Many-Objective Optimal Design of Sliding Mode Controls

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Yousef Sardahi ◽  
Jian-Qiao Sun
Keyword(s):  
Optimal Design ◽  
Pareto Front ◽  
Sliding Mode ◽  
Design Method ◽  
Tracking Error ◽  
Control Design ◽  
Processing Algorithm ◽  
Order System ◽  
Post Processing ◽  
Control Effort

This paper presents a many-objective optimal (MOO) control design of an adaptive and robust sliding mode control (SMC). A second-order system is used as an example to demonstrate the design method. The robustness of the closed-loop system in terms of stability and disturbance rejection are explicitly considered in the optimal design, in addition to the typical time-domain performance specifications such as the rise time, tracking error, and control effort. The genetic algorithm is used to solve for the many-objective optimization problem (MOOP). The optimal solutions known as the Pareto set and the corresponding objective functions known as the Pareto front are presented. To assist the decision-maker to choose from the solution set, we present a post-processing algorithm that operates on the Pareto front. Numerical simulations show that the proposed many-objective optimal control design and the post-processing algorithm are promising.

Integrated optimal design of a high-speed planar parallel manipulator

2018 ◽  
Vol 233 (9) ◽  
pp. 2976-2990 ◽  
Author(s):  
Zhengsheng Chen ◽  
Minxiu Kong
Keyword(s):  
Optimal Design ◽  
Parallel Manipulator ◽  
High Speed ◽  
Design Method ◽  
Tracking Error ◽  
Dimensional Synthesis ◽  
Tracking Accuracy ◽  
Nsga Ii ◽  
Parameters Tuning ◽  
Planar Parallel Manipulator

To obtain excellent comprehensive performances of the planar parallel manipulator for the high-speed application, an integrated optimal design method, which integrated dimensional synthesis, motors/reducers selection, and control parameters tuning, is proposed, and the 3RRR parallel manipulator was taken as the example. The kinematic and dynamic performances of condition number, velocity index, acceleration capability, and low-order frequency are taken into accounts for the dimensional synthesis. Then, to match motors/reducers parameters and keep an economical cost, the constraint equations and the parameters library are built, and the cost is chosen as one of the optimization objectives. Also, to get high tracking accuracy, the dynamic forward plus proportional–derivative control scheme is introduced, and the tracking error is chosen as one of the optimization objectives. Hence, the optimization model including dimensional synthesis, motors/reducers selection and controller parameters tuning is established, which is solved by the genetic algorithm II (NSGA-II). The result shows that comprehensive performances can be effectively promoted through the proposed integrated optimal design, and the prototype was constructed according to the Pareto-optimal front.

Chattering Reduction of Sliding Mode Control by Adopting Nonlinear Saturation Function

2010 ◽  
Vol 143-144 ◽  
pp. 53-61 ◽  
Author(s):  
Ning Bo Cheng ◽  
Li Wen Guan ◽  
Li Ping Wang ◽  
Jian Han
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Tracking Error ◽  
Nonlinear Function ◽  
Order System ◽  
Nonlinear Saturation ◽  
Simple Method ◽  
Mode Control ◽  
Computation Efficiency ◽  
Saturation Function

This paper proposes a simple method dealing with chattering phenomenon of sliding mode control. Instead of using a linear function to smooth the discontinuous control when the system is within the boundary layer, the controller adopts a smooth nonlinear function which we call a nonlinear saturation function (nsat function). Compared with the conventional linear saturation function (sat function), the nsat function can be constructed arbitrarily and shall satisfy eight conditions. Seven of the conditions are used to get a better effect in reducing chattering and one is used to keep a fast response performance by adjusting one constant parameter . As the nsat function can be specified by , it can be calculated in advance; this makes the nsat function of high computation efficiency and makes it acceptable in real time control systems. One candidate nsat function is constructed by adopting a hyperbolic tangent function and it is adopted in the simulations running on a second order system. Simulation results show that the nsat function also results in a smaller tracking error.

