Development of a fractional order based MIMO controller for high dynamic engine testbeds

Testbed are used to tune and assess automotive engines. As more High Dynamic (HD) scenarios need to be simulated, the testbeds require Multi Input Multi Output (MIMO) and robust control systems. A cooperation involving a major testbed manufacturer and two university laboratories was therefore set up. This paper presents the Control-System Design (CSD) methodology developed from system identification to the design and assessment of the MIMO robust controller for a HD testbed coupled with a spark-ignition engine. It is specially highlighted how the entire process has been automated and simplified and how the fractional order based MIMO CRONE CSD has been parameterized to obtain the best performance. Experimental results show that the proposed fractional order based MIMO control system is able to improve robustness and decoupling.     

Crone control of a nonlinear hydraulic actuator

The CRONE control (fractional robust control) of a hydraulic actuator whose dynamic model is nonlinear is presented. An input–output linearization under diffeomorphism and feedback is first achieved for the nominal plant. The relevance of this linearization when the parameters of the plant vary is then analyzed using the Volterra input–output representation in the frequency domain. CRONE control based on complex fractional differentiation is finally applied to control the velocity of the input–output linearized model when parametric variations occur.     

A linear differential operator approach to flatness based tracking for linear and non-linear systems

This contribution presents a flatness based solution to the tracking for linear systems in differential operator representation. Since the differential operator representation is a flat system representation, tracking controllers can easily be designed using dynamic output feedback. Then, the differential operator approach for flatness based tracking of linear systems is extended to non-linear systems. The design of the resulting linear time varying dynamic output feedback controller is based on a linearization about the trajectory, which directly yields the differential operator representation. Different from the non-linear flatness based controller design the new approach uses linear methods, both in stabilizing the tracking and in computing the output feedback controller. The proposed design procedure assures exact tracking in the steady state when no disturbances are present. A simple example demonstrates the design of a dynamic output feedback controller for the tracking of a non-linear system.     

Differential flatness‐based ADRC scheme for underactuated fractional‐order systems

This article mainly studies the fractional‐order active disturbance rejection control (FOADRC) schemes for the underactuated commensurate fractional‐order systems (FOSs). The FOADRC framework for linear FOSs‐based fractional proportion integration differentiation is constructed by using the fractional‐order tracking differentiator and the fractional‐order extended state observer, and the necessary conditions for the system to have stable controllers are provided. The FOADRC scheme for underactuated FOSs based on differential flatness is proposed. For underactuated FOSs, a set of flat output expressions with a fixed format is given under the controllable condition of the system. Moreover, making the flat output as the equivalent of the system output is simple and easy to analyze and calculate. Subsequently, the FOADRC scheme is designed by using the flat output. Finally, the scheme proposed in this article is verified by a simulation example.     

Derivative and integral terminal sliding mode control for a class of MIMO nonlinear systems

This paper presents derivative and integral terminal sliding mode control (TSMC) for a class of MIMO nonlinear systems in a unified viewpoint. First, integral TSMC is developed for robust output tracking of uncertain relative-degree-one systems by introducing sign and fractional integral terminal sliding modes. Next, by combining derivative and integral terminal sliding modes in a recursive structure, two derivative-integral terminal sliding mode control (DI-TMSC) methods are proposed to achieve exact or approximate finite-time convergence for the output tracking of higher order nonlinear systems. Different from traditional TSMC, this paper accomplishes finite convergence time for more general high-order MIMO systems and avoids the singular problem in the controller design. Furthermore, the control system is forced to start on the terminal sliding hyperplane, so that the reaching time of the sliding modes is eliminated. In other words, the transient response is improved under more relaxed stability conditions. Finally, several numerical simulations and experiments show the expected control performance.     

非匹配不确定系统的显式反步变结构控制

研究非线性多输入多输出不确定系统在非匹配条件下的鲁棒输出跟踪问题.基于相对阶的假设,给出了多输入多输出不确定系统的标准型;进而结合反步设计方法和变结构控制方法,提出一种非匹配条件下非线性不确定系统鲁棒输出跟踪问题的显式反步变结构控制器设计方法.所给跟踪算法不仅只由不确定性的变化范围直接确定,而且有效地克服了现有反步设计算法因隐式递推关系和复杂偏导数计算给实时控制带来的困难.     

