Multivariable Control Design Research Articles

Effective torque modeling of a gasoline-ethanol engine for multivariable adaptive control design

Effective torque modeling of a gasoline-ethanol engine for multivariable adaptive control design

Design of an Optimal Multivariable PID Controller for a Two-Link Robot Arm

Incorporating manipulator robots into various industries has revolutionized automation and manufacturing processes. Manipulator robots are versatile machines equipped with robotic arms and end-effectors, enabling them to handle complex tasks with precision and efficiency. This research aims to design an optimal Mutivariable PID (MPID) controller that ensures precise and accurate movements of two-link robot arm. Theoretical foundations of the MPID controller are discussed together with its relevance to robotic arm systems, and the challenges associated with its implementation. The research methodology involves mathematical modelling of the two-link robot arm dynamics, and the use of an optimization algorithm to determine the optimal MPID controller coefficients. Simulation results demonstrate performance enhancement and productivity of the two-link robot arm through the improved MPID controller.

Multivariable Iterative Learning Control Design for Precision Control of Flexible Feed Drives.

Advancements in machining technology demand higher speeds and precision, necessitating improved control systems in equipment like CNC machine tools. Due to lead errors, structural vibrations, and thermal deformation, commercial CNC controllers commonly use rotary encoders in the motor side to close the position loop, aiming to prevent insufficient stability and premature wear and damage of components. This paper introduces a multivariable iterative learning control (MILC) method tailored for flexible feed drive systems, focusing on enhancing dynamic positioning accuracy. The MILC employs error data from both the motor and table sides, enhancing precision by injecting compensation commands into both the reference trajectory and control command through a norm-optimization process. This method effectively mitigates conflicts between feedback control (FBC) and traditional iterative learning control (ILC) in flexible structures, achieving smaller tracking errors in the table side. The performance and efficacy of the MILC system are experimentally validated on an industrial biaxial CNC machine tool, demonstrating its potential for precision control in modern machining equipment.

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.

Radiation Force Modeling for a Wave Energy Converter Array

The motivation and focus of this work is to generate passive transfer function matrices that model the radiation forces for an array of WECs. Multivariable control design is often based on linear time-invariant (LTI) systems such as state-space or transfer function matrix models. The intended use is for designing real-time control strategies where knowledge of the model’s poles and zeros is helpful. This work presents a passivity-based approach to estimate radiation force transfer functions that accurately replace the convolution operation in the Cummins equation while preserving the physical properties of the radiation function. A two-stage numerical optimization approach is used, the first stage uses readily available algorithms for fitting a radiation damping transfer function matrix to the system’s radiation frequency response. The second stage enforces additional constraints on the form of the transfer function matrix to increase its passivity index. After introducing the passivity-based algorithm to estimate radiation force transfer functions for a single WEC, the algorithm was extended to a WEC array. The proposed approach ensures a high degree of match with the radiation function without degrading its passivity characteristics. The figures of merit that will be assessed are (i) the accuracy of the LTI systems in approximating the radiation function, as measured by the normalized root mean squared error (NRMSE), and (ii) the stability of the overall system, quantified by the input passivity index, ν, of the radiation force transfer function matrix.

Performance Analysis of Cascade Tank System Using Deep Learning Controller

The conventional proportional–integral–derivative (PID) controller is used in the majority of process industries. Although the most commonly used, the classic PID controller has several drawbacks like variable performance for the non-linear system, multivariable control design is not straightforward; the response is influenced by dead time, no constraints involvement, etc. The field of process control systems has grown quickly, and other controllers have been developed that try to overcome the weakness of PID controllers. Advances in artificial neural networks, specifically deep learning, have widened the application domain of process control systems. In this paper, a cascaded tank system, which is a benchmark problem, has been simulated. The input-output data of the plant has been generated and used to train a deep-learning controller using backpropagation. Several measures, such as time response, frequency response, and signal statics performance indices, are used to evaluate the outcomes of the proposed controller. The proposed model performs better on every assessment criterion than the traditional controller.

