Thyago Estrabis

Resonant controllers are widely used in power electronics to track sinusoidal references. According to the internal model principle (IMP), these controllers should embed the poles of the Laplace or Z transform of the reference for the closed-loop system to track the reference asymptotically. Thus, tracking a sinusoidal reference is difficult as the controller should adapt its structure to embed the poles of the sinusoidal reference with variable frequency, as those poles depend on that variable frequency. On the other hand, Generalized Predictive Control (GPC) is widespread in industry applications due to its fast response, robustness and capability to include constraints. Resonant controllers based on GPC, which satisfy IMP, have been developed. However, these controllers consider the sinusoidal frequency to be constant. This paper presents a new GPC-based resonant controller with an adaptive and simple control law to track references with variable frequencies. A PLL estimates the frequency of the reference. A multi-layer perceptron uses the estimated frequency to define the gain matrix required to calculate the GPC control action. The GPC control action and the estimated frequency define the control law, which satisfies IMP in steady-state conditions. The authors did not find in the literature the proposed mathematical development of an adaptive GPC resonant controller with a discrete-time augmented model whose control law satisfies IMP. Thus, the proposed approach is helpful to develop other adaptive predictive controllers. Experimental results show that the proposed controller can track sinusoidal references whose frequencies vary in time.

Some novel applications require the tracking/rejection of biased sinusoidal reference/distur-bances. According to the internal model principle (IMP), a controller must embed the model of a biased sinusoidal signal to track references and also reject perturbations modeled through the aforementioned signal. However, the design of that kind of controller is not straightforward, especially when they are implemented in digital processors. This paper presents a controller, based on generalized predictive control (GPC), designed for tracking/rejection of biased sinusoidal signals. In general, GPC is based on the prediction of the plant responses through an augmented prediction model. The proposed approach develops an augmented model that predicts the future errors. The prediction model and the control law used in the proposed approach embed the discrete-time model of a biased sinusoidal signal. Thus, the proposed controller can track/reject biased sinusoidal references/disturbances. The predicted errors and the future inputs of the proposed augmented model are used to define the cost function that measures the control performance. An optimization technique was applied to obtain the solution of the cost function, which is the optimal sequence of future model inputs that allows defining the control law. Experimental tests prove that the proposed controller can asymptotically track and reject biased sinusoidal signals.

This paper explores the application of polynomial reference tracking generalized predictive controller (Poly-GPC) to control the output current of the LCL filter connected to an AC grid. The Poly-GPC system allows the LCL output current to track the sinusoidal current reference generated to transfer the power from the Voltage Source Inverter (VSI) to the grid. The proposed controller considers that the sinusoidal current reference can be approximated as a set of polynomial signals. Simulation results show that the proposed controller can be used to control the LCL output current successfully.

Sinusoidal reference tracking is required in important practical applications. Resonant controllers are suitable for that task. However, stable implementation of these controllers in a digital processor is difficult to achieve. On the other hand, quasi-resonant controllers are easier to implement, but they do not guarantee asymptotic reference tracking. This paper proposes a new resonant controller based on Generalized Predictive Control (GPC) and Internal Model Principle (IMP). The first-order and second-order difference operators are applied to create a GPC system whose structure embeds the Z-transform of the sinusoidal reference. Thus, according to IMP, the proposed controller, named Resonant Generalized Predictive Control (RGPC), asymptotically tracks sinusoidal references. Besides, the proposed RGPC has the advantages of GPC, such as fast response and easy implementation in digital processors. Experimental tests prove that the proposed RGPC has better performance than other controllers for sinusoidal reference tracking.

Some important applications require control systems capable of tracking high-degree polynomial references. However, polynomial reference tracking is difficult because the controller must have a fast response to track variable references. Generalized Predictive Control (GPC), used in industrial applications, has a fast response. However, up to now, GPC approaches in the literature are not designed for high-degree polynomial reference tracking. For that reason, this brief proposes a GPC system for the tracking of polynomial references of any degree. The high-order backward difference operator was used to develop an augmented prediction model designed to have an arbitrary number of embedded integrators. Thus, according to the internal model principle, the proposed predictive controller can track polynomial references of any degree. An optimization technique is used to define future control actions, while the control law is defined through the receding horizon principle. Simulation and experimental results prove that the proposed controller performs better than other approaches described in the literature.

High-performance motor drives that operate in harsh conditions require an accurate and robust angular position measurement to correctly estimate the speed and reduce the torque ripple produced by angular estimation error. For that reason, a resolver is used in motor drives as a position sensor due to its robustness. A resolver-to-digital converter (RDC) is an observer used to get the angular position from the resolver signals. Most RDCs are based on angle tracking observers (ATOs). On the other hand, generalized predictive control (GPC) has become a powerful tool in developing controllers and observers for industrial applications. However, no GPC-based RDC with zero steady-state error during constant speed operation has been proposed. This paper proposes an RDC based on the second-order difference GPC (SOD-GPC). In SOD-GPC, the second-order difference operator is applied to design a GPC model with two embedded integrators. Thus, the SOD-GPC is used to design a type-II ATO whose steady-state angle estimation error tends to zero during constant speed operation. Simulation and experimental results prove that the proposed RDC system has better performance than other literature approaches.

High-performance motor drives that operate in harsh conditions require an accurate and robust angular position measurement to correctly estimate the speed and reduce the torque ripple produced by angular estimation error. For that reason, a resolver is used in motor drives as a position sensor due to its robustness. A resolver-to-digital converter (RDC) is an observer used to get the angular position from the resolver signals. Most RDCs are based on angle tracking observers (ATOs). On the other hand, generalized predictive control (GPC) has become a powerful tool in developing controllers and observers for industrial applications. However, no GPC-based RDC with zero steady-state error during constant speed operation was proposed. This paper proposes an RDC based on a second-order difference GPC (SOD-GPC). In SOD-GPC, the second-order difference operator is applied to design a GPC model with two embedded integrators. Thus, the SOD-GPC is used to design a type-II ATO whose steady-state angle estimation error tends to zero during constant speed operation. Simulation and experimental results prove that the proposed RDC system has better performance than other literature approaches.

This brief proposes an adaptation of the Generalized Predictive Control (GPC) for ramp-reference tracking. The second-order difference operation and the plant model are used to get an augmented model with two embedded integrators and whose output is the tracking error. Differently from other GPC-based tracking algorithms, the proposed approach does not require information about the reference parameters, and the GPC prediction horizon is composed of the predicted errors instead of the expected plant outputs. Thus, the optimization function and the receding horizon strategy used in conventional GPC can be applied to get the control law. Simulation and experimental results prove that the proposed approach can successfully track constant and ramp references. The proposed method is applicable for single-input single-outputs plants. However, the mathematical background presented in this brief can be used in the development of new GPC strategies.