuit hardware description language (VHDL) component, and a MicroBlaze processor are employed simultaneously to develop the controller. By utilizing the numerical regulator, the maglev rotary table realizes stable multiaxis motions. Comparative experiments with the existing analytical method illustrate that the numerical wrench model improves the static decoupling effect, decreases the positioning fluctuations, and enlarges the travel range.

Data-Driven Air-Fuel Path Control Design for Robust RCCI Engine Operation

Reactivity controlled compression ignition (RCCI) is a highly efficient and clean combustion concept, which enables the use of a wide range of renewable fuels. Consequently, this promising dual fuel combustion concept is of great interest for realizing climate neutral future transport. RCCI is very sensitive for operating conditions and requires advanced control strategies to guarantee stable and safe operation. For real-world RCCI implementation, we face control challenges related to transients and varying ambient conditions. Currently, a multivariable air–fuel path controller that can guarantee robust RCCI engine operation is lacking. In this work, we present a RCCI engine controller, which combines static decoupling and a diagonal MIMO feedback controller. For control design, a frequency domain-based approach is presented, which explicitly deals with cylinder-to-cylinder variations using data-driven, cylinder-individual combustion models. This approach enables a systematic trade-off between fast and robust performance and gives clear design criteria for stable operation. The performance of the developed multivariable engine controller is demonstrated on a six-cylinder diesel-E85 RCCI engine. From experimental results, it is concluded that the RCCI engine controller accurately tracks the five desired combustion and air path parameters, simultaneously. For the studied transient cycle, this results in 12.8% reduction in NOx emissions and peak in-cylinder pressure rise rates are reduced by 3.8 bar/deg CA. Compared to open-loop control, the stable and safe operating range is increased from 25 °C up to 35 °C intake manifold temperature and maximal load range is increased by 14.7% up to BMEP = 14.8 bar.

Iterative Design of Centralized PID Controllers Based on Equivalent Loop Transfer Functions and Linear Programming

This paper deals with the design problem of multivariable Proportional-Integral-Derivative (PID) controllers for square and stable multivariable processes when a linear margin at the Nyquist plot is considered as robustness specification for each closed loop. A tuning method is developed based on the new concept of equivalent loop transfer function, which is proposed for centralized control and allows an independent design for each loop considering the interactions with the other loops through an iterative procedure. For the k-th loop, the PID parameters of the k-th column of the control matrix are calculated in each iteration by a linear programming optimization that maximizes the integral gains while fulfilling the robustness specification and achieving static decoupling. The method uses a frequency response array as representation of the process, which allows its applicability to systems with multiple time delays without requiring model reductions or approximations. The effectiveness of the method is illustrated by means of two simulation examples with dimensions <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2 \times 2$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3 \times 3$ </tex-math></inline-formula> . Comparisons with other centralized control methodologies show that the proposed approach achieves similar or greater performance and a remarkable better disturbance rejection response.

Adaptive Droop Control of the MTDC System With High-Capacity Energy Storage Based on Dynamic and Static Power Decoupling Method

In a multiterminal DC (MTDC) system with a large number of different types of energy storage devices, the AC terminals and the energy storage devices need to cooperate to maintain the stability of the DC bus voltage. Due to the difference in the dynamic and static power capability of each energy storage unit, the dynamic and static power should be distributed separately. To solve the above problems, an adaptive droop control strategy based on the dynamic and static power decoupling is proposed in this paper. The impact of the virtual impedance values on the dynamic and static power flows between the DC voltage regulating terminals operating with the RC droop method is analyzed. Through optimized virtual capacitance and adaptive virtual resistance, the dynamic power and static power can be distributed according to the PCS capacity and the available charge–discharge battery capacity, respectively. In addition, a simple secondary control method is adopted to compensate the static deviation of the DC bus voltage. Finally, a six-terminal MTDC system model is established in Matlab/Simulink, and the simulation results verify the feasibility and effectiveness of the proposed control strategy.

Multivariable predictive functional control of a compound power-split hybrid electric vehicle

The Corun hybrid system (CHS) is a deeply coupled multiple-input–multiple-output (MIMO) hybrid system. The two inputs are the torques of the two motors. The two outputs are the carrier speed and transmission output torque. Using the traditional control method, the multi-objective control quality cannot be guaranteed because of the adopted static decoupling method and proportional–integral–derivative (PID) controllers. In this paper, the problems of the traditional control method are carefully analyzed, and a new control method is proposed. Instead of static decoupling, dynamic decoupling is adopted to improve the decoupling control effect. A predictive functional controller instead of a PID controller is adopted to deal with the pure delay caused by controller area network (CAN) communication. The tracking effect of the target value is further improved by predictive functional controllers. For the two decoupled subsystems, that is, the integral system and the second-order underdamped system, two predictive functional controllers are designed. The new control method was verified by simulations and tests. The results show that the new control method is superior to the traditional control method for CHS.

