Modelling And Predictive Control Of Inverted Pendulum

Multi-vector model predictive control of permanent magnet synchronous motor can effectively overcome the shortcomings of conventional single-vector model predictive control such as large motor current ripples and limited control accuracy, but its control performance is more susceptible to the influence of motor parameter perturbation. To improve the robustness of the multi-vector predictive control algorithm under the motor parameter perturbation, a novel nonparametric three-vector model predictive current control method for permanent magnet synchronous motors is proposed in this paper. Through constructing an ultra-local predictive current model based on the input and output signals of the permanent magnet synchronous motor, the influence of motor parameter perturbation on current prediction is avoided, and a disturbance observer is designed to estimate the non-modeled and perturbed parts of the ultra-local model. In addition, the direct calculation method of vector duty cycles based on current error is introduced to suppress the influence of motor parameter uncertainty on the duty cycle calculation link, which further improves the system robustness. Finally, simulations and experiments of the proposed method are demonstrated to compare with the conventional parametric three-vector model predictive current control, and the results show that the proposed control strategy can effectively suppress the disturbances caused by the motor parameters and ensure the steady-state performance during motor operation.

This paper presents a waypoint tracking method using model predictive control (MPC) for an autonomous driving vehicle. To solve vehicle speed variation in the MPC design, we propose a scheme using horizon-wise constant (HWC) MPC. The HWC MPC assumes that a prediction model uses a fixed parameter prediction model within a prediction horizon to resolve a parameter variation problem. To evaluate the performance of the proposed method, we performed three comparative studies with one speed variation MPC and two constant speed MPCs on a highway curve road. We verify the utility of the proposed MPC using HWC modeling and MPC using fixed velocity modeling. We have also confirmed that the proposed HWC MPC outperforms MPC at with fixed speed. The proposed controller is expected to be a solution to various parameter situations in waypoint tracking for the autonomous driving vehicle.

In this paper, constrained model predictive control (MPC) designs for a class of structured uncertain time-delay systems have been developed, where state delays as well as a random input delay have been taken into account. By replacing the control strategy with a freer one, an improved MPC design with larger initial feasible region has been developed. Furthermore, by analyzing the obtained algorithm, some useful properties of the solutions to the MPC optimization problem have been established. With these properties, a variant of the obtained algorithm with dramatically reduced number of online optimizing variables and hence the online computational burden has also been developed. However, the control performance degrades slightly. The two algorithms haven been proved to stabilize the closed loop system in the mean square sense and to guarantee the satisfaction of constraints. Finally a numeric example is given to illustrate the proposed results.

This paper proposes an improved constrained networked model predictive tracking control design for the chamber pressure of a coke furnace under uncertainty and packet losses. Unlike conventional constrained model predictive control (MPC) strategies that have a limitation in the consideration of both set-point tracking and the dynamic process responses, the system state variables and output tracking errors are combined and thus can be regulated simultaneously in the new MPC scheme. Based on such advantages, there are more degrees of freedom for the subsequent controller design and improved system performance can then be obtained. Case studies on the regulation of chamber pressure of a coke furnace under process uncertainties and packet losses are investigated to verify the proposed approach in comparison with typical traditional constrained MPC schemes.

In this paper, a model predictive control (MPC) design method is proposed for Hammerstein systems with multivariable nonlinearities. Iterative inversion is introduced such that classical linear MPC design can be used. The condition for which the numerical inversion is guaranteed to converge is derived. From this condition, the input space at which the nonlinear function is invertible can be obtained, which poses extra input constraints for MPC design. The overall constraints are transformed and approximated by a set of linear constraints by means of convex hull construction. Illustrative examples are presented to demonstrate the effectiveness of the proposed control method.

