Jian-Xin Xu

Nonlinear integral-type sliding surface for both matched and unmatched uncertain systems

This note presents a new nonlinear integral-type sliding surface which incorporates a virtual nonlinear nominal control to achieve prescribed specifications. First, the plant with matched uncertainties is considered. The resultant closed-loop system during ideal sliding mode behaves exactly like the nominal plant under the nonlinear nominal control, which completely nullifies the matched uncertainties and consequently satisfies the prescribed specifications. Second, the stability analysis of the proposed sliding mode for the systems with unmatched uncertainties is performed to exploit the stability conditions. Numerical results demonstrate the validity of the proposed concept.

Torque ripple minimization in PM synchronous motors using iterative learning control

Parasitic torque pulsations exist in permanent magnet synchronous motors (PMSMs) due to nonsinusoidal flux density distribution around the air-gap, errors in current measurements, and variable magnetic reluctance of the air-gap due to stator slots. These torque pulsations vary periodically with rotor position and are reflected as speed ripple, which degrades the PMSM drive performance, particularly at low speeds. Because of the periodic nature of torque ripple, iterative learning control (ILC) is intuitively an excellent choice for torque ripple minimization. In this paper, first we propose an ILC scheme implemented in time domain to reduce periodic torque pulsations. A forgetting factor is introduced in this scheme to increase the robustness of the algorithm against disturbance. However, this limits the extent to which torque pulsations can be suppressed. In order to eliminate this limitation, a modified ILC scheme implemented in frequency domain by means of Fourier series expansion is presented. Experimental evaluations of both proposed schemes are carried out on a DSP-controlled PMSM drive platform. Test results obtained demonstrate the effectiveness of the proposed control schemes in reducing torque ripple by a factor of approximately three under various operating conditions.

Consensus Based Approach for Economic Dispatch Problem in a Smart Grid

Economic dispatch problem (EDP) is an important problem in the smart grid. Its aim is to minimize the total cost when generating certain amount of power. This paper proposes a novel consensus based algorithm to solve EDP in a distributed fashion. The quadratic cost functions are adopted in the problem formulation, and the strongly connected communication topology is used for the information exchange. Unlike the centralized approach, the proposed algorithm allows generators to learn the mismatch information between demand and total power generation through a distributed manner. The estimated mismatch information is used as a feedback to adjust current power generation by each generator. With a tactical initial setup, generators can automatically minimize the total cost in a collective sense while satisfying power balance equation.

On the Discrete-Time Integral Sliding-Mode Control

A new discrete-time integral sliding-mode control (DISMC) scheme is proposed for sampled-data systems. The new control scheme is characterized by a discrete-time integral sliding manifold which inherits the desired properties of the continuous-time integral sliding manifold, such as full order sliding manifold with pole assignment, and elimination of the reaching phase. In particular, comparing with existing discrete-time sliding-mode control, the new scheme is able to achieve more precise tracking performance. It will be shown in this work that, the new control scheme achieves O(T2) steady-state error for state regulation with the widely adopted delay-based disturbance estimation. Another desirable feature is, the proposed DISMC prevents the generation of overlarge control actions due to deadbeat response, which is usually inevitable due to the existence of poles at the origin for a reduced order sliding manifold designed for sampled-data systems. Both the theoretical analysis and illustrative example demonstrate the validity of the proposed scheme

A survey on iterative learning control for nonlinear systems

In this article we review the recent advances in iterative learning control (ILC) for nonlinear dynamic systems. In the research field of ILC, two categories of system nonlinearities are considered, namely, the global Lipschitz continuous (GLC) functions and local Lipschitz continuous (LLC) functions. ILC for GLC systems is widely studied and analysed using contraction mapping approach, and the focus of recent exploration moves to application problems, though a number of theoretical issues remain open. ILC for LLC systems is currently a hot area and the recent research focuses on ILC design and analysis by means of Lyapunov approach. The objectives of this article are to introduce recent development and advances in nonlinear ILC schemes, highlight their effectiveness and limitations, as well as discuss the directions for further exploration of nonlinear ILC.