Frequency-based multivariable control design with stability margin constraints: A linear matrix inequality approach

In this paper, a proportional–integral–derivative controller design problem for stable multivariable process is considered. A frequency-based control technique is formulated as a convex optimization problem with linear matrix inequality constraint. The multivariable proportional–integral–derivative controller is designed so that H∞ norm of the difference between the designed loop gain function and a desired one is minimized. Linear matrix inequality constraints on the stability margin guarantees designed loop stability. Process frequency domain data is used to solve the proposed optimization problem. Knowledge of the process parametric model is not necessary. The desired loop gain transfer function is defined from the reference complementary sensitivity function. Simulation results show the comparison between the proposed technique and technique from the literature. In these examples, the proposed technique resulted in stable closed-loops different from the others and in a reduction of the performance indices.

A Control Method to Reduce Overshoots in High-Frequency Link Current and Voltages at Load Transients of a Dual-Active-Bridge Series-Resonant Converter

Dual Active Bridge Series Resonant Converter (DABSRC) is well researched in the literature to find out a suitable pulse width modulation (PWM) technique that can achieve voltage regulation, zero voltage switching (ZVS), and minimum rms current in high frequency (HF) link. Although the advanced PWM techniques achieve desired performance at steady state, the HF link current and voltages suffer from huge overshoots during the load transients, which can damage the semiconductor devices and can cause the saturation of the high frequency transformer. Therefore, in this paper, a relationship is derived between the pole positions and the percentage overshoot, so that any design with the trade-off between the fast dynamics and overshoot can be done analytically. As the system involves multiple state and input variables, which are also closely coupled, a multivariable state feedback controller design is proposed to control the dynamics of all the HF link state variables simultaneously. In any DAB-based topology, the peak volt-ampere (VA) rating of the passive components can increase by 80% due to these overshoots. The proposed control successfully restricts the overshoots below 25% with a settling time of 5 ms for the output voltage. The experimental verification is carried out in a 2.25 kW hardware prototype.

Multivariable Control Design for Grid-Forming Inverters With Decoupled Active and Reactive Power Loops

Grid-forming inverters (GFMIs) are recognized as a prominent driver toward achieving renewable energy-rich power grids. Unlike grid-following inverters (GFLIs), which are controlled as current sources, GFMIs are controlled as voltage sources. In GFMIs, dynamic control of the magnitude ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$V_{\mathrm{c}}$</tex-math></inline-formula> ) and angle ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\theta$</tex-math></inline-formula> ) of the point of common coupling (PCC) voltage is used to achieve active ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$P$</tex-math></inline-formula> ) and reactive ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> ) power transfer across a line. However, independent control of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$P$</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">$Q$</tex-math></inline-formula> via <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$V_{\mathrm{c}}$</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">$\theta$</tex-math></inline-formula> becomes challenging due to the coupling between <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$P$</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">$Q$</tex-math></inline-formula> loops. The coupling becomes severe as the resistance-to-reactance ratio of the grid impedance and the power angle between the GFMI and the grid voltages are increased. This article proposes a novel multivariable controller to completely decouple <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$P$</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">$Q$</tex-math></inline-formula> loops in GFMIs. The proposed multivariable controller could be designed based on the prevalent control structures for GFMIs such as droop controller, swing equation-based virtual synchronous generator (VSG) controller, zero steady-state error reactive power controller, and fixed steady-state error reactive power controller. The additional cross-channel decoupling controllers in the proposed multivariable controller provide superior decoupling action over the existing decoupling methods, such as the virtual inductor-based method. An <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_\infty$</tex-math></inline-formula> -based method is adopted to tune the proposed multivariable controller parameters, where the straightforward formulation of the desired closed-loop dynamics based on the open-loop system is clearly shown. The decoupling performance of the controller is experimentally validated extensively. The experimental results show that the proposed controller results in superior performance over the prevalent decoupling methods, such as the virtual-inductor decoupling method.

