Reference Setpoint Research Articles

A Nonlinear Optimal Control Approach for Dual-Arm Robotic Manipulators

Dual-arm robotic manipulators are used in industry and for assisting humans since they enable dexterous handling of objects and more agile and secure execution of pick-and-place, grasping or assembling tasks. In this paper, a nonlinear optimal control approach is proposed for the dynamic model of a dual robotic arm. In the considered application, the dual-arm robotic system has to transfer an object under synchronized motion of its two end-effectors so as to achieve precise positioning and to compensate for contact forces. The dynamic model of this robotic system is formulated while it is proven that the state-space description of the robot’s dynamics is differentially flat. Next, to solve the associated nonlinear optimal control problem, the dynamic model of the dual-arm robot undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the dual-arm robot, a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution to the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The proposed nonlinear optimal control approach achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs.

Predictive heating load management and energy flexibility analysis in residential sector using an archetype gray-box modeling approach: Application to an experimental house in Québec.

This paper presents a methodology to develop archetype gray-box models and use them in an economic model-based predictive control algorithm to simulate optimal heating load management in response to a newly-introduced static time-of-use tariff for Québec's residential sector, rate Flex-D. The methodology is evaluated through a case study, wherein in situ measurements from a two-storey unoccupied research house of Hydro-Québec are used to develop an 11R6C network with a heuristic zoning-by-floor approach and compute the sequence of optimal electric heating input for the next control horizon. Properly-tuned economic model-based predictive control under rate Flex-D shows potential for an approximately 30% reduction in daily heating cost compared to the reference operation, with a minimal average deviation of indoor air temperature from the reference setpoint. Also, the analysis of the response's sensitivity to weather forecast uncertainties indicates that the most influential uncontrolled input directing the performance of economic model-based predictive control is the structure price signal, rendering the impact of uncertainty in the weather forecast negligible.

A nonlinear optimal control approach for 3-DOF four-cable driven parallel robots

In this article, a nonlinear optimal control approach is proposed for the dynamic model of 3-DOF four-cable driven parallel robots (CDPR). To solve the associated nonlinear optimal control problem, the dynamic model of the 3-DOF cable-driven parallel robot undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the 3-DOF cable-driven parallel robot a stabilizing optimal (H-infinity) feedback controller is designed. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The proposed nonlinear optimal control approach achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs and a minimum dispersion of energy.

Nonlinear optimal control for robotic exoskeletons with electropneumatic actuators

Nonlinear optimal control for robotic exoskeletons with electropneumatic actuators

Optimal operation of reverse osmosis desalination process with deep reinforcement learning methods

The reverse osmosis (RO) process is a well-established desalination technology, wherein energy-efficient techniques and advanced process control methods significantly reduce production costs. This study proposes an optimal real-time management method to minimize the total daily operation cost of an RO desalination plant, integrating a storage tank system to meet varying daily freshwater demand. Utilizing the dynamic model of the RO process, a cascade structure with two reinforcement learning (RL) agents, namely the deep deterministic policy gradient (DDPG) and deep Q-Network (DQN), is developed to optimize the operation of the RO plant. The DDPG agent, manipulating the high-pressure pump, controls the permeate flow rate to track a reference setpoint value. Simultaneously, the DQN agent selects the optimal setpoint value and communicates it to the DDPG controller to minimize the plant’s operation cost. Monitoring storage tanks, permeate flow rates, and water demand enables the DQN agent to determine the required amount of permeate water, optimizing water quality and energy consumption. Additionally, the DQN agent monitors the storage tank’s water level to prevent overflow or underflow of permeate water. Simulation results demonstrate the effectiveness and practicality of the designed RL agents.

