Modified nonlinear predictive control of elastic manipulators

Two new types of control method have been developed based on model predictive control for stable-target tracking of a nonholonomic mobile robot. One method (Method 1) is a new nonlinear control method. This was developed based on model predictive control (predictive nonlinear control) to predict the next position of a mobile robot using the current velocities of the right and left wheels. This technique uses a tuning guideline in predictive nonlinear control. The other method (Method 2) is a combination of Method 1 and proportional control (predictive proportional nonlinear control). Method 2 involves a tuning guideline not only in a predictive nonlinear controller, but also in a proportional controller. In this technique, the selection of a tuning guideline in the proportional controller is enhanced, and thereby increases the control action in closed-loop responses. In Method 1, the nonlinear controller is derived from Liapunov stability theory, and is used to control the linear and angular velocities for locomotion control. Tuning parameters in the nonlinear controller (in Method 1) are selected to satisfy various design criteria, such as stability, performance, and robustness. Method 1 has certain limitations that result in a decrease of the performance criteria specified. Strong nonlinearities in the mobile robot system result in accumulated errors. To enhance performance further, we developed Method 2 as the solution for decreasing cumulative errors. Hence, the proportional controller is added to Method 1 in the closed-loop form in order to eliminate errors. The advantage of Method 2 is that it can cope with strong nonlinearities in the mobile vehicle system. The results of the performances of Method 1 and Method 2 are shown to demonstrate the effectiveness of both methods, and also the better performance of Method 2. The two new methods are effective in stable-target tracking, yielding an increase in performance and stability.

Nonlinear Inverse and Predictive End Point Trajectory Control of Flexible Macro-Micro Manipulators

This paper proposes the theoretical framework and the consequent application of the input-output Feedback Linearization (FL) control technique to Linear Induction Motors (LIM). LIM, additionally to Rotating Induction Motor (RIM), presents other strong non-linearities caused by the dynamic end effects, leading to a space-vector dynamic model with time-varying inductance and resistance terms and a braking force term. This paper, starting from a recently developed dynamic model of the LIM taking into consideration its end effects, defines a FL technique suited for LIMs, since it inherently considers its dynamic end effects. Additionally, it proposes a technique for the on-line estimation of the inductor resistance, based on Model Reference Adaptive System (MRAS) on-line estimator, exploited for adapting on-line the FL control action versus inductor resistance variations leading to undesirable steady-state tracking errors. The stability of the proposed MRAS on-line estimator has been proven theoretically, adopting the Popov’s criterion for hyperstability. The proposed approach has been validated experimentally on a suitably developed test set-up, under both no load and loaded conditions. It has been compared firstly with the simplest control structure, which is the scalar V/f control, secondly, under the same closed-loop bandwidths of the flux and speed systems, with the industrial standard in terms of high performance control technique: Field Oriented Control (FOC).

Feedback linearisation is perhaps the most important nonlinear control design strategy developed during the last few decades [5]. The main objective of the approach is to algebraically transform a nonlinear dynamic system into a linear dynamic system by using a static state feedback and a nonlinear coordinate transformation based on a differential geometric analysis of the system. By eliminating nonlinearities in the closed loop system, conventional linear control techniques can be applied. Our presentation of relative degree, normal forms, zero dynamics and feedback linearisation for nonlinear control affine systems given in Section 3.1 follows the notation that is used in the mainstream nonlinear control literature [5, 56]. The method of input-output feedback linearisation for nonlinear MIMO control affine systems, which is central in this book, is presented in Section 3.1.3. Other linearisation techniques, such as exact linearisation and Volterra linearisation, are reviewed in Section 3.2. Finally, two feedback linearisation techniques that are applicable to systems that are not control affine are briefly presented in Section 3.3.KeywordsRelative DegreeFeedback LinearisationCharacteristic MatrixZero DynamicDynamic Neural NetworkThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Based on the finite-time control technique, the position control problem of permanent magnet synchronous motor(PMSM) servo system is studied. Using backing-stepping method, a control scheme based on feedback linearization and finite-time control technique is proposed for position loop. Rigorous mathematical analysis is given for the close loop system performance in the presence of disturbances. The results show that, compared with the conventional control scheme based on PD and feedback linearization, this method not only makes the position tracking error of the closed loop system with a faster convergence rate, but also makes the boundary of steady-state error smaller by regulating the controller parameters, which means the closed loop system has stronger disturbance rejection property. The simulation results validate the efficiency of this method.

This paper deals with the nonlinear model predictive control of the superheated steam temperature in the power plant once-through boiler. Particularly the controller response on impulse of unmeasured disturbance in the form of flue gas heat is investigated. The two different nonlinear predictive controllers are described in the paper. The feedback of the first controller is closed by nonlinear open loop observer with correction for offset free reference tracking. The second controller works with the close loop state and unmeasured disturbance observer based on the nonlinear moving horizon algorithm. Responses of these two controllers and response of the original controller based on the adaptive PID are compared.

In this study, we propose a real-time nonlinear predictive control of a thermal process. The nonlinear dynamics of the process are mathematically modeled using a fractional Hammerstein structure. This estimated model is then employed as a prediction model in a nonlinear model predictive control scheme over a finite prediction horizon. The proposed algorithm generates the control sequence by optimizing a cost function with iterative nonlinear optimization methods, including the Nelder-Mead and gradient-based approaches. To evaluate its effectiveness, the nonlinear predictive control algorithm is implemented on an electric oven using the STM32F407VG micro-controller and compared in the tracking performances to a conventional proportional integral controller.