Operator-Based Robust Nonlinear Control for SISO and MIMO Nonlinear Systems With PI Hysteresis

In this paper, operator based robust nonlinear control for single-input single-output (SISO) and multi-input multi-output (MIMO) nonlinear uncertain systems preceded by generalized Prandtl-Ishlinskii (PI) hysteresis is considered respectively. In detail, by using operator based robust right coprime factorization approach, the control system design structures including feedforward and feedback controllers for both SISO and MIMO nonlinear uncertain systems are given, respectively. In which, the controller design includes the information of PI hysteresis and its inverse, and some sufficient conditions for the controllers in both SISO and MIMO systems should be satisfied are also derived respectively. Based on the proposed conditions, influence from hysteresis is rejected, the systems are robustly stable and output tracking performance can be realized. Finally, the effectiveness of the proposed method is confirmed by numerical simulations.      

CRONE control based anti-icing/deicing system for wind turbine blades

This paper presents an application of CRONE control, a robust control based on fractional order differentiation, to an anti-icing/deicing system for wind turbine blades. The deicing system uses an electrically conductive polymer paint applied on the blade at ice formation areas. The voltage applied to the paint leads to its heating. Based on a temperature measure provided by various sensors placed on the blade, a control system can thus be used to prevent the blade icing up during wind turbine operation or to deice the blade after a rest time. To design the control system, a thermal model of the blade with the paint was developed and its associated parameters were identified using tests in a climatic wind tunnel. A CRONE controller was then designed and its performance evaluated both on blade subparts in the climatic wind tunnel and on a floor-standing real blade.     

含时变不确定性线性系统的鲁棒跟踪控制

本文就含时变不确定性的线性系统,研究了鲁棒跟踪控制器的设计问题。文中利用Ｒｉｃ－ｃａｔｉ方程,给出了使系统输出鲁棒跟踪某一动态输入的线性控制律,对于匹配系统,跟踪误差可以任意小,从而得到实际跟踪;对于不满足匹配条件的系统,若另一些条件成立,则跟踪误差有界。     

Necessary and sufficient conditions for robust perfect tracking under variable structure control

The tracking control of linear MIMO systems with structured uncertainty is considered. A necessary and sufficient condition for robust asymptotic tracking employing variable structure techniques in the presence of multiplicative uncertainty is derived. The constructive proof of the theorem provides an explicit formula for controller synthesis. Copyright © 2002 John Wiley & Sons, Ltd.     

Robust Adaptive Tracking Control for Nonlinear Systems Based on Bounds of Fuzzy Approximation Parameters

A robust adaptive fuzzy control approach is developed for a class of multi-input-multi-output (MIMO) nonlinear systems with modeling uncertainties and external disturbances by using both the approximation property of the fuzzy logic systems and the backstepping technique. The MIMO systems are composed of interconnected subsystems in the strict-feedback form. The main characteristics of the developed approach are that the online computation burden is alleviated and the robustness to dynamic uncertainties and external disturbances is improved. It is proven that all the signals of the resulting closed-loop system are uniformly bounded and that the tracking errors converge to a small neighborhood around zero. Two simulation experiments are presented to demonstrate the feasibility of the approach developed in this paper.     

A robust MIMO terminal sliding mode control scheme for rigidrobotic manipulators

In this paper, a robust multi-input/multi-output (MIMO) terminal sliding mode control technique is developed for n-link rigid robotic manipulators. It is shown that an MIMO terminal switching plane variable vector is first defined, and the relationship between the terminal switching plane variable vector and system error dynamics is established. By using the MIMO terminal sliding mode technique and a few structural properties of rigid robotic manipulators, a robust controller can then be designed so that the output tracking error can converge to zero in a finite time, and strong robustness with respect to large uncertain dynamics can be guaranteed. It is also shown that the high gain of the terminal sliding mode controllers can be significantly reduced with respect to the one of the linear sliding mode controller where the sampling interval is nonzero     

Adaptive output feedback tracking control for a class of uncertain nonlinear systems using neural networks.

This correspondence addresses the problem of designing robust tracking control for a class of uncertain nonlinear MIMO second-order systems. An adaptive neural-network-based output feedback tracking controller is constructed such that all the states and signals involved are uniformly bounded and the tracking error is uniformly ultimately bounded. Only the output measurement is required for feedback. The implementation of the neural network basis functions depends only on the desired reference trajectory. Therefore, the intelligent adaptive output feedback controller developed here possesses the properties of computational simplicity and easy implementation. A simulation example of controlling mass-spring-damper mechanical systems is made to confirm the effectiveness and performance of the developed control scheme.     