Optimal model-based control for automated robotized abrasive blasting system

In robotic abrasive blasting operations, achieving the required surface roughness and cleanliness relies heavily on manually pre-set operational parameters. These parameters, such as stand-off distance, blasting angle, inlet air pressure, abrasive flow rate, and particle size, are set based on operator experience. However, given that optimal values for these parameters vary depending on specific blasting conditions and surface requirements, the pre-set values often fail to deliver both the desired surface quality and productivity. To address these challenges, we propose a solution employing a set of proxy models and a model predictive control system to achieve optimal operational outputs. For energy efficiency and productivity maximization, we utilize computational fluid dynamics with a multiphase flow solver to determine the optimal stand-off and offset distances, thus controlling the blasting nozzle effectively. Additionally, we build a data-driven model to obtain the optimal reference set point of air pressure at the sensor location based on the desired surface roughness. Moreover, we develop a dynamic process model to link the inlet air pressure and abrasive flow rate to the air pressure at the sensor location, which facilitates the development of a model-based control system. By applying this comprehensive approach, we evaluate and optimize the control and operational parameters to achieve the desired surface roughness and productivity targets. To validate the effectiveness of our newly developed control system and models, extensive tests are conducted both virtually (in silico) and on-site. The results confirm the stability and accuracy of the control system. In on-site reliability tests, the automated blasting system successfully delivers the desired surface roughness with a relative error of less than 5 % and a remarkable 30–50 % improvement in productivity. Overall, our innovative control system and models offer a reliable and efficient solution for robotic abrasive blasting, ensuring consistent surface quality and productivity enhancements.

Assessment of Linear Quadratic Regulator Based Optimal Stabilization of Weak-Grid-Following Inverter Interface

An optimal state- feedback based decentralized stabilizing control scheme for weak-grid connected inverter interfaces is proposed here. Linear Quadratic Regulator (LQR) based feedback control options viz. small-signal perturbations in the reference signals, and in the control gains are explored for the same. It is shown that, with full-state feedback of local control variables, the stability enhancement is not much effective with gain perturbations. Rather, the reference set-point change is shown to stabilize the inverter to weak-grid interconnection. Eliminating the need of communication assisted auxiliary inputs or the need for their estimation, the proposed approach is effective in achieving stability margin enhancement for wider range of X/R ratios and grid impedances. The cost of achieving stabilization using totally device-level information is the compromise made in set-point adjustment. However, this can be adopted for emergency weak-grid scenarios in a generic power system. The proposed control augmentation is analysed for different operating scenarios in which one or the other control loops are enabled, and corresponding modifications in the controller are discussed. The proposed claims are validated using small-signal models, simulation studies in MATLAB/Simulink as well as with a power-hardware-in-the-loop (PHIL) experimental setup.

Coordinated wind power plant and battery control for active power services

This article considers joint active power control of wind turbines and battery storage to follow a plant-level power reference signal. The joint control dynamically curtails the energy from a subset of the wind turbines and stores or withdraws energy from the battery to meet the power reference setpoint while accounting for wind plant aerodynamic interactions, such as wake losses. As a use case, we study the performance of the controller in maintaining a constant power output over hourly periods. A wind plant operating in this way would rely much less on other grid resources to meet its contractual agreements, thereby improving grid reliability, especially in grids with high penetration of wind and solar generation. We compare the operation of the wind plant under joint active power control to standard power-maximizing control with battery support. We present an analysis of the performance of the control system architecture. To study the impact of the battery size on performance, we simulate a 50-MW wind plant supported by batteries ranging from 8 to 64 MWh. We then evaluate the over and undergeneration penalties incurred by the plant during the simulation period.

A nonlinear optimal control approach for autonomous reentry space vehicles

Nonlinear control for autonomous reentry space vehicles has been a topic of intensive research during the last years in the area of aerospace science and technology. The associated dynamic model is obtained by expressing position variables and orientation angles of the space vehicle in different coordinate frames, namely an earth-fixed, an earth rotating and a body fixed frame. In this article, a nonlinear optimal control approach is proposed for the dynamic model of reentry space vehicles. It is proven that the longitudinal motion dynamic model of reentry space vehicles is differentially flat and a flatness-based controller is designed about it. Next, in the nonlinear optimal control approach, the dynamic model of the reentry space vehicle undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the reentry space vehicle a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution to the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The proposed nonlinear optimal control approach achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs and a minimum dispersion of energy.