Optimal Design of a Micro Series Elastic Actuator

2010 ◽  
Author(s):  
Ozan Tokatli ◽  
Volkan Patoglu
Keyword(s):  
Optimal Design ◽  
Force Control ◽  
Pareto Front ◽  
Position Control ◽  
Compliant Mechanism ◽  
Tracking Error ◽  
Movement Direction ◽  
Design Criteria ◽  
Coupling Element ◽  
Series Elastic

We propose using series elastic actuation (SEA) in micro mechanical devices to achieve precise control of the interaction forces. Using μSEA for force control removes the need for high-precision force sensors/actuators and allows for accurate force control through simple position control of the deflection of a compliant coupling element. Since the performance of a μSEA is highly dependent on the design of this compliant coupling element, we employ a design optimization framework to design this element. In particular, we propose a compliant, under-actuated half-pantograph mechanism as a feasible kinematic structure for this coupling element. Then, we consider multiple design objectives to optimize the performance of this compliant mechanism through dimensional synthesis, formulating an optimization problem to study the trade-offs between these design criteria. We optimize the directional manipulability of the mechanism, simultaneously with its task space stiffness, using a Pareto-front based framework. We select an optimal design by studying solutions on the Pareto-front curve and considering the linearity of the stiffness along the actuation direction as a secondary design criteria. The optimized mechanism possesses high manipulability and low stiffness along the movement direction of the actuator; hence, achieves a large stroke with high force resolution. At the same time, the mechanism has low manipulability and high stiffness along the direction perpendicular to the actuator motion, ensuring good disturbance rejection characteristics. We model the behavior of this compliant mechanism and utilize this model to synthesize a controller for μSEA to study its dynamic response. Simulated closed loop performance of the μSEA with optimized coupling element indicates that force references can be tracked without significant overshoot and with low tracking error (about 1.1%) even for periodic reference signals.

Iterative Learning Control for Hybrid Systems

2020 ◽  
Author(s):  
Kirti D. Mishra ◽  
K. Srinivasan
Keyword(s):  
Hybrid Systems ◽  
Iterative Learning Control ◽  
Design Method ◽  
Tracking Error ◽  
Control Design ◽  
Learning Control ◽  
Iterative Learning ◽  
Linear Matrix ◽  
Triangular Structure ◽  
Form Representation

Abstract Iterative learning control (ILC) has been growing in applicability, along with growth in theory for classes of linear and nonlinear systems, and this study extends the theory of ILC to hybrid systems. A lifted form representation of hybrid systems with input-output dependent switching rules is developed, and the proposed lifted form representation is modeled as a switched system with arbitrary/unconstrained switching rules in the trial domain for control design. The causality of hybrid systems in the time domain results in the (lower) triangular structure of switched systems in the trial domain, the triangular structure enabling systematic and efficient control design. A unique aspect of the control design method developed for ILC of hybrid systems in this study is that a solution to the required set of linear matrix inequalities (LMIs) is guaranteed to exist under mild assumptions, which is in contrast to many other studies proposing LMI based solutions in controls literature. The proposed method is validated numerically for a motion control application, and robust and monotonic convergence of the tracking error to zero is demonstrated.

scholarly journals MISSILE CONTROL DESIGN BASED ON THE LINEAR MULTIPLE SLIDING MODE RECURSIVE METHOD

2008 ◽  
Vol 49 (4) ◽  
pp. 573-587 ◽  
Author(s):  
Y. J. SHI ◽  
G. F. MA
Keyword(s):  
Critical State ◽  
Sliding Mode ◽  
Design Method ◽  
Control Design ◽  
Variable Structure ◽  
Structure Theory ◽  
Cruise Missile ◽  
Design Specification ◽  
High Attitude ◽  
Sliding Mode Variable Structure

AbstractTo ensure that the elevator of a cruise missile is operating within the design specification in high-attitude flight, we present a design method for the construction of a sliding mode recursive variable structure controller. In this design method, a target sliding mode surface is first designed without considering the engineering specification of the elevator. Secondly, by using this specification, the critical state is solved. Then, the transitional sliding mode surfaces are designed recursively by using the critical state of the previous sliding mode surface so that the state will move smoothly from one transitional sliding mode surface to the next until the target sliding mode surface. This design method is based on linear sliding mode variable structure theory. Thus, the controller obtained is simple in structure and practical. Furthermore, the elevator will operate within the engineering specification. The simulation results show the effectiveness of the proposed method.

