# Overview of Predictive Control Technology for Permanent Magnet Synchronous Motor Systems
## Composition of a PMSM Drive System Based on Predictive Control
### Analysis of the Predictive Control Principle  
First of all, the following analysis is based on a one-step forecast unless otherwise stated. Deadbeat control makes use of the discrete mathematical model of the system to predict the output required by the system at the next time according to the state of system at the current time. This algorithm can theoretically make the error of the controlled quantity zero. For example, for the deadbeat current prediction, its derivation formula is shown in Equation (8). \[u_{x}^{ref}=R_{s}i_{x}(k)+\frac{L_{x}}{T_{s}}\Big{(}i_{x}^{ref}-i_{x}(k)\Big{)} +E_{x} \tag{8}\]  
where \(u_{x}^{ref}=[u_{d}^{ref}u_{q}^{ref}]^{T}\); \(i_{x}^{ref}=[i_{d}^{ref}i_{q}^{ref}]^{T}\); \(L_{x}=[L_{d}\ L_{q}]^{T}\); and \(E_{x}\), respectively, represent the counter electromotive force on the \(d\)-\(q\) axis. For the deadbeat predictive control current control, it calculates the reference voltage at the next time through the discrete mathematical model of the motor and the predicted current value and outputs the switching signal to drive the motor through the pulse width modulation technology. The control flow chart is shown in Figure 3. In Figures 3 and 4, * represents the reference value. However, because its prediction depends on the precise mathematical model, disturbance or parameter mismatch will affect its control performance, which is also the main direction of current research. Figure 4: (**a**) Control block diagram of FCS-MPC; (**b**) control block diagram of CCS-MPC. Figure 3: Deadbeat predictive control diagram. The MPC constrains the control target through the cost function. The basic design is the cost function design to ensure the system tracking characteristics and realize the reference tracking control. This part is the core of the system control. Usually, the cost function is designed as Equation (9). \[J(x)=\sum_{m=1}^{n}Q_{m}\Big{|}x_{m}^{*}-x_{m}^{p}\Big{|}=Q_{1}\cdot\Big{|}x_{1} ^{*}-x_{1}^{p}\Big{|}+Q_{2}\cdot\Big{|}x_{2}^{*}-x_{2}^{p}\Big{|}+\ldots+Q_{n} \cdot\Big{|}x_{n}^{*}-x_{n}^{p}\Big{|} \tag{9}\]  
where \(n\) represents the number of tracked items, \(x^{*}\) represents the reference value, and \(x^{p}\) represents the predicted value based on the model. For the FCS-MPC current control, it calculates the finite number of voltage vectors through the cost function according to the characteristics of the voltage source inverter. By selecting the vector output with the minimum value of the cost function, the switch of the inverter is driven to make the motor system run, and its control block diagram is shown in Figure 4a. In contrast with FCS-MPC, the CCS-MPC uses an iterative approach to continuously approach the optimal solution. Its objective function is complex, and can be expressed as:  
\[\left\{ \begin{array}{l}J(x),x\in D\subset R\\ g_{u}(x)\geq 0,u=1,2,\ldots,s\\ h_{v}(x)=0,v=1,2,\ldots,q\end{array} \right. \tag{10}\]  
where \(J(x)\) represents the optimization objective function, that is, the value function; \(D\) is the value range of \(x\); and \(g_{u}\) and \(h_{v}\) represent s numbers of inequalities and q numbers of equality constraints, respectively. According to the nonlinear optimization theory, the general solution method of Equation (10) is the interior point method, which is a method to approach the optimal solution through iteration. For CCS-MPC, it uses pulse width modulation technology to provide precise and fast current and speed control by using a voltage vector with arbitrary amplitude and phase angle on the voltage complex plane. Figure 4b is the control block diagram of CCS-MPC. However, since the constrained quadratic optimization problem has no explicit solution, it is tough to determine the optimal resolution in a short time by iterative solution, which limits the application of continuous model predictive control in motor drive systems. According to the brief introduction and analysis of the above theories, many problems with them can be found.