Linear Matrix Inequality-Based Multivariable Controller Design for Boost Cascaded Charge-Pump-Based Double-Input DC–DC Converter

An analysis and controller design of double-input dc–dc converter (DIDDC) is introduced in this article. This converter is integrated with buck and boost converters at the front-end and a charge pump on the back-end. Salient features of this topology are as follows: (i) ripple content is low in source currents, (ii) both the dc sources are connected through an inductor, which gives rise to a smooth source current waveform, (iii) both the sources supply power to load either in standalone or simultaneously together, and (iv) two control–loops (one for source current regulation, while the second one for load voltage regulation) are sufficient enough to ensure power transfer/management from dc sources to load. To ensure power management on the input dc sources while keeping a stable closed-loop converter system, a multivariable diagonal controller is designed. The first diagonal controller performs the load voltage regulation task, while the second controller regulates input of source-2 dc current. From the control point of view, the double-input single-output converter becomes a two-input two-output control problem and exhibits control–loop interactions due to the power flow from two different sources to load through common elements. The impact of off-diagonal elements’ interactions is accounted by using decouplers. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> robust control theory and linear matrix inequality (LMI) principles are adopted to design reliable controllers. The structured controller of fixed order (PID) is designed by enforcing the necessary type LMIs. To demonstrate the feasibility and effectiveness of multivariable controllers of the DIDDC, a 60/24 V to 48 V, 150 W, 50 kHz topology prototype is constructed, and the power management aspects are investigated experimentally. Load voltage regulation, source current regulation, load sharing on the input dc sources, and power management aspects of LMI-based controllers were tested extensively for all possible disturbances. In all these test cases, the closed-loop double-input converter system is stable and robust in rejecting a variety of disturbances created.

A Multivariable Controller in Synchronous Frame Integrating Phase-Locked Loop to Enhance Performance of Three-Phase Grid-Connected Inverters in Weak Grids

This article presents a new current controller in the synchronous reference frame and its associated design for enhancing the performance of three-phase grid-connected inverters, especially against weak-grid conditions. The existing controllers do not perform strongly during high-impedance grid conditions and lead to oscillations and instability issues due to the interactions between the synchronization and control units. The proposed controller addresses this issue by 1) deriving a linear model of the three-phase phase-locked loop (PLL), 2) integrating the PLL model into the current controller design, 3) using a multivariable control design for multi-input multi-output systems, and 4) designing the controller gains using optimal linear quadratic theory. The proposed controller has superior performance over a substantially wider range of weak-grid conditions compared to conventional controllers. Extensive simulation and experimental results are presented in order to validate and reveal the desirable performance of the proposed controller.

Multivariable Model-Free Adaptive Controller Design With Differential Characteristic for Load Reduction of Wind Turbines

The asymmetric loads on wind turbines are becoming a fatal constraint factor with the increase of wind turbine size. In order to tackle this challenge, individual pitch control mechanism is introduced into the wind turbines. However, the application scopeof the traditional individual pitch control (IPC) is limited due to the complex dynamic coupling among wind turbine components, the strong nonlinearity of the pitch system and the inevitable unmodeled dynamics. Therefore, a multivariable model-free adaptive control (MIMO-DE-MFAC) strategy with differential characteristic is first proposed in this paper. Then, the proposed method is applied to the individual pitch control of the 5MW wind turbine. The simulation results from FAST demonstrate that the MIMO-DE-MFAC achieves a notable performance improvement on blade root compared with the PI. Furthermore, compared with other existing model-free adaptive control (MFAC) strategies, the proposed method not only achieves the optimal control results, but also has stronger robustness in speed-varying wind fields. Finally, the hardware-in-the-loop (HIL) experiment further verifies the reliability of the above simulation results, which provides a useful reference value for the field test.

Fuzzy model based multivariable predictive control design for rapid and efficient speed-sensorless maximum power extraction of renewable wind generators