Flight Attitude Sliding Mode Control Design Based on the Compensation of Extended State Observer

2014 ◽  
Vol 716-717 ◽  
pp. 1689-1693
Author(s):  
Hai Long Xing ◽  
Juan Li
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Design Method ◽  
Control Design ◽  
Control Object ◽  
State Observer ◽  
Extended State Observer ◽  
Sliding Mode Controller ◽  
Extended State ◽  
Mode Control

This paper proposes the sliding mode control design based on extended state observer control approch for the flight attitude system.The extended state observer (ESO) with new structure is used to estimate the total disturbance and to compensate the control object so that the flight attitude system can be simplified. Then a sliding mode controller is used to stabilize this simplified system. Finally, a numerical simulation shows the effectiveness of the proposed control design method.

scholarly journals Dynamic Feedback Backstepping Control for a Class of MIMO Nonaffine Block Nonlinear Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Hai-Yan Li ◽  
Yun-An Hu ◽  
Jian-Cun Ren ◽  
Min Zhu
Keyword(s):  
Nonlinear Systems ◽  
Feedback Linearization ◽  
Closed Loop ◽  
Sliding Mode ◽  
Design Method ◽  
Control Design ◽  
Backstepping Control ◽  
Dynamic Feedback ◽  
Closed Loop System ◽  
Linearization Techniques

For a class of MIMO nonaffine block nonlinear systems, a neural network- (NN-) based dynamic feedback backstepping control design method is proposed to solve the tracking problem. This problem is difficult to be dealt with in the control literature, mainly because the inverse controls of block nonaffine systems are not easy to resolve. To overcome this difficulty, dynamic feedback, backstepping design, sliding mode-like technique, NN, and feedback linearization techniques are incorporated to deal with this problem, in which the NNs are used to approximate and adaptively cancel the uncertainties. It is proved that the whole closed-loop system is stable in the sense of Lyapunov. Finally, simulations verify the effectiveness of the proposed scheme.

Reduced-Order Model-Based Feedback Control of Flow Over an Obstacle Using Center Manifold Methods

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Coşku Kasnakoğlu ◽  
R. Chris Camphouse ◽  
Andrea Serrani
Keyword(s):  
Boundary Control ◽  
Center Manifold ◽  
Controller Design ◽  
Tracking Error ◽  
Reduced Order Model ◽  
Order System ◽  
Linear Quadratic ◽  
Order Model ◽  
Control Effort ◽  
Reduced Order

In this paper, we consider a boundary control problem governed by the two-dimensional Burgers’ equation for a configuration describing convective flow over an obstacle. Flows over obstacles are important as they arise in many practical applications. Burgers’ equations are also significant as they represent a simpler form of the more general Navier–Stokes momentum equation describing fluid flow. The aim of the work is to develop a reduced-order boundary control-oriented model for the system with subsequent nonlinear control law design. The control objective is to drive the full order system to a desired 2D profile. Reduced-order modeling involves the application of an L2 optimization based actuation mode expansion technique for input separation, demonstrating how one can obtain a reduced-order Galerkin model in which the control inputs appear as explicit terms. Controller design is based on averaging and center manifold techniques and is validated with full order numerical simulation. Closed-loop results are compared to a standard linear quadratic regulator design based on a linearization of the reduced-order model. The averaging∕center manifold based controller design provides smoother response with less control effort and smaller tracking error.

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