Technical communique: Adaptive ILC for a class of discrete-time systems with iteration-varying trajectory and random initial condition

In this work we present a discrete-time adaptive iterative learning control (AILC) scheme to deal with systems with time-varying parametric uncertainties. Using the analogy between the discrete-time axis and the iterative learning axis, the new adaptive ILC can incorporate a Recursive Least Squares (RLS) algorithm, hence the learning gain can be tuned iteratively along the learning axis and pointwisely along the time axis. When the initial states are random and the reference trajectory is iteration-varying, the new AILC can achieve the pointwise convergence over a finite time interval asymptotically along the iterative learning axis.

A modular control scheme for PMSM speed control with pulsating torque minimization

In this paper, a modular control approach is applied to a permanent-magnet synchronous motor (PMSM) speed control. Based on the functioning of the individual module, the modular approach enables the powerfully intelligent and robust control modules to easily replace any existing module which does not perform well, meanwhile retaining other existing modules which are still effective. Property analysis is first conducted for the existing function modules in a conventional PMSM control system: proportional-integral (PI) speed control module, reference current-generating module, and PI current control module. Next, it is shown that the conventional PMSM controller is not able to reject the torque pulsation which is the main hurdle when PMSM is used as a high-performance servo. By virtue of the internal model, to nullify the torque pulsation it is imperative to incorporate an internal model in the feed-through path. This is achieved by replacing the reference current-generating module with an iterative learning control (ILC) module. The ILC module records the cyclic torque and reference current signals over one entire cycle, and then uses those signals to update the reference current for the next cycle. As a consequence, the torque pulsation can be reduced significantly. In order to estimate the torque ripples which may exceed certain bandwidth of a torque transducer, a novel torque estimation module using a gain-shaped sliding-mode observer is further developed to facilitate the implementation of torque learning control. The proposed control system is evaluated through real-time implementation and experimental results validate the effectiveness.

Guaranteed cost control for uncertain Markovian jump systems with mode-dependent time-delays

This note concerns the robust guaranteed cost control problem for a class of continuous-time Markovian jump linear system with norm-bounded uncertainties and mode-dependent time-delays. The problem is to design a memoryless state feedback control law such that the closed-loop system is stochastically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. Based on linear matrix inequality, delay-dependent sufficient conditions for the existence of such controller are derived by using a descriptor model transformation of the system and by applying Moons inequality for bounding cross terms. Sufficient conditions which depend on the difference between the largest and the smallest time-delays are also presented. Two numerical examples are given for illustration of the proposed theoretical results.

Brief Parallel structure and tuning of a fuzzy PID controller

In this paper, a parallel structure of fuzzy PID control systems is proposed. It is associated with a new tuning method which, based on gain margin and phase margin specifications, determines the parameters of the fuzzy PID controller. In comparison with conventional PID controllers, the proposed fuzzy PID controller shows higher control gains when system states are away from equilibrium and, at the same time, retains a lower profile of control signals. Consequently, better control performance is achieved. With the proposed formula, the weighting factors of a fuzzy logic controller can be systematically selected according to the plant under control. By virtue of using the simplest structure of fuzzy logic control, the stability of the nonlinear control system can be analyzed and a sufficient BIBO stability condition is given. The superior performance of the proposed controller is demonstrated through an experimental example.

On iterative learning from different tracking tasks in the presence of time-varying uncertainties

In this paper, we introduce a new iterative learning control (ILC) method, which enables learning from different tracking control tasks. The proposed method overcomes the imitation of traditional ILC in that, the target trajectories of any two consecutive iterations can be completely different. For non-linear systems with time-varying and time-invariant parametric uncertainties, the new learning method works effectively to nullify the tracking error. To facilitate the learning control system design and analysis, in the paper we use a composite energy function (CEF) index, which consists of a positive scalar function and L2 norm of the function approximation error.