Introduction. A wind energy conversion system needs a maximum power point tracking algorithm. In the literature, several works have interested in the search for a maximum power point wind energy conversion system. Generally, their goals are to optimize the mechanical rotation or the generator torque and the direct current or the duty cycle switchers. The power output of a wind energy conversion system depends on the accuracy of the maximum power tracking controller, as wind speed changes constantly throughout the day. Maximum power point tracking systems that do not require mechanical sensors to measure the wind speed offer several advantages over systems using mechanical sensors. The novelty. The proposed work introduces an intelligent maximum power point tracking technique based on a fuzzy model and multivariable predictive controller to extract the maximum energy for a small-scale wind energy conversion system coupled to the electrical network. The suggested algorithm does not need the measurement of the wind velocity or the knowledge of turbine parameters. Purpose. Building an intelligent maximum power point tracking algorithm that does not use mechanical sensors to measure the wind speed and extracts the maximum possible power from the wind generator, and is simple and easy to implement. Methods. In this control approach, a fuzzy system is mainly utilized to generate the reference DC-current corresponding to the maximum power point based on the changes in the DC-power and the rectified DC-voltage. In contrast, the fuzzy model-based multivariable predictive regulator follows the resultant reference current with minimum steady-state error. The significant issues of the suggested maximum power point tracking method, such as the detailed design process and implementation of the two controllers, have been thoroughly investigated and presented. The considered maximum power point tracking approach has been applied to a wind system driving a 5 kW permanent magnet synchronous generator in variable speed mode through the simulation tests. Practical value. A practical implementation has been executed on a 5 kW test bench consisting of a dSPACEds1104 controller board, permanent magnet synchronous generator, and DC-motor drives to confirm the simulation results. Comparative experimental results under varying wind speed have confirmed the achievable significant performance enhancements on the maximum wind energy generation and overall system response by using the suggested control method compared with a traditional proportional integral maximum power point tracking controller.

A State Space Modeling Method for Aero-Engine Based on AFOS-ELM

State space models (SSMs) are important for multi-variable performance analysis and controller design of aero-engines. In order to solve the problems of the traditional state space modeling methods that rely on component-level models (CLMs) and cannot be carried out in real time, an aero-engine state space modeling method based on adaptive forgetting factor online sequential extreme learning machine (AFOS-ELM) is proposed in this paper. The structure of the extreme learning machine (ELM) is determined according to the form of the state space model, and the inverse-free ELM algorithm is used to automatically select the appropriate number of hidden nodes to improve the efficiency of offline initialization. The focus of the ELM on current operation performance is enhanced by the adaptive renewed forgetting factor, which reduces the impact of aero-engine history and deviated data on the current output and improves the accuracy of the model. Then, according to the analytical equation of the ELM model, the state space model of an aero-engine at each sampling time is obtained by using the partial derivative method. The simulation results based on engine test data show that the real-time performance and accuracy of the state space model established online in this paper can meet the needs of aero-engine control system requirement.

Robust multivariable control design for HVDC systems considering AC grid impedance uncertainties

High-voltage direct current (HVDC) transmission system based on modular multilevel converter (MMC) technology is considered as an attractive solution for the interconnection of two AC grids to enhance the security of supply. Several studies have concluded that the AC grid impedance is a key parameter for the control system design of the MMC. Such important design parameter, however, is subject to wide variations due to the time-varying nature of AC grid and the future modifications and expansions. Therefore, the grid impedance has to be considered as an uncertain parameter during control design stage. To this end, this paper suggests a robust multivariable controller which is able to maintain system stability and performance for an extended range of grid impedance uncertainties. To ensure that the controller operates robustly in a wide range of grid impedances, structured singular value of the system (known as μ) is minimized via an iterative procedure. In such procedure, the uncertainties are separated from the nominal linear model of the system and the weighing functions are tuned to fulfill the robustness criteria defined by the small-gain theorem. The effectiveness of the suggested controller and the design procedure is validated by means of simulation results.

Utopia constrained multi objective optimisation evolutionary algorithm

ABSTRACT A new multiobjective evolutionary optimisation algorithm (MOEA) to solve multimodal, multidimensional, nonconvex, nonlinear, dynamic multiobjective optimisation problems (MOPs) is the need of the hour. The quality of an MOEA lies in a good balance between the exploration and exploitation stages of the MOEA. Utopia constrained MOEA (U-MOEA) is proposed in this paper that improves the exploitation in the replacement step to achieve a perfect balance between exploration and exploitation. The proposed U-MOEA is tested on benchmark MOPs and a multivariable controller design problem. The performance of the proposed algorithm is also compared with other MOEAs such as NSGA-II and ICMDRA concerning hyper volume, nondomination count, combined Pareto set metric, and Cmetric . The performance metrics show better hyper volume and spread metric values for the proposed algorithm, indicating the ability in attaining trade-off region closeness along with diversified Pareto front for U-MOEA when compared to the other two algorithms. Results clearly show that the proposed U-MOEA produces good convergence, diversity characteristics with many numbers of trade-off solutions in a Pareto front.

