Outer Control Research Articles

Development of Prototype Fractional Order Controller for a Grid-Tied Photovoltaic System

This paper presents design of a robust fractional order proportional-integral (FO-PI) prototype controller for a grid connected photovoltaic (PV) system. The robustness in face of parameter variation is handled by designing a suitable controller considering sensitivity function, gain margin and phase margin for both inner and outer control loops. As FO-PI controller is not yet available in physical form and due to complexity involved in grid-tied PV system, we propose an alternative way of hardware implementation of inner loop FO-PI controller by using fractor through RC ladder network. Firstly, an emulator circuit of the inner current loop comprising the FO-PI controller (including fractor and the proportional gain) along with the transfer function of inverter and filter is developed and the response is verified through a real-time simulator (OPAL-RT). Finally, the FO-PI part of the emulator circuit is interfaced with the PC target to form a hardware-in-loop (HIL) by employing OPAL-RT. The performance of the complete system is verified through OPAL-RT simulator. The result shows the improved robustness by the proposed control design method.

Control of a Semi-autonomous Powered Wheelchair

A model reference controller for a powered wheelchair is described. The chair is fitted with sensor systems to assist a disabled user with steering their chair. The controller can cope with varying circumstances and situations. Non-linear terms are compensated for using an adaptive and automatic scheme. Consistent and dependable veer-controll is considered and the system was able to deal with uncertainties, for example changing surfaces, different shifting weights of users, hills, bumps, slopes and differences in tires and wheels. The controller has a quasi-linear closed-loop behaviour and that means that extra outer control loops can be appended later, for example path-following algorithms. An assistive agent was also created so that sperate wheelchairs will be able to communicate with each other in the future.

Improvement of the Control of a Grid Connected Photovoltaic System Based on Synergetic and Sliding Mode Controllers Using a Reinforcement Learning Deep Deterministic Policy Gradient Agent

This article presents the control of a grid connected PV (GC-PV) array system, starting from a benchmark. The control structure used in this article was a cascade-type structure, in which PI or synergetic (SYN) controllers were used for the inner control loop of id and iq currents and PI or sliding mode control (SMC) controllers were used for the outer control loop of the udc voltage from the DC intermediate circuit. This paper presents the mathematical model of the PV array together with the main component blocks: simulated inputs for the PV array; the PV array itself; the MPPT algorithm; the DC-DC boost converter; the voltage and current measurements for the DC intermediate circuit; the load and connection to power grid; the DC-AC converter; and the power grid. It also presents the stages of building and training the reinforcement learning (RL) agent. To improve the performance of the control system for the GC-PV array system without using controllers with a more complicated mathematical description, the advantages provided by the RL agent on process controls could also be used. This technique does not require exact knowledge of the mathematical model of the controlled system or the type of uncertainties. The improvement in the control system performance for the GC-PV array system, both when using simple PI-type controllers or complex SMC- and SYN-type controllers, was achieved using an RL agent based on the Deep Deterministic Policy Gradient (DDPG). The variant of DDPG used in this study was the Twin-Delayed (TD3). The improvement in performance of the control system were obtained by using the correction command signals provided by the trained RL agent, which were added to the command signals ud, uq and idref. The parametric robustness of the proposed control system based on SMC and SYN controllers for the GC-PV array system was proven in the case of a variation of 30% caused by the three-phase load. Moreover, the results of the numerical simulations are shown comparatively and the validation of the synthesis of the proposed control system was obtained. This was achieved by comparing the proposed system with a software benchmark for the control of a GC-PV array system performed in MATLAB Simulink. The numerical simulations proved the superiority of the performance of control systems that use the RL-TD3 agent.

Modeling and Cascade Control of a Pneumatic Positioning System

Abstract A robust cascade control system based on active disturbance rejection controller (ADRC) is originally developed for accurate position control of a pneumatic servo system, which is usually characterized by nonlinearity, uncertainty, and disturbance. The proposed control system consists of inner and outer control loops. Particularly, a linear ADRC (LADRC) is utilized to adjust valve position for a linear spool valve dynamics in the inner loop. A nonlinear ADRC (NADRC) is designed to control the position of a nonlinear pneumatic actuator subsystem in the outer loop. LADRC and NADRC contain linear and nonlinear extended state observers (ESOs), respectively. The ESO can estimate both unknown nonlinear dynamics and external disturbances and thus make the ADRC robust against system uncertainties and disturbances. Simulation results successfully demonstrate the effectiveness and robustness of the proposed cascade control system. The stabilities of the inner and outer control loops were proved separately using a Lyapunov approach.

