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To enhance the control performance of permanent magnet synchronous motors (PMSMs), a generalized predictive control (GPC)-based proportional integral feedforward (PIF) controller is proposed for the speed control system. In this new approach, firstly, based on the online identification of controlled model parameters, a simplified GPC law supplies the PIF controller with suitable control parameters according to the uncertainties in the operating conditions. Secondly, the speed reference curve for PMSMs is usually required to be continuous and continuously differentiable according to the general servo system design requirements, so the adaptation of the speed reference is discussed in details in this paper. Hence, the performance of the speed control system using a GPC-based PIF controller is improved for tracking some specified signals. The main motivation of this paper is the extension of GPC law to replace the traditional PI or PIF controllers in industrial applications. The efficacy and usefulness of the proposed controller are verified through experimental results.

High-performance servo systems for permanent magnet synchronous motors (PMSMs) are essential in many applications such as precision engineering and industrial automation because of their advantages of high efficiency, high power factor and high power density [

Self-tuning strategies for industrial applications have been also widely investigated. Roughly speaking, there are two lines of thought to self-tune the controller parameters so that the controllers can adapt to the varying conditions: model-based methods and rule-based methods [

In order to solve the problem considering the accuracy of the controlled model, many PID controllers based on a generalized predictive control (GPC) law have been proposed to improve the performance of the control system [

In this paper, a PI plus feedforward (PIF) controller, in the form of a commercially available 2Dof PI controller, is used to improve the regulatory control performance and the closed-loop control system robustness simultaneously. The main motivation of this paper is to further advance the application of GPC in adaptive control for PMSM systems. There are possibly two contributions in design of a GPC-based PIF controller.

First, the mainly disadvantage of GPC law is that the computational expense to obtain the solution of an optimization process is considerable at each sampling time [

Second, conventional GPC-based PID controllers use the future reference trajectory to obtain control performance as good as that of the GPC law, and have been designed to follow a step-type or a ramp-type reference command [

The paper is organized as follows: in Section 2, the system model of the PMSM is built in detail. In Section 3, the model parameters of a dynamic process object for a PMSM will be obtained in real time by using an RLS method, then, based on the controlled model and the future speed reference, a GPC law will supply a PIF controller with the suitable controller parameters to ensure good control performance. Experimental results are presented in Section 4 and conclusions are drawn in the final section.

Under perfect field orientation and sensing technique conditions, the complicated coupled nonlinear dynamic performance of a PMSM can be significantly improved, whereby torque and flux can be tuned separately by two closed loops [

In the high-performance speed control system, a considerable high-bandwidth current loop is designed to ensure accurate current tracking and act as a current source amplifier within the current loop bandwidth [_{f}_{qr}_{f}_{dist}

The uncertainties of the servo system mainly include the load inertia and load torque. In the running of a servo system, system inertia may change. When the system inertia increases, the response of the servo system will speed up with system overshoot, which is likely to cause system instability. On the contrary, when the system inertia decreases, dynamic response will occur with system oscillation as well as turbulence. Meanwhile, the main role of the servo system is to drive the load operation, but in many industries, the load carried by servo system is not constant. Changes in the load torque will have a significant impact on servo control performance: in the running of a servo system, the sudden increase or reduce of load torque would result in fluctuations in servo speed control, affecting the accuracy of positioning and control performance.

Aside from the above reasons, the true controlled model may be more complex and of high-order since the current sensor and position sensor are nonlinear systems [

Based on _{s}_{1}_{0}^{−1}.

The control structure of PIF controller is shown in _{pv}_{iv}_{fv}_{qr}_{qr}

The basic function of the GPC law is to calculate a sequence of future control signals in such a way that it minimizes a cost function defined over a prediction horizon [

In order to obtain predictions of the speed control performance, continuous recognition should be applied to the model parameters of the controlled object. The model parameters can be generally obtained by a RLS algorithm, so the parameters in the polynomial of ^{−1}) and ^{−1}) in _{Γ}_{Γ} < ∞).

To simplify the GPC law, the trajectory will be ignored, and a cost function of the speed control system is designed by using output error and quadratic indicators form of weighted control increments:
_{1} is minimum predictive horizon, usually choose _{1} = 1; _{2} is maximum predictive horizon; _{u}_{u}_{2};

Because ^{−1}) is zero order polynomial, simplified Diophantine _{f}

Then the

Obviously, in the right hand part of

The vector form of

The vector form of the cost Function in

Since _{qr}_{qr}

The use of the first element of _{qr}

Compared with the increment control output in [

If the speed command cannot be expressed as

Using

Using

Based on

Then comparing

With the above discussion, the implementation of a GPC-based PIF controller design is summarized as follows:

Step 1: Given the related parameters for an RLS law and a GPC algorithm.

Step 2: The controlled model parameters _{1} and _{0} are updated online by the RLS law.

Step 3: Based on the controlled model, Diophantine _{f}_{qr}

Step 4: Speed command can be expressed as

Step 5: Set

The apparatus for the experimental platform contains three major parts and some data transferring buses, as shown in

In the experimental tests, the maximum value of the speed command is set to 1,200 r/min, its rise time and drop time are set to 1 s. Finally, all experimental data from the SSTT are plotted by using Matlab 6.5. The related parameters for the RLS algorithm and the GPC law are: _{1} = 1, _{2} = 10, _{u}

In this test, the load inertia is a triple rotor inertia, and is applied to confirm the robustness and the effectiveness of the proposed controller. It is noted that the control gains of traditional PI controller and traditional PIF controller are the same as in test 1.

In this test, load torque is applied to confirm the robustness and the effectiveness of the proposed controller. The initial load torque is set to 2 Nm, and became to be 9 Nm when

The speed control systems of the PMSMs employed in various industries are almost always controlled by traditional PI and PIF controllers. In order to meet the development requirements of high performance servo systems, this paper has proposed a new GPC-based PIF controller to increase the robustness of servo systems. In this method, controlled model parameters can be obtained online by an RLS algorithm. Based on the controlled model, a high performance and simplified GPC supplies the PIF controller with suitable control parameters according to the uncertainties in the operating conditions. The experimental results show a good control performance and strong robustness of the speed control system can be maintained.

The work is supported by the National Natural Science Foundation of China (NSFC) (Grant NO. 50905069), the National Science and Technology Major Project (Grant NO. 2012ZX04001012), and the National Science and Technology Major Project (Grant NO. 2012ZX04001022).

Assuming the speed command curve for a PMSM is arbitrary-order continuously differentiable at

So, Taylor series expansions of _{r}_{r}

Substituting

For example, a three-order polynomial function is chosen as the rise stage curve for speed command and can be expressed as following equation:

Vector-controlled PMSM servo system.

Average model of PMSM.

The structure of PIF controller.

The principle diagram of a PIF control-based GPC.

The apparatus for the experimental platform.

Speed response (test 1).

Speed error (test 1).

Control parameters (test 1).

Model parameters (test 1).

Speed response (test 2).

Speed error (test 2).

Control parameters (test 2).

Model parameters (test 2).

Speed response (test 3).

Speed error (test 3).

Control parameters (test 3).

Model parameters (test 3).

Specification of the PMSM.

Phase current | 3.7 A |

The number of poles | 3 |

Rated torque | 4.5 Nm |

Rotor inertia | 0.00067 kgm^{2} |

Rated speed | 1,200 r/min |