Flexible operation of coal-fired power plants is becoming increasingly necessary for successful integration of large-scale renewable power generation into the power grid. The maximum ramp rate and the number of load cycles are generally limited by the thermal stress experienced by the boiler pressure parts, turbine metallurgy and creep and fatigue of critical thick-walled components Main steam temperature is a critical operating parameter that must be controlled within acceptable limits for safe operation. Main steam temperature deviation beyond acceptable limit has impact on boiler pressure parts and turbine material of construction due to creep and fatigue effect. Base load operating units do not require steep ramp rate and hence recommended ramping rates are kept low within the safe operating zone in comparison to the flexible operation of the units with wide range load change width. Thermal stresses are caused by the temperature changes inside the thick-walled components and turbine steam admission parameters. Hence, the quality of main steam temperature control plays a vital role in flexible operation of the coal fired units. Conventional cascaded PID temperature control loop architecture performs well at steady state condition within a limited variation of load change at low ramp rate but it acts slowly and performs poorly at transient operating conditions of flexible operation of the boiler turbine with wide range load variation and load cycle with high ramp rate and remains far from rated conditions. In this paper, a Multi-Input Multi-Output (MIMO) Non-linear Model Predictive Control (MPC) design for regulation of the main steam temperature of a Once-Through supercritical Boiler is proposed. The controller is based on a non-linear dynamic model which incorporates dynamics of the variables of interest. It has the capability to operate effectively across a wide load range while maintaining main steam temperature within acceptable limits. A notable advancement in this design of MPC is the incorporation of coal flow demand and feedwater flow demand as additional control inputs alongside primary and secondary spray flows. In simulation test cases, the MPC controller demonstrates satisfactory performance and computational efficiency.

Modeling, estimation, and control in large-scale urban road networks with remaining travel distance dynamics

The need for cost-effective fuel economy improvements has driven the introduction of automatic transmissions with an increasing number of gear ratios. Incorporation of interlocking dog clutches in these transmissions decreases package space and increases efficiency, as compared to conventional dry or wet clutches. Unlike friction based clutches, interlocking dog clutches require very precise rotational speed matching prior to engagement. Precise engine speed control is therefore critical to maintaining high shift quality. This research focuses on controlling the engine speed during a gearshift period by manipulating throttle position and combustion phasing. Model predictive control (MPC) is advantageous in this application since the speed profile of a future prediction horizon is known with relatively high confidence. The MPC can find the optimal control actions to achieve the designated speed target without invoking unnecessary actuator manipulation and violating hardware and combustion constraints. This research utilizes linear parameter varying (LPV) MPC to control the engine speed during the gearshift period. Combustion stability constraints are considered with a control oriented covariance of indicated mean effective pressure model (COV of IMEP). The proposed MPC engine speed controller is validated with a high-fidelity 0-dimensional engine model with crank angle resolution. Four case studies, based on simulation, investigate the impact of different MPC design parameters. They also demonstrate that the proposed MPC engine controller successfully achieves the speed reference tracking objective while considering combustion variation constraints.

Model predictive control (MPC) as a nonlinear control method, is being studied for a wide variety of power electronics applications targeting various power ranges. The fast dynamic response, robustness under different load conditions, multi-objective control, and simplicity of implementation are the main features of MPC. However, the implementation of finite control set MPC (FCS-MPC) or direct MPC in its basic form for multilevel converters (MLCs) demonstrates the inability to generate the staircase multilevel output voltage waveform in a voltage sourced inverter (VSI) application. Adding a reference evaluation block to the basic FCS-MPC method can significantly improve its multilevel voltage generation capability. In this paper, an enhanced model predictive nearest level control (EMP-NLC) is proposed and implemented on a 5-Level flying capacitor multilevel converter (FCMC). The proposed method is simulated under different load conditions, while a comparison against existing MPC techniques is also presented. Experimental results verified the efficacy of the proposed controller.

Model predictive control (MPC) presents important advantages in the control of the power converter and drives such as, fast dynamic response and capability to include nonlinear constrains. These have positioned MPC as a powerful and realistic control strategy, however, it also has disadvantages such as variable switching frequency and parameter sensitivity. This paper applied a modulated model predictive speed control that guarantees a fix switching frequency and, thanks to disturbance compensation, robustness to parameters variation. The strategy is validated and compared to finite set model predictive speed control through simulation results.