Positioning control of liquid crystal elastomer actuator based on double closed-loop system structure

This paper proposes a control strategy with a double closed-loop system structure to achieve the positioning control of the photo-responsive liquid crystal elastomer (LCE) actuator. This work helps developing photo-responsive soft robot applications that are totally different from conventional electro-driven ones. In the proposed strategy, the outer loop is a combination of a PID controller in parallel with a feed-forward controller, the PID controller ensures that the positioning control target can be reached, and the feed-forward controller is an inverse model of the temperature-deformation relationship of the LCE actuator developed recently, to calculate the target temperature of the LCE actuator. The inner loop is a PID controller, which ensures that the temperature of the LCE actuator converges to the target value calculated by the feed-forward controller. Parameters of the inner PID controller are tuned using a simulation-experiment combined method based on the Hammerstein–Wiener model, and parameters of the outer PID controller are tuned based on experiments. Experiments are performed to show the effectiveness of the proposed method, and comparisons are made with conventional single closed-loop control structure. Such a double closed-loop structure has faster response and higher accuracy, and it lays a basis for possible photo-responsive soft robot applications.

Assessing Age-Friendliness: Individualistic vs. Collectivistic Cultures

ABSTRACT A major task ahead for South Korea is to create age-friendly communities and environments that can support older residents’ health, well-being, and quality of life. To that end, international partnerships have emerged to share information, assess need, and develop response strategies. In this study, the transferability of a US-developed age-friendly community resident survey, based on the WHO framework, was tested in two South Korean cities by comparing results to the same survey conducted in a US city. Descriptive, relational, and predictive analyses revealed the survey items were a better fit for the US city than the South Korean cities. Limited response variances collected in the Korean cities challenged the comparison of data between the Korean sites. Thus, a cultural lens was used to explain response patterns that reflect their understanding of social norms including avoiding disagreement and conflict in order to maintain social equilibrium and five cultural dimensions found in Western and Eastern societies (Individualism vs. collectivism, universalism vs. particularism, low vs. high power distance, low vs. high context, and inner vs, outer control). Recommendations for future assessments in South Korea include shifting focus away from the individual to the individual’s social network and community to improve understanding of need.

Longitudinal Control of Autonomous Vehicles Consisting Power-Train With Non-Linear Characteristics

The autonomous vehicle studiesrecently have been accelerated to ensure more secure, efficient, and comfortable transportation. Non-linearity in the power-train makes longitudinal control of autonomous vehicles difficult at low speeds. Additionally, rapid acceleration and deceleration (due to the behavior of the surrounding vehicles) increase complexity in control of such systems. In this study, we designed a novel longitudinal controller including the reverse plant model of the vehicle to overcome these problems. The complete controller is designed using parameters known to OEMs (Original Equipment Manufacturer) with vehicle CAN bus signals. The longitudinal controller consists of two parts: The outer controller which determines the target speed according to lead vehicle’s speed and the inner controller which determines the accelerator pedal percentage and brake requests. The inner controller includes PI followed by the reverse plant model with a virtual load sensor. This model enables control of a vehicle with non-linear power-train. The designed controller performance was tested on a city bus with a diesel engine and automatic transmission. Vehicle test results proved, that the designed controller is capable of controlling an autonomous vehicle with nonlinear power-train dynamics with onboard computational capacity even at low speeds.

Anti‐saturation GPC speed control of induction motor drives

One of the most critical issues in the fast and large step change in the speed control of an induction motor is the excessive generated current command, and consequently, if the speed controller does not have output magnitude limiter, this might end up damaging the power electronics converter and the motor itself. This paper is devoted to overcoming the speed controller saturation phenomenon. Firstly, predictive controllers in polynomial form are designed for the speed control loop and for the two inner currents control loops. Then, the outer predictive speed controller is retuned by convex optimization of the Youla parameter considering temporal and frequency constraints, so that the resulting controller assures that the speed response to the reference remains in an imposed template with a minimal current command in transient periods and, in other hand, it keeps the closed loop features obtained by the initial predictive controller. Simulations results show the speed control performance of the proposed control system for various operating conditions of the motor.

