Discrete‐Time Sliding Mode Control with Outputs of Relative Degree More than One

This work deals with sliding mode control of discrete‐time systems where the outputs are defined or chosen to be of relative degrees more than one. The analysis brings forward important advancements in the direction of discrete‐time sliding mode control, such as improved robustness and performance of the system. It is proved that the ultimate band about the sliding surface could be greatly reduced by the choice of higher relative degree outputs, thus increasing the robustness of the system. Moreover, finite‐time stability in absence of uncertainties is proved for such a choice of higher relative degree output. In presence of uncertainties, the system states become finite time ultimately bounded in nature. The work presents in some detail the case with relative degree two outputs, deducing switching and non‐switching reaching laws for the same, while for arbitrary relative degree outputs, it shows a general formalisation of a control structure specific for a certain type of linear systems

Discrete-time output feedback sliding-mode control design for uncertain systems using linear matrix inequalities

An output feedback-based sliding-mode control design methodology for discrete-time systems is considered in this article. In previous work, it has been shown that by identifying a minimal set of current and past outputs, an augmented system can be obtained which permits the design of a sliding surface based upon output information only, if the invariant zeros of this augmented system are stable. In this work, a procedure for realising discrete-time controllers via a particular set of extended outputs is presented for non-square systems with uncertainties. This method is applicable when unstable invariant zeros are present in the original system. The conditions for existence of a sliding manifold guaranteeing a stable sliding motion are given. A procedure to obtain a Lyapunov matrix, which simultaneously satisfies both a Riccati inequality and a structural constraint, is used to formulate the corresponding control to solve the reachability problem. A numerical method using linear matrix inequalities is suggested to obtain the Lyapunov matrix. Finally, the design approach given in this article is applied to an aircraft problem and the use of the method as a reconfigurable control strategy in the presence of sensor failure is demonstrated

Predictive Second Order Sliding Control of Constrained Linear Systems with Application to Automotive Control Systems

This paper presents a new predictive second order sliding controller (PSSC) formulation for setpoint tracking of constrained linear systems. The PSSC scheme is developed by combining the concepts of model predictive control (MPC) and second order discrete sliding mode control. In order to guarantee the feasibility of the PSSC during setpoint changes, a virtual reference variable is added to the PSSC cost function to calculate the closest admissible set point. The states of the system are then driven asymptotically to this admissible setpoint by the control action of the PSSC. The performance of the proposed PSSC is evaluated for an advanced automotive engine case study, where a high fidelity physics-based model of a reactivity controlled compression ignition (RCCI) engine is utilized to serve as the virtual test-bed for the simulations. Considering the hard physical constraints on the RCCI engine states and control inputs, simultaneous tracking of engine load and optimal combustion phasing is a challenging objective to achieve. The simulation results of testing the proposed PSSC on the high fidelity RCCI model show that the developed predictive controller is able to track desired engine load and combustion phasing setpoints, with minimum steady state error, and no overshoot. Moreover, the simulation results confirm the robust tracking performance of the PSSC during transient operations, in the presence of engine cyclic variability.Comment: 6 pages, 5 figures, 2018 American Control Conferance (ACC), June 27-29, 2018, Milwaukee, WI, USA. [Accepted in Jan. 2018

Scaled bilateral teleoperation using discrete-time sliding mode controller

In this paper, the design of a discrete-time slidingmode controller based on Lyapunov theory is presented along with a robust disturbance observer and is applied to a piezostage for high-precision motion. A linear model of a piezostage was used with nominal parameters to compensate the disturbance acting on the system in order to achieve nanometer accuracy. The effectiveness of the controller and disturbance observer is validated in terms of closed-loop position performance for nanometer references. The control structure has been applied to a scaled bilateral structure for the custom-built telemicromanipulation setup. A piezoresistive atomic force microscope cantilever with a built-in Wheatstone bridge is utilized to achieve the nanonewtonlevel interaction forces between the piezoresistive probe tip and the environment. Experimental results are provided for the nanonewton-range force sensing, and good agreement between the experimental data and the theoretical estimates has been demonstrated. Force/position tracking and transparency between the master and the slave has been clearly demonstrated after necessary scalin

Discrete-time exponentially stabilizing fuzzy sliding mode control via lyapunov's method

The exponentially stabilizing state feedback control algorithm is developed by Lyapunov's second method leading to the variable structure system with chattering free sliding modes. Linear time-invariant discrete-time second order plant is considered and the control law is obtained by using a simple fuzzy controller. The analytical structure of the proposed controller is derived and used to prove exponential stability of sliding subspace. Essentially, the control algorithm drives the system from an arbitrary initial state to a prescribed so-called sliding subspace S, in finite time and with prescribed velocity estimate. Inside the sliding subspace S, the system is switched to the sliding mode regime and stays in it forever. The proposed algorithm is tested on the real system in practice, DC servo motor, and simulation and experimental results are given