A parametrization of all the unfalsified plant models for MIMOsystems

The results of the parametrization of all the unfalsified models for single-input/single-output systems are extended to multi-input/multi-output (MIMO) systems. In this parametrization, the assumed a priori plant and noise information are upper bounds of the H _∞-norm of the plant matrix-valued transfer function and the noise magnitude. The parametrization is on the basis of several series of plant time-domain identification experiment data. It is shown that for MIMO systems, all the unfalsified plant matrix-valued transfer functions can still be expressed by the linear fractional transformation of a fixed matrix-valued transfer function and an H_∞-norm bounded structure fixed, but uncertain matrix-valued transfer function. However, the high dimensions of the matrix-valued transfer functions involved in the parametrization hamper the direct application of these results to robust controller design. To overcome these difficulties, further efforts are needed     

Robust‐decentralized tracking control for a class of uncertain MIMO nonlinear systems with time‐varying delays

A new control design method based on signal compensation is proposed for a class of uncertain multi‐input multi‐output (MIMO) nonlinear systems in block‐triangular form with nonlinear uncertainties, unknown virtual control coefficients, strongly coupled interconnections, time‐varying delays, and external disturbances. By this method, the controller design is performed in a backstepping manner. At each step of backstepping procedure, a nominal virtual controller is first designed to get desired output tracking for the nominal disturbance‐free subsystem, and then a robust virtual compensator is designed to restrain the effect of the uncertainties, delays involved in the subsystem, and the couplings among the subsystems. The designed controller is linear and time‐invariant, so the explosion of complexity in the control law is avoid. It is proved that robust stability and robust practical tracking property of the closed‐loop system can be ensured, and the tracking errors can be made as small as desired. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive Control of MIMO Mechanical Systems with Unknown Actuator Nonlinearities Based on the Nussbaum Gain Approach

This paper investigates MIMO mechanical systems with unknown actuator nonlinearities. A novel Nussbaum analysis tool for MIMO systems is established such that unknown timevarying control coefficients are tackled. In contrast to existing literatures on continuous-times systems, the newly-developed Nussbaum tool focuses on extending the traditional Nussbaum result from one dimensional case to the multiple one. Specifically, not only the multiple unknown input coefficients are extended to the time-varying, but also the limitation of the prior knowledge of coefficients' upper and lower bounds is removed. Furthermore, an adaptive robust controller associated with the proposed tool is presented. The asymptotic tracking of MIMO mechanical systems is guaranteed with the help of the Lyapunov Theorem. Finally, a simulation example is provided to examine the validity of the proposed scheme.      

A robust sliding-mode output tracking control for a class of relative degree zero and non-minimum phase plants: A chemical process application

A well-known robust observer-based sliding-mode output tracking control developed for strictly proper, minimum phase systems is extended to the control of relative degree zero, MIMO non-minimum phase plants. By assuming that the class of uncertainty is limited to an appropriate sub-space of the actuator range-space, a sliding-mode tracking control for non-minimum phase systems is posed. By introducing some dynamics, in the form of a plant output filter, relative degree zero plants are proved to be robustly controllable. The design of the linear components of the tracking control and the observer gains is posed in an H ₂-framework. The control law is exemplified on the control of a highly non-linear, benzene producing, large scale chemical process.     

Robust Output Tracking for MIMO Nonlinear Time-Varying Mismatched Uncertain Systems Via Hybrid Control Strategy

This paper considers the problem of robust output tracking control for multi-input multi-output (MIMO) nonlinear systems in the presence of mismatched time-varying uncertainties. Using singular perturbation method and variable structure control technique, we derive a new hybrid controller for MIMO systems with unknown time-varying uncertainties and disturbances to track a desired trajectory. It is shown that the hybrid controller not only stabilizes the closed-loop systems, but also guarantees the tracking errors remain in an O() neighbourhood of the origin where is a small design parameter of the controller. Moreover, by selecting the parameter properly, the tracking errors can be made arbitrarily small.     

MIMO线性离散系统的最优鲁棒跟踪控制

将MIMO线性离散定常系统在指定信号输入下获取最优时域指标的最优跟踪控制器设计问题归纳为求解一个有限维线性规划问题, 并证明这种最优跟踪控制器也是鲁棒稳定控制器.