A Novel Predictive Control Scheme for Interleaved Buck Converter in Low Power Applications

This paper presents a model predictive control (MPC) approach for Inter-leaved Buck Converter in low power applications. Traditional PI-based con-trol strategies have an arduous tuning process and can affect its performancewhen there are fluctuations in the operating point. Therefore, an MPC-basedcontrol strategy is proposed because of its simplicity, intuitiveness, easeof implementation, and inclusion of nonlinearities and constraints. Firstly,the model of Interleaved Buck Converter (IBC) is developed. Secondly, atwo-loop control strategy is developed with predictive inner current controland outer voltage control for DC link voltage regulation. In comparisonto traditional control strategies, the proposed one has a better dynamicresponse. Finally, simulation studies are done using MATLAB Simulink, and a prototype experimental setup is developed to validate the effectiveness ofthe proposed control strategy in the dSPACE1104 platform.

Learning-based hierarchical control of water reservoir systems

The optimal control of a water reservoir system represents a challenging problem, due to uncertain hydrologic inputs and the need to adapt to changing environment and varying control objectives. In this work, we propose a real-time learning-based control strategy based on a hierarchical predictive control architecture. Two control loops are implemented: the inner loop is aimed to make the overall dynamics similar to an assigned linear model through data-driven control design, then the outer economic model-predictive controller compensates for model mismatches, enforces suitable constraints, and boosts the tracking performance. The effectiveness of the proposed approach is illustrated on an accurate simulator of the Hoa Binh reservoir in Vietnam. Results show that the proposed approach outperforms stochastic dynamic programming.

Grey‐prediction‐based double model predictive control strategy for the speed and current control of permanent magnet synchronous motor

AbstractTo solve the problems of slow response speed of the permanent magnet synchronous motor (PMSM) system when the external disturbance occurs and the poor disturbance rejection performance, a double model predictive control (MPC) strategy for PMSM to control speed and current is proposed in this paper. Further, in order to improve the dynamic performance and disturbance rejection performance of PMSM control system, a grey prediction is introduced, and then a grey‐prediction‐based double MPC strategy is proposed. To be specific, firstly, the mathematical model of PMSM is established under the dq coordinate system, and the traditional control strategy (outer speed loop PI controller and inner current loop deadbeat prediction controller) is elaborated. Secondly, we propose the double MPC strategy where MPC controller is used in the outer speed loop and deadbeat prediction controller is used in the inner current loop. Finally, the grey‐prediction‐based double MPC strategy is proposed where MPC is combined with grey prediction to improve the dynamic performance in the inner current loop. By comparing the traditional control strategy with the double MPC and the grey‐prediction‐based double MPC strategy, the simulation results show that the double MPC and the grey‐prediction‐based double MPC system have no overshoot and the grey‐prediction‐based double MPC system has better steady‐state performance, faster dynamic response and stronger disturbance rejection performance, which proves the effectiveness of the proposed strategy.

Comprehensive Modeling, Analysis, and Comparison of State-Space and Admittance Models of PLL-Based Grid-Following Inverters Considering Different Outer Control Modes