A cart inverted pendulum system is one of the most common case to be considered for testing many control algorithms, since it has some challenging problems associated with non linearity, complexity and underactuated system model. In fact, non-linearity behaviour of the inverted pendulum can be observed easily. Different pendulum angle response can be obtained by giving the same velocity in the cart. The cart inverted pendulum can be understood as an under actuated system since the system has a lower number of actuator than the degrees of freedom. One of the most convenient method to model the inverted pendulum system is to use Lagrange's equation. However, at present, many presented inverted pendulum models have been derived using simplified physical model. This simplified model may lead to problems for the implementation of the control algorithm in a real physical inverted pendulum system. In this paper, an inverted pendulum system model is presented, where a mechanical transmission system and a motor models have been included in the derivation of the inverted pendulum model. Hence, the problems for the control implementation in a real system can be minimized. The mathematical model of the inverted pendulum was derived using Lagrange's equation. The determination of the pole zero of the system is discussed. A simple method of pole placement is proposed to stabilise the pendulum at the desired position of the cart. Matlab simulation results show the effectiveness of the proposed method. And yet, this intuitive approach can lead to better understanding of the control behaviours.

This paper presents a movement control methodology with obstacle avoidance control for personal robots that can work alongside humans. The methodology attempts to secure safety for users and stability of robots. These safety and stability are very important parameters in designing personal robot, and the personal robot controller must consider these parameters. The proposed approach uses model predictive control (MPC) that is a suitable control technique to achieve safety and stability whenever the robot avoids obstacles. Furthermore, the personal robot in this study interacts with people. In this study, we adequately select a two-wheel inverted pendulum (IP) type robot. The proposed controller can continue to secure safety and stability by imposing additional constraints on the robot coping with obstacles. To achieve this function, the proposed controller has the functions to control multi variables such as distance, velocity, turn-angle, tilt-angle and so on, in same time under some constraints on controlled objects. The proposed controller has time-varying constraints in relation to velocity for ensuring safety on obstacle avoidance motion by only turn­angle control. In addition, it has also time-invariant constraints on the controller input and body tilt angle for stability. Finally, the simulation validation results from a movement control with obstacle avoidance for an IP robot.

Fifty-seven per cent of all water supply systems in the Netherlands are controlled by model predictive flow control; the other 43% are controlled by conventional level-based flow control. The differences between conventional level-based flow control and model predictive control were investigated in experiments at five full-scale water supply systems in the first half of 2011. Quality parameters of the drinking water and energy consumption of the treatment and distribution processes were measured and analysed. The experiments showed that the turbidity values are 12–28% lower, and particle volume values 12–42% lower for the systems which are controlled by model predictive flow control. The overall energy consumption of water supply systems controlled by predictive flow control is 1.0–5.3% lower than conventional level-based flow controlled systems, and the overall energy costs are 1.7–7.4% lower.

The development of the Light Detection and Ranging (LIDAR) technology has enabled wider options for wind turbine control, in particular regarding disturbance rejection. The LIDAR measurements provide a spatial, preview wind information, based on which the controller has a better chance to cope with the wind disturbance before it affects the turbine operation. In this paper, a model predictive controller for above-rated wind turbine control was developed with the use of pseudo-LIDAR wind measurements data. A predictive control algorithm was developed based on a linearised wind turbine model, in which the disturbance from the incoming wind was computed by the LIDAR simulator. The optimal control action was applied to the nonlinear turbine model. The developed controller was compared with the baseline control and a previously developed LIDAR-assisted control combining a feedback-and-feedforward design. Our simulation studies on a 5 MW nonlinear wind turbine model, under different wind conditions, demonstrated that the developed LIDAR-based predictive control achieved improved performance in the presence of small variations in the out-of-plane rotor torque and fore-aft tower acceleration, as well as a smoother generator speed regulation and satisfied pitch activity control constraints.

Linear switched reluctance motor (LSRM) has the advantages of simple structure, strong robustness, high efficiency, low cost, and low maintenance. They are used in many fields. This paper mainly studies the position tracking control of linear switched reluctance motor and its model predictive controller design. First, the physical system of the linear switched reluctance motor is analyzed and a discrete equation of its state space model is constructed. In order to better eliminate the static error of the motor during position tracking, the increment form of the state equation of the linear switched reluctance motor is further given. By constructing the prediction equation of the motor and predicting the system output in a given time domain. The problem of solving the optimal control sequence online at each sampling time is further transformed into a standard quadratic programming problem. So the optimal control sequence with state constraints and control quantity constraints can be further obtained. To further optimize the design of the model predictive controller, the effects are compared among different prediction horizon, control horizon, weighting factors, and sampling time on the control performance of the model predictive controller to achieve the optimal control effect. Finally, simulation results prove that the model predictive controller has a good control effect on the position tracking of the linear switched reluctance motor.