A nonlinear adaptive predictive control strategy using orthogonal wavelet network model is presented. Based on a set of orthogonal wavelet functions, wavelet neural network performs a nonlinear mapping from the network input space to the wavelons output space in hidden layer. Its weight coefficients can be simply estimated by a linear least-square estimation algorithm. The excellent statistic properties of the weight parameters of wavelet network also can be obtained. A single input single output (SISO) nonlinear predictive control strategy is implemented in the simulation of a Polypropylene process.

Dynamics of the aircraft configuration considered in this paper shows a unique characteristic that mere are no stable attractors in the entire high angle of attack flight envelope. As a result, once the aircraft has departed from die normal flight regime, no standard technique can be applied to recover me aircraft. In mis paper, using feedback linearisation technique, a nonlinear controller is designed at high angles of attack which is engaged after the aircraft departs from normal flight regime. This controller stabilises the aircraft into a stable spin. Then a set of synthetic pilot inputs are applied to cause an automatic transition from the spin equilibrium to low angles of attack where the second controller is connected. This controller is a normal gain scheduled controller designed to have a large domain of attraction at low angles of attack. It traps me aircraft into a low angle of attack level flight This entire concept of recovery has been verified using six degree of freedom nonlinear simulation. Feedback linearisation technique used to design a controller ensures internal stability only if the nonlinear plant has stable zero dynamics. Since zero dynamics depend upon the selection of outputs, a new method of choosing outputs is described to obtain a plant which has stable zero dynamics.

Bridging the gap between the linear and nonlinear predictive control: Adaptations for efficient building climate control

In integrated permanent magnet synchronous motors (IPMSMs) coupled with mechanical devices such as ball screws and reducers, complex nonlinear friction characteristics often arise, leading to asymmetrical distortions such as position “flat-top” and speed “ramp-up”. These phenomena significantly degrade the system’s positioning accuracy. To address this issue, this paper introduces a symmetry-inspired nonlinear predictive speed control approach based on the Stribeck piecewise linearized friction compensation and a generalized proportional integral (GPI) observer. The proposed method leverages the inherent symmetry in the Stribeck friction model to describe the nonlinear behavior, employing online piecewise linearization via the least squares method. A GPI observer was designed to estimate the lumped disturbance, including time-varying components in the speed dynamics, friction model deviations, and external loads. By incorporating these estimates, a nonlinear predictive controller was developed, employing a quadratic cost function to derive the optimal control law. The experimental results demonstrate that, compared to traditional integral NPC and PI controllers, the proposed method effectively restores system symmetry by eliminating the “flat-top” and “ramp-up” distortions while maintaining computational efficiency.

While safety is a critical criterion of the autonomous wheelchair and attracted much attention over the last few decades, the user comfort has not been considered as an important factor yet. Therefore, this article proposes a path following controller for an electric powered wheelchair (EPW) which aims to assure the comfort and safety of users during the navigation tasks. This controller is a combination of transverse feedback linearization (TFL) and model predictive control (MPC) techniques. The main contribution of this work is to consider the jerks and acceleration of EPW, directly linked to the user's relaxation, as constraints in solving an optimal control problem to design MPC controller. TFL allows to achieve path invariance properties, which is useful for path following task. The simulations are conducted in both circular path and arbitrary path in a typical office environment. Simulation results illustrate the perspective of the proposed approach where the desired path is well followed and the constraints on user's comfort are respected.

An approach to design using a monovariable generalized predictive control law, with multiple reference model (GPC/MRM) is proposed in the paper, to control rotor speed and rotor flux amplitude of an induction machine. The GPC algorithm is combined with the nonlinear input-output linearizing control properties; moreover a new formulation of the reference signals is introduced, which enables us to track flux and speed nominal profiles and to satisfy motor constraints. The global control law is also presented with a flux observer and the simulation results obtained in the case of nominal and mismatched parameters on the complete nonlinear model are discussed.

This study proposes a new semi-analytical design and implementation method for nonlinear partial differential equation (PDE) control of a flexible manipulator. The proposed scheme considers the effects of the boundary input force and gravity on the payload, which results in non-homogenous boundary conditions. This objective is achieved based on a model transformation scheme for homogenizing boundary conditions, obtaining semi-analytical solutions for the corresponding PDE model. Model transformation is assigned as a hybrid exponential–polynomial function whose coefficients are conveniently calculable without the need for any additional boundary condition measurements. This eliminates the need to use intensive numerical solvers—for example, methods based on finite element analysis—and allows the implementation of sophisticated PDE control schemes considering fully nonlinear PDE models with high computation speed. The presented controller is robust to parametric model uncertainty due to its adaptive design. The precision and efficiency of calculating distributed states using the proposed model transformation are demonstrated based on experimental data for the flexible manipulator with respect to the ground truth camera-based motion capture system. Model transformation is also numerically implemented for the proposed nonlinear endpoint control method based on the original PDE model. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This paper investigates the difficulty of obtaining data describing the flexible manipulator pose required for precise control and analysis and proposes a computationally efficient method to overcome this issue.

The question of end-point trajectory control of flexible macro-micro manipulator based on variable structure control (VSC) and predictive control techniques is considered. A VSC law is derived for the end point trajectory control of the rigid micro manipulator. For the end-point control of the flexible macro manipulator, a predictive control law is derived. The predictive control law is obtained by minimizing a quadratic function of the tip tracking error of the flexible link (macro), the elastic deflection, and the input torque of the macro manipulator. The combination of the VSC and the predictive controllers accomplishes precise end-effector trajectory tracking and elastic mode stabilization. These results are applied to a planar macro-micro manipulator system consisting of one flexible link and two micro rigid links. Simulation results are presented to show that in the closed-loop system time varying end point trajectory control and elastic mode stabilization are accomplished.