The phase-locked loop (PLL)-based grid-following inverters have been widely used as the interface between renewable energy resources (e.g., wind and solar power) and the utility grid. In addition to the basic PLL and inner current control loop that are responsible for tracking the phase angle of the point of common coupling (PCC) voltage and regulating the current injection according to the estimated phase angle, respectively, these grid-following inverters are commonly also equipped with outer power and voltage control loops. Some examples are outer active power/dc-link voltage control loops and outer reactive power/PCC voltage control loops, which provide the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$dq$ </tex-math></inline-formula> -axis current references for the inner current control loop. However, the existing literature generally focuses on specific outer control modes within a specific small-signal modeling framework, e.g., state-space or admittance modeling framework. In addition, different research groups usually repeatedly derive these small-signal models without a systematic modeling and analysis procedure. Furthermore, the systematic and comprehensive comparative modal and admittance analysis of these outer control modes is still missing in the literature. To avoid reinventing the wheel, provide the small-signal stability analysis community with handy both state-space and admittance models, and investigate the effects of various outer control loops on the small-signal models, this article presents a comprehensive and systematic small-signal modeling, analysis, and comparison framework of the PLL-based grid-following inverters, where the state-space and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$dq$ </tex-math></inline-formula> -domain admittance models of eleven control modes are derived step by step in a completely followable style. All of these derived small-signal models are verified by the time-domain step responses and frequency-domain <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$dq$ </tex-math></inline-formula> -domain admittance measurement. The insights into the effects of these outer control modes on the poles and residues of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$dq$ </tex-math></inline-formula> -domain admittance model are also explored, which help to understand how these outer control modes contribute to the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$dq$ </tex-math></inline-formula> -domain admittance shaping.

Dual-Loop Optimal Control of a Robot Manipulator and Its Application in Warehouse Automation

The goal of this work is to develop the next generation of coordinated optimal planning and control schemes for real-world robotic applications, with cost-effective intelligent robots that can safely and robustly perform the tasks at hand. This article presents a dual-loop optimal hierarchical control scheme for robotic manipulators consisting of outer and inner loops. The outer kinematic control loop in the operational space provides a joint velocity reference signal to the inner one. The kinematic control is formulated as a closed-loop optimal control approach to trajectory generation where the desired target (possibly time-varying) is obtained by acting upon the feedback from the actual state of the robot. The kinematic control is obtained using a closed-form analytic solution of the Hamilton–Jacobi–Bellman (HJB) equation. The proposed methodology defines the task in terms of the integral cost function, which results in a global optimal solution. The inner dynamic control loop consists of a neural network (NN)-based adaptive critic (AC) optimal tracking control scheme. The online NN approximator-based dynamic controller learns the infinite-horizon cost function related to inner loop error dynamics in continuous time and calculates the corresponding optimal control input to minimize the cost function forward in time. The stability and the performance of the proposed control scheme are shown theoretically via the Lyapunov approach and also verified experimentally using a 7-DOF Barrett WAM robot manipulator. The warehousing applications of the proposed dual-loop control scheme have been demonstrated experimentally in an exact warehouse setting. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This article was motivated by our previous experiences in the Amazon Robotics Challenge (ARC) competitions as a participant. Although the major lessons from those events revealed many important issues toward warehouse automation both from robotic vision and grasping aspects, the application aspects of control engineering to solution for these real-world problems could significantly benefit the today’s highly automated society. The intention of this article is to address this situation by designing a cost-effective robot manipulator control scheme by optimizing robot manipulation trajectories in the outer loop along with the actuator input in the inner loop. Therefore, we propose a dual-loop optimal control scheme for robotic manipulations under a cost-optimal framework with guaranteed stability proof via the Lyapunov approach. This results in smoother trajectories with cost-effective control actuator inputs than the state-of-the-art methods. We believe that this work can be beneficial for academic and industrial research to design more advanced and optimized solutions in this domain.

Control of single-phase photovoltaic H6 inverter in grid-connected and stand-alone modes of operation

This paper proposes a control strategy for single-phase transformerless photovoltaic H6 inverter with capability of operation in both grid connected and stand-alone modes. This control strategy enables seamless transition between two modes without any reconfiguration of control structure and need of any external communication. A multi-loop control structure including an inner voltage and current control with PR controller and outer power control with droop controller is utilised to make the inverter operate in both modes. In grid-connected mode, the power control loop regulates reference voltage and frequency for voltage control loop, to adjust power flow of inverter to the main grid while in islanded mode, reference voltage and frequency are determined according to droop characteristic of inverter to supply local load demand. The simulation and experimental result are used to verify the performance of the proposed control.