Indirect adaptive higher-order sliding-mode control using the certainty-equivalence principle

Seit den 50er Jahren werden große Anstrengungen unternommen, Algorithmen zu entwickeln, welche in der Lage sind Unsicherheiten und Störungen in Regelkreisen zu kompensieren. Früh wurden hierzu adaptive Verfahren, die eine kontinuierliche Anpassung der Reglerparameter vornehmen, genutzt, um die Stabilisierung zu ermöglichen. Die fortlaufende Modifikation der Parameter sorgt dabei dafür, dass strukturelle Änderungen im Systemmodell sich nicht auf die Regelgüte auswirken. Eine deutlich andere Herangehensweise wird durch strukturvariable Systeme, insbesondere die sogenannte Sliding-Mode Regelung, verfolgt. Hierbei wird ein sehr schnell schaltendes Stellsignal für die Kompensation auftretender Störungen und Modellunsicherheiten so genutzt, dass bereits ohne besonderes Vorwissen über die Störeinflüsse eine beachtliche Regelgüte erreicht werden kann. Die vorliegende Arbeit befasst sich mit dem Thema, diese beiden sehr unterschiedlichen Strategien miteinander zu verbinden und dabei die Vorteile der ursprünglichen Umsetzung zu erhalten. So benötigen Sliding-Mode Verfahren generell nur wenige Informationen über die Störung, zeigen jedoch Defizite bei Unsicherheiten, die vom Systemzustand abhängen. Auf der anderen Seite können adaptive Regelungen sehr gut parametrische Unsicherheiten kompensieren, wohingegen unmodellierte Störungen zu einer verschlechterten Regelgüte führen. Ziel dieser Arbeit ist es daher, eine kombinierte Entwurfsmethodik zu entwickeln, welche die verfügbaren Informationen über die Störeinflüsse bestmöglich ausnutzt. Hierbei wird insbesondere Wert auf einen theoretisch fundierten Stabilitätsnachweis gelegt, welcher erst durch Erkenntnisse der letzten Jahre im Bereich der Lyapunov-Theorie im Zusammenhang mit Sliding-Mode ermöglicht wurde. Anhand der gestellten Anforderungen werden Regelalgorithmen entworfen, die eine Kombination von Sliding-Mode Reglern höherer Ordnung und adaptiven Verfahren darstellen. Neben den theoretischen Betrachtungen werden die Vorteile des Verfahrens auch anhand von Simulationsbeispielen und eines Laborversuchs nachgewiesen. Es zeigt sich hierbei, dass die vorgeschlagenen Algorithmen eine Verbesserung hinsichtlich der Regelgüte als auch der Robustheit gegenüber den konventionellen Verfahren erzielen.Since the late 50s, huge efforts have been made to improve the control algorithms that are capable of compensating for uncertainties and disturbances. Adaptive controllers that adjust their parameters continuously have been used from the beginning to solve this task. This adaptation of the controller allows to maintain a constant performance even under changing conditions. A different idea is proposed by variable structure systems, in particular by the so-called sliding-mode control. The idea is to employ a very fast switching signal to compensate for disturbances or uncertainties. This thesis deals with a combination of these two rather different approaches while preserving the advantages of each method. The design of a sliding-mode controller normally does not demand sophisticated knowledge about the disturbance, while the controller's robustness against state-dependent uncertainties might be poor. On the other hand, adaptive controllers are well suited to compensate for parametric uncertainties while unstructured influence may result in a degraded performance. Hence, the objective of this work is to design sliding-mode controllers that use as much information about the uncertainty as possible and exploit this knowledge in the design. An important point is that the design procedure is based on a rigorous proof of the stability of the combined approach. Only recent results on Lyapunov theory in the field of sliding-mode made this analysis possible. It is shown that the Lyapunov function of the nominal sliding-mode controller has a direct impact on the adaptation law. Therefore, this Lyapunov function has to meet certain conditions in order to allow a proper implementation of the proposed algorithms. The main contributions of this thesis are sliding-mode controllers, extended by an adaptive part using the certainty-equivalence principle. It is shown that the combination of both approaches results in a novel controller design that is able to solve a control task even in the presence of different classes of uncertainties. In addition to the theoretical analysis, the advantages of the proposed method are demonstrated in a selection of simulation examples and on a laboratory test-bench. The experiments show that the proposed control algorithm delivers better performance in regard to chattering and robustness compared to classical sliding-mode controllers