A nonlinear optimal control approach for multi-DOF redundant robotic manipulators

A nonlinear optimal (H-infinity) control approach is proposed for the dynamic model of multi-DOF redundant robotic manipulators. Because of the complicated kinematics and dynamics and the high dimensionality of the state-space model of such robots, the related control problem is of elevated difficulty. In the present article, a three-link planar robotic manipulator it considered. The article’s approach relies first on approximate linearization of the state-space model of the redundant robotic manipulator, according to first-order Taylor series expansion and the computation of the related Jacobian matrices. For the approximately linearized model of the manipulator, a stabilizing H-infinity feedback controller is designed. To compute the controller’s gains an algebraic Riccati equation is solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. The proposed control method retains the advantages of typical optimal control, that is fast and accurate tracking of the reference setpoints under moderate variations of the control inputs.

Extending the Thermal Comfort Band in Residential Buildings: A Strategy towards a Less Energy-Intensive Society

Extending set-point temperatures in residential buildings has a significant impact on energy demand and thermal comfort. European governments have adopted this strategy to mitigate the energy crisis. Previous studies attempting to quantify energy savings by extending set-point temperatures were limited due to a lack of building stock characterisation, poor climate representation, and the absence of uniformity in the reference set-point temperature. In this study, a large-scale simulation was conducted, which included six building models covering 90% of southern Europe Köppen–Geiger climates, where 20 °C and 25 °C were the reference heating and cooling set-point temperatures, respectively. This also accounted for the thermal characteristics of the older building stock, built more than 15 years ago, and the new buildings built under the latest version of Directive 2010/31/EU. The results show that reducing the heating set-point temperature by 1 °C can lead to an average demand reduction of 20%, while raising the cooling set-point temperature by 1 °C can lead to a 25% cooling demand reduction. The oldest building stock shows a higher absolute savings potential. Adjusting thermostats by 1 °C in Spanish homes during the winter season could represent a saved natural gas volume of 1.8 million normal cubic meters, nearly 40% of the gas demand of households in 2022. These findings suggest that extending the set-point temperatures in residential buildings can be a promising strategy towards a more energy-efficient society without compromising the occupant’s thermal comfort.

A nonlinear optimal control approach for voltage source inverter-fed three-phase PMSMs

A nonlinear optimal control approach for voltage source inverter-fed three-phase PMSMs

Nonlinear optimal control for a 4-DOF SCARA robotic manipulator

AbstractSelective compliance articulated robot arms (SCARA) robotic manipulators find wide use in industry. A nonlinear optimal control approach is proposed for the dynamic model of the 4-degrees of freedom (DOF) SCARA robotic manipulator. The dynamic model of the SCARA robot undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the system, a stabilizing optimal (H-infinity) feedback controller is designed. To compute the controller’s feedback gains, an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The proposed control method is advantageous because: (i) unlike the popular computed torque method for robotic manipulators, it is characterized by optimality and is also applicable when the number of control inputs is not equal to the robot’s number of DOFs and (ii) it achieves fast and accurate tracking of reference setpoints under minimal energy consumption by the robot’s actuators. The nonlinear optimal controller for the 4-DOF SCARA robot is finally compared against a flatness-based controller implemented in successive loops.