Virtual Conductance Based Cascade Voltage Controller for VSCs in Islanded Operation Mode

Voltage source converters have become the main enabler for the integration of distributed energy resources in microgrids. In the case of islanded operation, these devices normally set the amplitude and frequency of the network voltage by means of a cascade controller composed of an outer voltage control loop and an inner current control loop. Several strategies to compute the gains of both control loops have been proposed in the literature in order to obtain a fast and decoupled response of the voltages at the point of common coupling. This paper proposes an alternative and simple methodology based on the introduction of a virtual conductance in the classic cascade control. This strategy allows to design each control loop independently, obtaining a closed-loop response of a first-order system. In this way, the gains of each control loop are easily derived from the parameters of the LC coupling filter and the desired closed-loop time constants. Furthermore, a state observer is included in the controller to estimate the inductor current of the LC filter in order to reduce the number of required measurements. A laboratory testbed is used to validate and compare the proposed controller. The experimental results demonstrate the effectiveness of the proposal both in steady-state and transient regimes.

Sistem Pengatur Tegangan Otomatis : Analisa Peralihan Dengan Pengendali Tunggal Dan Kaskade

This journal describes the design and analysis of the response of a single controller and cascade direct current type of Automatic Voltage Regulator (AVR) system. The direct current AVR system is represented form of a transfer function. For single and cascade controllers, it is designed using a parallel architecture using MATLAB software with predetermined design criteria. The types of controllers used consist of Proportional Differential (PD), Proportional Integral (PI), Proportional Integral Differential (PID), Proportional Differential with First Order Filters in the Differential Section (PDF) and Proportional Integral Differentials with First Order Filters in the Differential Section(PIDF). For the transition analysis, the observed parameters consist of rise time, peak time, steady state time, maximum pass value and peak value. The results of the analysis show that the controllers that meet the design criteria are Proportional Differential (PD) controllers and Proportional Differential controllers with First Order Filters in Differential Sections (PDF) for single controllers and cascade controllers. For a single controller, the value of the Proportional constant (Kp) is 0.6280 and the value of the Differential constant (KD) is 0.1710 for the Proportional Differential (PD) controller. Proportional constant value (Kp) is 0.6130, Differential constant value (KD) is 0.1710 and filter constant value (Tf) is 0.0009 for Proportional Differential controller with First Order Filter in Differential Section (PDF). Cascade controllers and Proportional Differential (PD) controllers, the Proportional constant (Kp) is 1.7300 and the Differential constant (KD) is 0.0242 for the inner circle (C2). Outer ring controller (C1), the proportional constant (Kp) is 179,000 and the Differential constant (KD) is 2.4600. Cascade controllers and Proportional Differential controller types with First Order Filters in the Differential Section (PDF), the Proportional constant (Kp) value is 1.5900, the Differential constant (KD) value is 0.0246, the filter constant value (Tf) is 0.0018 for the inner circumference (C2 ). For the outer ring controller (C1), the Proportional constant (Kp) value is 134,0000, the Differential constant (KD) value is 2.2900 and the filter constant value (Tf) is 0.00008.

Task performance-based adaptive velocity assist-as-needed control for an upper limb exoskeleton

In this paper, a task performance-based adaptive velocity assist-as-needed (TPAVAAN) controller is developed for an upper limb exoskeleton to stimulate subject’s participation in the rehabilitation process. This controller includes an inner position and velocity based double impedance control (PVDIC) loop to calculate the assistive force, and an outer barrier Lyapunov function-based time-delay estimation controller with neural network compensation (NN-BLFTDEC) to drive the exoskeleton to provide the required assistive force. In the PVDIC loop, the assistive force is determined by a position based impedance controller to encourage subject in following the desired trajectory, and a velocity based impedance controller to assist the subject to perform the task at the desired velocity. A task performance function that considers position tracking error and assistive force is established to assess the subject’s motor capability and adjust the desired velocity. For the inner loop, the NN-BLFTDEC is designed based on a barrier Lyapunov function (BLF) to constrain the tracking error. A time-delay estimation (TDE) method and radial basis function neural network (RBFNN) are applied to estimate uncertain exoskeleton dynamics. Co-simulation studies are performed in SolidWorks and Matlab/Simulink. The mean tracking errors of the subject are 0.013m and 0.039m with and without the developed controller, respectively. Besides, with the enhancement of subject’s motor capability, the value of the performance function decreases from 7.94 to 1.77, while the desired velocity increases from 0.025m/s to 0.118m/s. The proposed TPAVAAN controller has potential to improve subjects’ task performance and modulate the assistance level adaptively.

