This article investigates the global robust output regulation of a class of multi-input multi-output (MIMO) time-varying (TV) nonlinear systems with a TV exosystem. Existing linear or nonlinear internal model designs are inadequate for the output regulation problem in TV situations. Therefore, we first transform this control problem into a global robust stabilization problem (GRSP) for a more complex MIMO TV augmented nonlinear system by constructing a TV internal model. Under a series of standard assumptions, this system can be globally stabilized by a recursive state feedback controller. Finally, the proposed algorithm is applied to the disturbance rejection problem of a permanent magnet synchronous motor (PMSM) position servo system, and the experimental results demonstrate its effectiveness.

The double inverted pendulum (DIP) system is a benchmark underactuated mechanical system. The control problem of the DIP system is challenging since it not only has high nonlinearity, but also has underactuation degree equal to two. In this article, a switched energy-based swing-up and neural network (NN) controller is proposed to solve the swing-up and tracking control problem of the DIP system when the desired position is time varying. The implementation of the proposed controller can be divided into three steps. In step one, the energy-based control method is adopted to drive the first pendulum from the downward position to the neighborhood of the upright position. In step two, the sliding mode control method is adopted to stabilize the first pendulum. Meanwhile, a method combining energy-based control and “equivalent cart” is adopted to swing up the second pendulum. In step three, on the basis of approximate nonlinear output regulation theory, the NN controller is used for achieving satisfactory position tracking performance. Finally, the effectiveness of our design is verified by experimental results.

Over the past few decades, the nonlinear output regulation (NOR) theory has attracted extensive attentions in control society. However, few experimental results have been reported about the NOR theory. This article first presents experimental results on discrete-time NOR problem for a linear motor driven inverted pendulum (LMDIP) system. To solve this problem, it is essential to find the solution of the complicated discrete regulator equations (DREs). Moreover, the friction force commonly exists in mechanical systems and cannot be neglected for control systems requiring high precision tracking performance. We present a novel discrete-time controller by combining neural network (NN) approach and friction-feedforward compensation mechanism. Finally, we verify the proposed control algorithm by experiment and make some comparisons with the linear controller.

Much recently, an internal model approach from output regulation theory has been adopted to solve the speed tracking control problem of the permanent magnet synchronous motor (PMSM) system on simulation level. A striking advantage of this approach is that it can achieve multiple goals including trajectory tracking, disturbance rejection, and robustness simultaneously. This article further studies a position tracking control problem of the PMSM system under nonlinear load torque disturbance. A nonlinear internal model based output feedback controller is proposed, which can achieve exact position tracking and allow certain parameter uncertainties. Besides simulation results, a real-time experimental setup is built and experimental results are provided to illustrate the effectiveness of the proposed controller. It is worth mentioning that the proposed controller can lead to a high precision position tracking performance under nonlinear load torque disturbance.

In recent years, the tracking problem of spherical inverted pendulum (SIP) system with multi-input, multi-output nature and unstable zero dynamics has been well addressed based on continuous-time nonlinear output regulation (NOR) theory. For the convenience of digital implementation, this paper further investigates the approximate NOR problem of the SIP system in discrete-time framework. The key for solving the discrete-time NOR problem lies in how to solve a set of algebraic functional equations known as discrete regulator equations (DRE). Since the equations are very complicated, the accurate solution of the DRE can not be obtained. In this paper, we first show that the DRE associated with the SIP system are solvable by center manifold theorem and then use neural network approach to tackle with the tracking problem. Finally, we compare our method with polynomial approximation method.