Novel combinator surface concept for efficiency optimization of ship propulsion system

This paper describes a methodology to design and generate a novel optimal combinator surface suitable for mechanical propulsion systems on ships with controllable-pitch propellers (CPPs). The combinator surface is an extension and enhancement of conventional combinator curves, considering the effect of both the advance speed and the propeller thrust for the selection of optimal operation setpoints for propeller RPM and pitch. The generation of optimal combinator surface does not require the estimation of the ship resistance, wake fraction, and thrust deduction fraction, enabling automatic reference setpoint searching during the steady state as well as acceleration and deceleration. The optimization algorithm is created based on the maximization of the power and propulsion efficiency, taking the prime mover and propeller constraints into consideration. The proposed methodology is illustrated using a longliner as a case study ship. From thrust and ship speed analysis, the proposed combinator surface method benefits vessels working with frequently changing operations. The ship propulsion efficiency is improved greatly for ship acceleration. The comparison of the efficiency performance using the conventional combinator curve and the proposed combinator surface demonstrates that the new concept of combinator surface enables more efficient propulsion for ships operating under varying loading and sea state conditions.

Robust 2DoF PI tuning rules for integrating processes with dead time via frequency response model matching

The integrating characteristics are commonly found in composition control and level control of a distillation column in chemical processes. This paper presents a simple and intuitive robust tuning method of two-degree-of-freedom (2DoF) proportional-integral (PI) controller for integrating processes with dead time. The frequency response model matching approach is utilized with performance and robustness considerations for both regulatory and servo control issues. The regulatory control issue aims at matching the frequency response of the closed-loop system with that of the reference model for disturbance rejection, where the feedback controller parameters are calculated by solving a group of overdetermined algebraic equations subject to a robustness constraint evaluated by the maximum sensitivity. The target of the servo response is to follow a prescribed set-point reference trajectory, with the set-point weighting factor tuned to satisfy a defined tracking performance metric. A curve fitting procedure is utilized to generate analytical tuning rules in terms of the process model parameters and the desired robustness specification. It is shown that, apart from giving more exact achievement of the control system robustness, the tuning rules presented work well for a wider range of process dynamics than the existing methods. Illustrative examples are given to show the effectiveness of the proposed method.

Tilt-fractional order proportional integral derivative control for DC motor using particle swarm optimization

Introduction. Recently, the most desired goal in DC motor control is to achieve a good robustness and tracking dynamic of the set-point reference speed of the feedback control system. Problem. The used model should be as general as possible and consistently represent systems heterogeneous (which may contain electrical, mechanical, thermal, magnetic and so on). Goal. In this paper, the robust tilt-fractional order proportional integral derivative control is proposed. The objective is to optimize the controller parameters from solving the criterion integral time absolute error by particle swarm optimization. The control strategy is applied on DC motor to validate the efficiency of the proposed idea. Methods. The proposed control technique is applied on DC motor where its dynamic behavior is modeled by external disturbances and measurement noises. Novelty. The proposed control strategy, the synthesized robust tilt-fractional order proportional integral derivative speed controller is applied on the DC motor. Their performance and robustness are compared to those provided by a proportional integral derivative and fractional order proportional integral derivative controllers. Results. This comparison reveals superiority of the proposed robust tilt-fractional order proportional integral derivative speed controller over the remaining controllers in terms of robustness and tracking dynamic of the set-point reference speed with reduced control energy.

A sensorless, physiologic feedback control strategy to increase vascular pulsatility for rotary blood pumps

Continuous flow rotary blood pumps (RBP) operating clinically at constant rotational speeds cannot match cardiac demand during varying physical activities, are susceptible to suction, diminish vascular pulsatility, and have an increased risk of adverse events. A sensorless, physiologic feedback control strategy for RBP was developed to mitigate these limitations. The proposed algorithm used intrinsic pump speed to obtain differential pump speed (ΔRPM). The proposed gain-scheduled proportional-integral controller, switching of setpoints between a higher pump speed differential setpoint (ΔRPMHr) and a lower pump speed differential setpoint (ΔRPMLr), generated pulsatility and physiologic perfusion, while avoiding suction. The switching between ΔRPMHr and ΔRPMLr setpoints occurred when the measured ΔRPM reached the pump differential reference setpoint. In-silico tests were implemented to assess the proposed algorithm during rest, exercise, a rapid 3-fold pulmonary vascular resistance increase, rapid change from exercise to rest, and compared with maintaining a constant pump speed setpoint. The proposed control algorithm augmented aortic pressure pulsatility to over 35 mmHg during rest and around 30 mmHg during exercise. Significantly, ventricular suction was avoided, and adequate cardiac output was maintained under all simulated conditions. The performance of the sensorless algorithm using estimation was similar to the performance of sensor-based method. This study demonstrated that augmentation of vascular pulsatility was feasible while avoiding ventricular suction and providing physiological pump outflows. Augmentation of vascular pulsatility can minimize adverse events that have been associated with diminished pulsatility. Mock circulation and animal studies would be conducted to validate these results.