Comparison of Two Control Strategies for VSC-MTDC with Wind Farm

: Two VSC-MTDC control strategies with different combinations of controllers are proposed to eliminate transient fluctuations in the DC voltage stability, resulting from a power imbalance in a VSC-MTDC connected to wind farms. First, an analysis is performed of a topological model of a VSC converter station and a VSC-MTDC, as well as of a mathematical model of a wind turbine. Then, the principles and characteristics of DC voltage slope control, constant active power control, and inner loop current control used in the VSC-MTDC are introduced. Finally, the PSCAD/EMTDC platform is used to establish an electromagnetic transient model of a wind farm connected to a parallel three-terminal VSC-HVDC. An analysis is performed for three cases of single- phase grounding faults on the rectifier and inverter sides of a converter station and of the withdrawal of the converter station on the rectifier side. Next, the fault response characteristics of VSCMTDC are compared and analyzed. The simulation results verify the effectiveness of the two control strategies, both of which enable the system to maintain DC voltage stability and active power balance in the event of a fault. Background: The use of a VSC-MTDC to connect wind power to the grid has attracted considerable attention in recent years. A suitable VSC-MTDC control method can enable the stable operation of a power grid. Objective: The study aims to eliminate transient fluctuations in the DC voltage stability resulting from a power imbalance in a VSC-MTDC connected to a wind farm. Methods: First, the topological structure and a model of a three-terminal VSC-HVDC system connected to wind farms are studied. Second, an analysis is performed of the outer loop DC voltage slope control, constant active power control and inner loop current control of the converter station of a VSC-MTDC. Two different control strategies are proposed for the parallel three-terminal VSCHVDC system: the first is DC voltage slope control for the rectifier station and constant active power control for the inverter station, and the second is DC voltage slope control for the inverter station and constant active power for the rectifier station. Finally, a parallel three-terminal VSC-HVDC model is built based on the PSCAD/EMTDC platform and used to verify the accuracy and effectiveness of the proposed control strategy. Results: The results of simulation analysis of the faults on the rectifier and inverter sides of the system show that both strategies can restore the system to the stable operation. The effectiveness of the proposed control strategy is thus verified. Conclusion: The control strategy proposed in this paper provides a technical reference for designing a VSC-MTDC system for wind farms.

Model-Based Control System Design of Brushless Doubly Fed Reluctance Machines Using an Unscented Kalman Filter

The Brushless Doubly Fed Reluctance Machine (BDFRM) is an emerging alternative for variable speed drive systems, providing a significant downsizing of the power electronics converter. This paper proposes a new view on the machine equations, allowing the reuse of the standard control system design for conventional synchronous and asynchronous machines: a cascade control system with an inner current control- and outer speed control loop. The assumptions and simplifications made on the machine model allow for a simple, model-based approach to set the controller gains in a brushless doubly fed machine drive system. The cascade control scheme is combined with an Unscented Kalman Filter as a state observer, capable of estimating the load torque and losses. The performance of the proposed control system design is checked in simulation and tested in real-time on a low power BDFRM prototype.

Orthogonal Time Sequency Multiplexing Modulation: Analysis and Low-Complexity Receiver Design

This paper proposes orthogonal time sequency multiplexing (OTSM), a novel single carrier modulation scheme that places information symbols in the delay-sequency domain followed by a cascade of time-division multiplexing (TDM) and Walsh-Hadamard sequence multiplexing. Thanks to the Walsh Hadamard transform (WHT), the modulation and demodulation do not require complex domain multiplications. For the proposed OTSM, we first derive the input-output relation in the delay-sequency domain and present a low complexity detection method taking advantage of zero-padding. We demonstrate via simulations that OTSM offers high performance gains over orthogonal frequency division multiplexing (OFDM) and similar performance to orthogonal time frequency space (OTFS), but at lower complexity owing to WHT. Then we propose a low complexity time-domain channel estimation method. Finally, we show how to include an outer error control code and a turbo decoder to improve error performance of the coded system.