Coupling analysis and dynamic stability boundary of spinning missiles considering actuator dynamics and autopilot

This paper focuses on coupling property and dynamic stability of spinning missiles equipped with a two-loop autopilot. The closed-loop characteristic equation is established in the complex form, on which we investigated the dominant factors of the cross coupling, i.e., actuator dynamics, airframe configuration and autopilot, to provide physical understandings of coupling property. By coupling analysis, it is found that coupling can be mitigated by the autopilot. However, the proposed static decoupling approach is necessary to eliminate steady coupling completely. Furthermore, by solving the forth-order characteristic equations with Cardan formula, the dynamic stability boundary is derived numerically. As actuator dynamics is extremely significant to stability, the proposed stability boundary is derived with consideration of it, and thus, it is more practical than results in previous studies. The effectiveness of decoupling method and the correctness of dynamic stability boundary is verified by mathematical simulations. Theoretical and numerical results also reveal that high actuator bandwidth and less time delay is beneficial to dynamic stability.

Globally Stable Delay Alignment for Feedback Control Over Wireless Multipoint Connections

The 5-G ultra reliable low latency communication standard is intended, for example, to enable new use cases based on networked feedback control. This article argues why additional delay control and alignment are needed, to meet the well-established feedback control requirements on low end-to-end loop delay and jitter. The main contribution of this article is a novel re-engineered delay aligning data flow controller, where a new static decoupling matrix is introduced. The intention is to obtain a multiple single loop control architecture that allows global robust $\mathcal {L}_2$ -stability to be proven. The algorithm is suitable to regulate $n+1$ end-to-end roundtrip delays of a 5-G multiconnectivity connection toward zero pair-wise delay differences. The new stability result is decisive for massive deployment, since weaker results would increase the need for supervision and raise operating costs significantly. A robot arm control loop application operating over three data paths illustrates the performance advantages associated with delay alignment and the proposed algorithm.

Static Decoupling Performance Analysis and Design of Bionic Elbow Joint

The static decoupling performance is closely related to the efficiency of the bionic elbow joint mechanism. The bionic elbow joint has good static decoupling and has high efficiency and carrying capacity. First, the movement structure and characteristics of the elbow joint are analyzed, a kind of bionic elbow joint is proposed, the position inverse solution is deduced, and force Jacobin matrix of the bionic elbow joint is obtained. Second, the static coupling performance evaluation index and the global static coupling performance index are established, the performance atlas are drawn. Thirdly, by use of the Monte Carlo method the structural parameters of the bionic elbow joint are optimized and selected based on the spatial model theory, and a novel the bionic elbow joint is designed based on parameters optimization, and the static decoupling is verified by the simulation experiment of the bionic elbow joint. The analysis results shows the static decoupling performance of the bionic elbow joint is symmetrical, and with the working space of the attitude output angle increases, the static decoupling decreases gradually. Structural parameters and have great influence on the global static decoupling performance. The structural parameters of is 90mm, is 70mm,and is 30mm, the bionic elbow joint has good static decoupling. This paper lays a foundation for further analysis and research of the bionic elbow joint.

An optimized BP neural network based on genetic algorithm for static decoupling of a six-axis force/torque sensor

In order to improve the measurement precision of 6-axis force/torque sensor for robot, BP decoupling algorithm optimized by GA (GA-BP algorithm) is proposed in this paper. The weights and thresholds of a BP neural network with 6-10-6 topology are optimized by GA to develop decouple a six-axis force/torque sensor. By comparison with other traditional decoupling algorithm, calculating the pseudo-inverse matrix of calibration and classical BP algorithm, the decoupling results validate the good decoupling performance of GA-BP algorithm and the coupling errors are reduced.

Compound control for speed and tension multivariable coupling system of reversible cold strip mill

To weaken the nonlinear coupling influence among the variables in the speed and tension system of reversible cold strip mill, a compound control (CC) strategy based on invariance principle was proposed. Firstly, invariance principle was used to realize static decoupling between the speed and tension of reversible cold strip mill. Then, considering the influence caused by the time variation of steel coil radius and rotational inertia of the left and right coilers, as well as the uncertainties, a CC strategy that is composed of extended state observer (ESO) and global sliding mode control (GSMC) with backstepping adaptive was proposed, which further realized dynamic decoupling and coordination control for the speed and tension system. Theoretical analysis shows that the resulting closed-loop system is global bounded stable. Finally, the simulation was carried out on the speed and tension system of a 1422 mm reversible cold strip mill by using the actual data, and through the comparison of the other control strategies, validity of the proposed CC strategy was shown by the results.

