A system for regulating drilling fluid pressure, the system comprising: a pressure relief device comprising a diverter valve connected to piping between a discharge of a drilling fluid pump and an inlet of a drill string, the diverter valve sized to decrease the pressure of the drilling fluid in the piping by approximately 30% by diverting at least a portion of the drilling fluid out of the piping; and a processor connected to the pressure relief device, the processor configured to: receive pressure measurement signals representative of a pressure of the drilling fluid in the piping, receive flow parameter signals representative of a flow of the drilling fluid through the piping, determine, from the pressure measurement signals and the flow parameter signals, that a target pressure parameter of the drilling fluid in the piping is not satisfied, and in response to determining that the target pressure parameter is not satisfied, lower the pressure of the drilling fluid in the piping until the target pressure parameter is satisfied by at least partially opening the pressure relief device, wherein the target pressure parameter is a rate of increase in pressure of the drilling fluid in the piping, and wherein determining that the rate of increase of the drilling fluid is not satisfied comprises: determining an effective rate of increase in pressure of the drilling fluid in the piping from the pressure represented by the pressure measurement signals and flow pressure represented by the flow parameter signals; and determining that the effective rate of increase in pressure is greater than the rate of increase in pressure. a pressure relief device comprising a diverter valve connected to piping between a discharge of a drilling fluid pump and an inlet of a drill string, the diverter valve sized to decrease the pressure of the drilling fluid in the piping by approximately 30% by diverting at least a portion of the drilling fluid out of the piping; and a processor connected to the pressure relief device, the processor configured to: receive pressure measurement signals representative of a pressure of the drilling fluid in the piping, receive flow parameter signals representative of a flow of the drilling fluid through the piping, determine, from the pressure measurement signals and the flow parameter signals, that a target pressure parameter of the drilling fluid in the piping is not satisfied, and in response to determining that the target pressure parameter is not satisfied, lower the pressure of the drilling fluid in the piping until the target pressure parameter is satisfied by at least partially opening the pressure relief device, wherein the target pressure parameter is a rate of increase in pressure of the drilling fluid in the piping, and wherein determining that the rate of increase of the drilling fluid is not satisfied comprises: determining an effective rate of increase in pressure of the drilling fluid in the piping from the pressure represented by the pressure measurement signals and flow pressure represented by the flow parameter signals; and determining that the effective rate of increase in pressure is greater than the rate of increase in pressure. receive pressure measurement signals representative of a pressure of the drilling fluid in the piping, receive flow parameter signals representative of a flow of the drilling fluid through the piping, determine, from the pressure measurement signals and the flow parameter signals, that a target pressure parameter of the drilling fluid in the piping is not satisfied, and in response to determining that the target pressure parameter is not satisfied, lower the pressure of the drilling fluid in the piping until the target pressure parameter is satisfied by at least partially opening the pressure relief device, wherein the target pressure parameter is a rate of increase in pressure of the drilling fluid in the piping, and wherein determining that the rate of increase of the drilling fluid is not satisfied comprises: determining an effective rate of increase in pressure of the drilling fluid in the piping from the pressure represented by the pressure measurement signals and flow pressure represented by the flow parameter signals; and determining that the effective rate of increase in pressure is greater than the rate of increase in pressure. determining an effective rate of increase in pressure of the drilling fluid in the piping from the pressure represented by the pressure measurement signals and flow pressure represented by the flow parameter signals; and determining that the effective rate of increase in pressure is greater than the rate of increase in pressure.