Comparison of PLL-Based and PLL-Less Vector Current Controllers

This article presents a detailed and rigorous comparison between two vector current control (VCC) approaches for voltage source converters (VSC). A PLL-less VCC (also called the direct power control) has recently been proposed in several major publications with the assumption that it will improve the performance of conventional PLL-based VCC during weak grid conditions. In this article, first, we introduce an enhancement to both the PLL-based and PLL-less VCCs by using an optimal multivariable control design for both of them. Then, we show that both controllers perform equally during normal and weak grid conditions. However, the PLL-less VCC produces errors when the grid frequency variations occur and eventually becomes unstable when the grid is also weakened. Furthermore, the PLL-less VCC cannot produce a clean output current when unbalanced grid disturbances occur. This article proposes a method to address this latter issue. It also proves that the filters used in PLL-less VCC introduce similar dynamics to those of PLL. This article concludes that the PLL-based VCC is still the preferred choice for the grid-interfaced VSCs. Laboratory-scale experimental results are also included to validate the simulation results.

Weighted sensitivity design of multivariable PID controllers via a new iterative LMI approach

This paper addresses the weighted sensitivity design of multivariable proportional–integral–derivative (PID) controllers for multi-input multi-output (MIMO) processes. First, the PID reference tracking problem is formulated into an H∞ PID control problem by using the weighted sensitivity synthesis, and the problem is further casted into an H∞ SOF control problem. Second, based on the idea of T–K iteration, a new iterative LMI algorithm has been developed to locally solve the optimal H∞ SOF control problem. Then, a design procedure is presented for weighted sensitivity design of multivariable PID Controllers for MIMO processes. Finally, three application examples are provided to show the effectiveness and good performance of our method for practical industrial processes.

A novel multivariable nonlinear robust control design for turbofan engines

Traditional steady-state control methods are applied to turbofan engines operating in the small region near certain operating conditions, which need to switch controllers for operating in the large region and then may lead to instability and performance degradation of the closed-loop system. In this paper, a novel multivariable nonlinear robust control method for turbofan engines is proposed to improve the control performance within the large region. To enlarge the controllable region, a polynomial state-space model describes the nonlinear characteristics of turbofan engines. Based on the analysis of the closed-loop control system, by using the Lyapunov function theorems, a polynomial robust controller is designed to ensure the stability and desired nonlinear control performance of turbofan engines. Compared with the classical PI, mixed sensitivity, and H∞ control, simulation results show that the proposed method has better transient responses, disturbance rejection, and other control performance for the turbofan engine within the large region.

Multivariable State-Feedback Controller Design for PV Inverter Connected to a Weak Grid

This paper presents a robust multi-input multi-output (MIMO) state-feedback control scheme for a photovoltaic (PV) inverter connected to a weak grid. For a weak grid, the point of common coupling (PCC) voltage is very sensitive to the power disturbances and it is dynamically coupled to the PLL dynamics. So far, most of the control methods do not take into accounts these couplings. Therefore, in this paper, the MIMO controller was designed taking into account the dynamics of the phase-locked loop (PLL) and coupling effects between PCC voltage and the active power to enhance the system’s robustness. As result, the robust performance of the PV inverter interfaced to a weak grid was yielded. In addition, the sensitivity of the system to PLL was eliminated, allowing the use of larger PLL bandwidth even in a very weak grid. Based on the eigenvalues analysis method, a comparative study between the proposed control method and the conventional vector control method was performed. The proposed method is verified with simulations in PLECS and real-time simulations in the RT Box. The results show that the proposed MIMO control method preserves the system stability robustness against any change of grid strength, generated power and PLL bandwidth.