Static Decouplers with P-PI Dual Loop Controllers for Unstable System

The applicability of static decoupler followed by tuning of diagonal proportional integral controllers for unstable multivariable process is studied. The need of static decouplers for an unstable multivariable system where the conventional decouplers becomes unstable is brought about by using three examples of a two-input two-output processes. Further, dual loop controllers are tuned for the approximated decoupled system. Use of P-PI (Proportional – Proportional and Integral) dual loop control system reduces the overshoot significantly.

Simple method of designing centralized PI controllers for multivariable systems based on SSGM

A method is given to design multivariable PI/PID controllers for stable and unstable multivariable systems. The method needs only the steady state gain matrix (SSGM). The method is based on the static decoupler design followed by SISO PI/PID controllers design and combining the resulted decoupler and the diagonal PI(D) controllers as the centralized controllers. The result of the present method is shown to be equivalent to the empirical method proposed by Davison EJ. Multivariable tuning regulators: the feed-forward and robust control of general servo-mechanism problem. IEEE Trans Autom Control 1976;21:35–41. Three simulation examples are given. The performance of the controllers is compared with that of the reported centralized controller based on the multivariable transfer function matrix.

Robust Air-to-Fuel Ratio and Boost Pressure Controller Design for the EGR and VGT Systems Using Quantitative Feedback Theory

This paper describes robust multi-input, multi-output controller for the exhaust gas recirculation (EGR) and variable geometry turbocharger (VGT) systems of passenger car diesel engines. The air-to-fuel ratio of the exhaust gas and boost pressure of the intake manifold were selected as performance indicators in this paper. To enable the online calibration of the controller, proportional-integral-derivative (PID) was used as a feedback controller. Using quantitative feedback theory (QFT), two control loops for air-to-fuel ratio and boost pressure were independently designed with linearized models and parameter uncertainties. The prefilters and PID gains of two control loops were designed for satisfying required robust stability and tracking performance using the QFT design framework. Furthermore, the problems originated from the cross-coupled dynamics between the EGR and VGT systems were mitigated by a static decoupler. Using the proposed design steps, PID and decoupler gains of the representative 15 engine operating points which are mainly used in New European Driving Cycle were obtained. The proposed controller was validated through various test conditions of engine experiments. From the step responses and transient experiments, it was demonstrated that the required robustness and tracking performance were successfully achieved.

Synthesized ADRC for One-Level Inverted Pendulum System through Combination of Separating and Assembling

Inverted pendulum system is the ideal study object of nonlinear system. The ADRC has good estimate for disturbances, strong robustness and using static decoupling instead of dynamical decoupling. The one-level inverted pendulum system can be regarded as composing of the pendulum angel system and the cart position system. The former is faster and the later is slower. The synthesized ADRC for one-level inverted pendulum system is built through combination of separating and assembling to reduce difficulty in optimizing ADRC parameters of the inverted pendulum system. The synthesized controller is simulated by Matlab under different parameters of the inverted pendulum. Simulation results show that the pendulum angle and the cart position are well controlled.

Centralized Discrete State Space Model Predictive Control And Decentralized Pi-D Controller Of An Aerothermic Process

Abstract The aerothermic process is a pilot scale heating and ventilation system equipped with a heater grid and a centrifugal blower. The interaction between its main variables is considered as challenging for mono-variable controllers. A change in the ventilator speed affects the temperature behavior which represents a factor that must be managed for energy saving and the human welfare. This paper presents an experimental comparison between a Centralized Discrete State Space Model Predictive Control (CDSSMPC) and a Decentralized PI-D (DPI-D) controller. These both techniques are designed by using respectively the Laguerres functions and the static decoupler approach. To demonstrate the effectiveness of the two methods, an implementation on an aerothermic process is performed. This pilot scale is fully connected through the Humusoft MF624 data acquisition system for real time control. The results show satisfactory performance in closed-loop of the DPI-D controller compared to the CDSSMPC and the conventional PID ones.

An Improved Mixed Gas Pipeline Multivariable Decoupling Control Method Based on ADRC Technology

According to the serious decoupling, uncertainty, easily disturbed and nonlinear characters of the gas mixture of butterfly valve string couplets system, an ADRC static decoupling technology and the dynamic decoupling method based on extended state observer (ESO) were proposed. In this method, coupling from other input, parameters time-varying and external disturbances are all regarded as a total disturbance. The total disturbance can be estimated by ESO and feedback to controller, and coupling is achieved. In order to improve response speed of the system, and reduce the computation, this control system use nonlinear tracking-differentiator(TD),ESO and the nonlinear state error feedback control law (NLSEF) uses nonlinear function.Simulation results shows that, in this method, the decoupling is simplified, and the requirement of the model is reduced. The novel method can also ask for less calculation with faster response and better robustness, still with good tracking performance and disturbance rejection capability, the decoupling effect is fine.