Nonlinear Optimal Control for the Nine-Phase Permanent Magnet Synchronous Motor

Abstract Multi-phase electric motors and in particular nine-phase permanent magnet synchronous motors (9-phase PMSMs) find use in electric actuation, traction and propulsion systems. They exhibit advantages comparing to three-phase motors because of achieving high power and torque rates under moderate variations of voltage and currents in their phases, while also exhibiting fault tolerance. In this article a novel nonlinear optimal control method is developed for the dynamic model of nine-phase PMSMs. First it is proven that the dynamic model of these motors is differentially flat. Next, to apply the proposed nonlinear optimal control, the state-space model of the nine-phase PMSM undergoes an approximate linearization process at each sampling instance. The linearisation procedure is based on first-order Taylor-series expansion and on the computation of the system’s Jacobian matrices. It takes place at each sampling interval around a temporary operating point which is defined by the present value of the system’s state vector and by the last sampled value of the control inputs vector. For the linearized model of the system an H-infinity feedback controller is designed. To compute the feedback gains of this controller an algebraic Riccati equation is repetitively solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. First it is demonstrated that the H-infinity tracking performance criterion is satisfied, which signifies robustness of the control scheme against model uncertainty and perturbations. Moreover, under mild assumptions it is also proven that the control loop is globally asymptotically stable. Additionally it is experimentally confirmed through simulation tests, that the nonlinear optimal control method achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs. Finally, to apply state estimation-based control without the need to measure the entire state vector of the nine-phase PMSM, the H-infinity Kalman Filter is used as a robust state estimator.

A Nonlinear Optimal Control Method for Attitude Stabilization of Micro-Satellites

Attitude control and stabilization of micro-satellites is a nontrivial problem due to the highly nonlinear and multivariable structure of the satellites’ state-space model. In this paper, a novel nonlinear optimal (H-infinity) control approach is developed for this control problem. The dynamic model of the satellite’s attitude dynamics undergoes first approximate linearization around a temporary operating point which is updated at each iteration of the control algorithm. The linearization process relies on first-order Taylor series expansion and on the computation of the Jacobian matrices of the state-space model of the satellite’s attitude dynamics. For the approximately linearized description of the satellite’s attitude a stabilizing H-infinity feedback controller is designed. To compute the controller’s feedback gains, an algebraic Riccati equation is solved at each time-step of the control method. The stability properties of the control scheme are proven through Lyapunov analysis. It is also demonstrated that the control method retains the advantages of linear optimal control that is fast and accurate tracking of the reference setpoints under moderate variations of the control inputs.

Nonlinear optimal control for the 4-DOF underactuated robotic tower crane

Tower cranes find wide use in construction works, in ports and in several loading and unloading procedures met in industry. A nonlinear optimal control approach is proposed for the dynamic model of the 4-DOF underactuated tower crane. The dynamic model of the robotic crane undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the system a stabilizing optimal (H-infinity) feedback controller is designed. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The proposed control approach is advantageous because: (i) unlike the popular computed torque method for robotic manipulators, the new control approach is characterized by optimality and is also applicable when the number of control inputs is not equal to the robot’s number of DOFs, (ii) it achieves fast and accurate tracking of reference setpoints under minimal energy consumption by the robot’s actuators, (iii) unlike the popular Nonlinear Model Predictive Control method, the article’s nonlinear optimal control scheme is of proven global stability and convergence to the optimum.